movie-recommendation-system-using-r.r

{"cells":[{"source":"<a href=\"https://www.kaggle.com/code/amirmotefaker/movie-recommendation-system-using-r?scriptVersionId=177989945\" target=\"_blank\"><img align=\"left\" alt=\"Kaggle\" title=\"Open in Kaggle\" src=\"https://kaggle.com/static/images/open-in-kaggle.svg\"></a>","metadata":{},"cell_type":"markdown"},{"cell_type":"markdown","id":"74dacc67","metadata":{"_execution_state":"idle","_uuid":"051d70d956493feee0c6d64651c6a088724dca2a","papermill":{"duration":0.02077,"end_time":"2024-05-16T11:25:18.356523","exception":false,"start_time":"2024-05-16T11:25:18.335753","status":"completed"},"tags":[]},"source":["# What Is a Recommendation System?\n","- A recommendation system is an artificial intelligence or AI algorithm, usually associated with machine learning, that uses Big Data to suggest or recommend additional products to consumers. These can be based on various criteria, including past purchases, search history, demographic information, and other factors. Recommender systems are highly useful as they help users discover products and services they might otherwise have not found on their own.\n","\n","- Recommender systems are trained to understand the preferences, previous decisions, and characteristics of people and products using data gathered about their interactions. These include impressions, clicks, likes, and purchases. Because of their capability to predict consumer interests and desires on a highly personalized level, recommender systems are a favorite with content and product providers. They can drive consumers to just about any product or service that interests them, from books to videos to health classes to clothing.\n","\n","# What is a product recommendation\n","- In the product discovery phase, you can use more than one tool to show the consumer the most suitable options, offer the right personalized products, and design a satisfying experience. Product recommendations are one of the most powerful of these tools.\n","\n","# Advantage of product recommendations\n","- Recommendations for related products: \n","    - Provides a list of related products that are similar to the chosen one, either in use or in price which creates a cross-selling opportunity. For example at the cart step, offering complementary products to the ones already added to the cart, you can encourage your customer to shop a little bit more.\n","- Recommendations based on past purchases: \n","    - If you already bought a digital camera, a recommendation of its lenses might make sense.\n","- Recommendations based on search: \n","    - Product recommendation engines may look at search history to suggest products based on terms consumers have used.\n","\n","# Types of Recommendation Systems:\n","- **Collaborative filtering** algorithms recommend items (this is the filtering part) based on preference information from many users (this is the collaborative part). \n","\n","- **Content filtering**, by contrast, uses the attributes or features of an item  (this is the content part) to recommend other items similar to the user’s preferences. \n","\n","- **Hybrid recommender systems** combine the advantages of the types above to create a more comprehensive recommending system.\n","\n","- **Context filtering** includes users’ contextual information in the recommendation process. \n","\n","# Recommendation Engine Benefits\n","- Drive Traffic\n","    - Through personalized email messages and targeted blasts, a recommendation engine can encourage elevated amounts of traffic to your site, thus increasing the opportunity to scoop up more data to further enrich a customer profile.\n","\n","- Deliver Relevant Content\n","    - By analyzing the customer’s current site usage and previous browsing history, a recommendation engine can deliver relevant product recommendations as he or she shops based on said profile. The data is collected in real time so the software can react as shopping habits change on the fly.\n","\n","- Engage Shoppers\n","    - Shoppers become more engaged when personalized product recommendations are made to them across the customer journey. Through individualized product recs, customers are able to delve more deeply into your product line without having to dive into (and very likely get lost in) an ecommerce rabbit hole.\n","\n","- Convert Shoppers to Customers\n","    - Converting shoppers into customers takes a special touch. Personalized interactions from a recommendation engine show your customer that he or she is valued as an individual, in turn, engendering long-term loyalty.\n","\n","- Increase Average Order Value\n","    - Average order values typically go up when an engine is leveraged to display personalized options as shoppers are more willing to spend generously on items they thoroughly covet.\n","\n","- Increase Number of Items per Order\n","    - In addition to the average order value rising, the number of items per order also typically rises when an engine is employed. When the customer is shown options that meet his or her interest, they are far more likely to add items to to their active purchase cart.\n","\n","- Control Merchandising and Inventory Rules\n","    - A recommendation engine can add your marketing and inventory control directives to a customer’s profile to feature products that are on clearance or overstocked so as to avoid unnecessary shopping friction and tone deafness.\n","\n","- Reduce Workload and Overhead\n","    - The volume of data required to create a personal shopping experience for each customer is usually far too large to be managed manually. Using an engine automates this process, easing the workload for your IT staff.\n","\n","- A Recommendation Engine Provides Reports\n","    - Detailed reports are an integral part of a personalization system. Accurate and up-to-the-minute reporting will allow you to make informed decisions about the direction of a campaign or the structure of a product page.\n","\n","- Offer Advice and Direction\n","    - An experienced recommendation provider like Kibo can offer advice on how to use the data collected from your recommendation engine. Acting as a partner and a consultant, the provider should have the industry know-how needed to help guide you and your ecommerce site to a prosperous future.\n","\n","\n","Dataset: [MovieLens](https://grouplens.org/datasets/movielens/)\n","\n","### The main goal of this machine learning project is to build a recommendation system that recommends movies to users."]},{"cell_type":"markdown","id":"418ef0d1","metadata":{"papermill":{"duration":0.018096,"end_time":"2024-05-16T11:25:18.392786","exception":false,"start_time":"2024-05-16T11:25:18.37469","status":"completed"},"tags":[]},"source":["# Importing Libraries"]},{"cell_type":"code","execution_count":1,"id":"7a6499d0","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:25:18.436259Z","iopub.status.busy":"2024-05-16T11:25:18.432904Z","iopub.status.idle":"2024-05-16T11:25:21.775776Z","shell.execute_reply":"2024-05-16T11:25:21.773118Z"},"papermill":{"duration":3.36782,"end_time":"2024-05-16T11:25:21.77893","exception":false,"start_time":"2024-05-16T11:25:18.41111","status":"completed"},"tags":[]},"outputs":[{"name":"stderr","output_type":"stream","text":["Loading required package: Matrix\n","\n","Loading required package: arules\n","\n","\n","Attaching package: ‘arules’\n","\n","\n","The following objects are masked from ‘package:base’:\n","\n","    abbreviate, write\n","\n","\n","Loading required package: proxy\n","\n","\n","Attaching package: ‘proxy’\n","\n","\n","The following object is masked from ‘package:Matrix’:\n","\n","    as.matrix\n","\n","\n","The following objects are masked from ‘package:stats’:\n","\n","    as.dist, dist\n","\n","\n","The following object is masked from ‘package:base’:\n","\n","    as.matrix\n","\n","\n","Loading required package: registry\n","\n","Registered S3 methods overwritten by 'registry':\n","  method               from \n","  print.registry_field proxy\n","  print.registry_entry proxy\n","\n","\n","Attaching package: ‘reshape2’\n","\n","\n","The following objects are masked from ‘package:data.table’:\n","\n","    dcast, melt\n","\n","\n"]}],"source":["library(recommenderlab)  # Lab for Developing and Testing Recommender Algorithms\n","library(ggplot2)   # ggplot2 is a system for declaratively creating graphics, based on The Grammar of Graphics.                  \n","library(data.table)  # data.table is an R package that provides an enhanced version of data.frames, which are the standard data structure for storing data in base R.\n","library(reshape2)  # reshape2 is an R package written by Hadley Wickham that makes it easy to transform data between wide and long formats."]},{"cell_type":"markdown","id":"148277ad","metadata":{"papermill":{"duration":0.020662,"end_time":"2024-05-16T11:25:21.819805","exception":false,"start_time":"2024-05-16T11:25:21.799143","status":"completed"},"tags":[]},"source":["# Retrieving the Data"]},{"cell_type":"code","execution_count":2,"id":"8a7e9ebc","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:25:21.893465Z","iopub.status.busy":"2024-05-16T11:25:21.859329Z","iopub.status.idle":"2024-05-16T11:25:22.238294Z","shell.execute_reply":"2024-05-16T11:25:22.236107Z"},"papermill":{"duration":0.402677,"end_time":"2024-05-16T11:25:22.241328","exception":false,"start_time":"2024-05-16T11:25:21.838651","status":"completed"},"tags":[]},"outputs":[{"name":"stdout","output_type":"stream","text":["'data.frame':\t10329 obs. of  3 variables:\n"," $ movieId: int  1 2 3 4 5 6 7 8 9 10 ...\n"," $ title  : chr  \"Toy Story (1995)\" \"Jumanji (1995)\" \"Grumpier Old Men (1995)\" \"Waiting to Exhale (1995)\" ...\n"," $ genres : chr  \"Adventure|Animation|Children|Comedy|Fantasy\" \"Adventure|Children|Fantasy\" \"Comedy|Romance\" \"Comedy|Drama|Romance\" ...\n"]}],"source":["movie_data <- read.csv(\"/kaggle/input/movielens-dataset-movies/movies.csv\",stringsAsFactors=FALSE)\n","rating_data <- read.csv(\"/kaggle/input/movielens-dataset-for-recommendation-system/ratings.csv\")\n","str(movie_data)"]},{"cell_type":"code","execution_count":3,"id":"d858d14c","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:25:22.299825Z","iopub.status.busy":"2024-05-16T11:25:22.296586Z","iopub.status.idle":"2024-05-16T11:25:22.322887Z","shell.execute_reply":"2024-05-16T11:25:22.320877Z"},"papermill":{"duration":0.060327,"end_time":"2024-05-16T11:25:22.325939","exception":false,"start_time":"2024-05-16T11:25:22.265612","status":"completed"},"tags":[]},"outputs":[{"data":{"text/plain":["    movieId          title              genres         \n"," Min.   :     1   Length:10329       Length:10329      \n"," 1st Qu.:  3240   Class :character   Class :character  \n"," Median :  7088   Mode  :character   Mode  :character  \n"," Mean   : 31924                                        \n"," 3rd Qu.: 59900                                        \n"," Max.   :149532                                        "]},"metadata":{},"output_type":"display_data"}],"source":["summary(movie_data)"]},{"cell_type":"code","execution_count":4,"id":"216fb968","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:25:22.383982Z","iopub.status.busy":"2024-05-16T11:25:22.382196Z","iopub.status.idle":"2024-05-16T11:25:22.414228Z","shell.execute_reply":"2024-05-16T11:25:22.412103Z"},"papermill":{"duration":0.064228,"end_time":"2024-05-16T11:25:22.417353","exception":false,"start_time":"2024-05-16T11:25:22.353125","status":"completed"},"tags":[]},"outputs":[{"data":{"text/html":["<table class=\"dataframe\">\n","<caption>A data.frame: 6 × 3</caption>\n","<thead>\n","\t<tr><th></th><th scope=col>movieId</th><th scope=col>title</th><th scope=col>genres</th></tr>\n","\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n","</thead>\n","<tbody>\n","\t<tr><th scope=row>1</th><td>1</td><td>Toy Story (1995)                  </td><td>Adventure|Animation|Children|Comedy|Fantasy</td></tr>\n","\t<tr><th scope=row>2</th><td>2</td><td>Jumanji (1995)                    </td><td>Adventure|Children|Fantasy                 </td></tr>\n","\t<tr><th scope=row>3</th><td>3</td><td>Grumpier Old Men (1995)           </td><td>Comedy|Romance                             </td></tr>\n","\t<tr><th scope=row>4</th><td>4</td><td>Waiting to Exhale (1995)          </td><td>Comedy|Drama|Romance                       </td></tr>\n","\t<tr><th scope=row>5</th><td>5</td><td>Father of the Bride Part II (1995)</td><td>Comedy                                     </td></tr>\n","\t<tr><th scope=row>6</th><td>6</td><td>Heat (1995)                       </td><td>Action|Crime|Thriller                      </td></tr>\n","</tbody>\n","</table>\n"],"text/latex":["A data.frame: 6 × 3\n","\\begin{tabular}{r|lll}\n","  & movieId & title & genres\\\\\n","  & <int> & <chr> & <chr>\\\\\n","\\hline\n","\t1 & 1 & Toy Story (1995)                   & Adventure\\textbar{}Animation\\textbar{}Children\\textbar{}Comedy\\textbar{}Fantasy\\\\\n","\t2 & 2 & Jumanji (1995)                     & Adventure\\textbar{}Children\\textbar{}Fantasy                 \\\\\n","\t3 & 3 & Grumpier Old Men (1995)            & Comedy\\textbar{}Romance                             \\\\\n","\t4 & 4 & Waiting to Exhale (1995)           & Comedy\\textbar{}Drama\\textbar{}Romance                       \\\\\n","\t5 & 5 & Father of the Bride Part II (1995) & Comedy                                     \\\\\n","\t6 & 6 & Heat (1995)                        & Action\\textbar{}Crime\\textbar{}Thriller                      \\\\\n","\\end{tabular}\n"],"text/markdown":["\n","A data.frame: 6 × 3\n","\n","| <!--/--> | movieId &lt;int&gt; | title &lt;chr&gt; | genres &lt;chr&gt; |\n","|---|---|---|---|\n","| 1 | 1 | Toy Story (1995)                   | Adventure|Animation|Children|Comedy|Fantasy |\n","| 2 | 2 | Jumanji (1995)                     | Adventure|Children|Fantasy                  |\n","| 3 | 3 | Grumpier Old Men (1995)            | Comedy|Romance                              |\n","| 4 | 4 | Waiting to Exhale (1995)           | Comedy|Drama|Romance                        |\n","| 5 | 5 | Father of the Bride Part II (1995) | Comedy                                      |\n","| 6 | 6 | Heat (1995)                        | Action|Crime|Thriller                       |\n","\n"],"text/plain":["  movieId title                             \n","1 1       Toy Story (1995)                  \n","2 2       Jumanji (1995)                    \n","3 3       Grumpier Old Men (1995)           \n","4 4       Waiting to Exhale (1995)          \n","5 5       Father of the Bride Part II (1995)\n","6 6       Heat (1995)                       \n","  genres                                     \n","1 Adventure|Animation|Children|Comedy|Fantasy\n","2 Adventure|Children|Fantasy                 \n","3 Comedy|Romance                             \n","4 Comedy|Drama|Romance                       \n","5 Comedy                                     \n","6 Action|Crime|Thriller                      "]},"metadata":{},"output_type":"display_data"}],"source":["head(movie_data)"]},{"cell_type":"code","execution_count":5,"id":"d5c93c3b","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:25:22.466784Z","iopub.status.busy":"2024-05-16T11:25:22.464914Z","iopub.status.idle":"2024-05-16T11:25:22.526563Z","shell.execute_reply":"2024-05-16T11:25:22.524117Z"},"papermill":{"duration":0.087017,"end_time":"2024-05-16T11:25:22.52978","exception":false,"start_time":"2024-05-16T11:25:22.442763","status":"completed"},"tags":[]},"outputs":[{"data":{"text/plain":["     userId         movieId           rating        timestamp        \n"," Min.   :  1.0   Min.   :     1   Min.   :0.500   Min.   :8.286e+08  \n"," 1st Qu.:192.0   1st Qu.:  1073   1st Qu.:3.000   1st Qu.:9.711e+08  \n"," Median :383.0   Median :  2497   Median :3.500   Median :1.115e+09  \n"," Mean   :364.9   Mean   : 13381   Mean   :3.517   Mean   :1.130e+09  \n"," 3rd Qu.:557.0   3rd Qu.:  5991   3rd Qu.:4.000   3rd Qu.:1.275e+09  \n"," Max.   :668.0   Max.   :149532   Max.   :5.000   Max.   :1.452e+09  "]},"metadata":{},"output_type":"display_data"}],"source":["summary(rating_data)"]},{"cell_type":"code","execution_count":6,"id":"7d365fb4","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:25:22.573691Z","iopub.status.busy":"2024-05-16T11:25:22.571936Z","iopub.status.idle":"2024-05-16T11:25:22.602673Z","shell.execute_reply":"2024-05-16T11:25:22.600055Z"},"papermill":{"duration":0.055863,"end_time":"2024-05-16T11:25:22.606158","exception":false,"start_time":"2024-05-16T11:25:22.550295","status":"completed"},"tags":[]},"outputs":[{"data":{"text/html":["<table class=\"dataframe\">\n","<caption>A data.frame: 6 × 4</caption>\n","<thead>\n","\t<tr><th></th><th scope=col>userId</th><th scope=col>movieId</th><th scope=col>rating</th><th scope=col>timestamp</th></tr>\n","\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n","</thead>\n","<tbody>\n","\t<tr><th scope=row>1</th><td>1</td><td> 16</td><td>4.0</td><td>1217897793</td></tr>\n","\t<tr><th scope=row>2</th><td>1</td><td> 24</td><td>1.5</td><td>1217895807</td></tr>\n","\t<tr><th scope=row>3</th><td>1</td><td> 32</td><td>4.0</td><td>1217896246</td></tr>\n","\t<tr><th scope=row>4</th><td>1</td><td> 47</td><td>4.0</td><td>1217896556</td></tr>\n","\t<tr><th scope=row>5</th><td>1</td><td> 50</td><td>4.0</td><td>1217896523</td></tr>\n","\t<tr><th scope=row>6</th><td>1</td><td>110</td><td>4.0</td><td>1217896150</td></tr>\n","</tbody>\n","</table>\n"],"text/latex":["A data.frame: 6 × 4\n","\\begin{tabular}{r|llll}\n","  & userId & movieId & rating & timestamp\\\\\n","  & <int> & <int> & <dbl> & <int>\\\\\n","\\hline\n","\t1 & 1 &  16 & 4.0 & 1217897793\\\\\n","\t2 & 1 &  24 & 1.5 & 1217895807\\\\\n","\t3 & 1 &  32 & 4.0 & 1217896246\\\\\n","\t4 & 1 &  47 & 4.0 & 1217896556\\\\\n","\t5 & 1 &  50 & 4.0 & 1217896523\\\\\n","\t6 & 1 & 110 & 4.0 & 1217896150\\\\\n","\\end{tabular}\n"],"text/markdown":["\n","A data.frame: 6 × 4\n","\n","| <!--/--> | userId &lt;int&gt; | movieId &lt;int&gt; | rating &lt;dbl&gt; | timestamp &lt;int&gt; |\n","|---|---|---|---|---|\n","| 1 | 1 |  16 | 4.0 | 1217897793 |\n","| 2 | 1 |  24 | 1.5 | 1217895807 |\n","| 3 | 1 |  32 | 4.0 | 1217896246 |\n","| 4 | 1 |  47 | 4.0 | 1217896556 |\n","| 5 | 1 |  50 | 4.0 | 1217896523 |\n","| 6 | 1 | 110 | 4.0 | 1217896150 |\n","\n"],"text/plain":["  userId movieId rating timestamp \n","1 1       16     4.0    1217897793\n","2 1       24     1.5    1217895807\n","3 1       32     4.0    1217896246\n","4 1       47     4.0    1217896556\n","5 1       50     4.0    1217896523\n","6 1      110     4.0    1217896150"]},"metadata":{},"output_type":"display_data"}],"source":["head(rating_data)"]},{"cell_type":"markdown","id":"6d874975","metadata":{"papermill":{"duration":0.020935,"end_time":"2024-05-16T11:25:22.647082","exception":false,"start_time":"2024-05-16T11:25:22.626147","status":"completed"},"tags":[]},"source":["# Data Pre-processing\n","\n","- From the above table, we observe that the userId column, as well as the movie I'd column, consists of integers. Furthermore, we need to convert the genres present in the movie_data data frame into a more usable format for the users. In order to do so, we will first create a one-hot encoding to create a matrix that comprises corresponding genres for each of the films."]},{"cell_type":"code","execution_count":7,"id":"23158cac","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:25:22.694376Z","iopub.status.busy":"2024-05-16T11:25:22.692737Z","iopub.status.idle":"2024-05-16T11:25:26.155642Z","shell.execute_reply":"2024-05-16T11:25:26.152755Z"},"papermill":{"duration":3.490915,"end_time":"2024-05-16T11:25:26.159189","exception":false,"start_time":"2024-05-16T11:25:22.668274","status":"completed"},"tags":[]},"outputs":[{"name":"stdout","output_type":"stream","text":["'data.frame':\t10329 obs. of  18 variables:\n"," $ Action     : int  0 0 0 0 0 1 0 0 1 1 ...\n"," $ Adventure  : int  1 1 0 0 0 0 0 1 0 1 ...\n"," $ Animation  : int  1 0 0 0 0 0 0 0 0 0 ...\n"," $ Children   : int  1 1 0 0 0 0 0 1 0 0 ...\n"," $ Comedy     : int  1 0 1 1 1 0 1 0 0 0 ...\n"," $ Crime      : int  0 0 0 0 0 1 0 0 0 0 ...\n"," $ Documentary: int  0 0 0 0 0 0 0 0 0 0 ...\n"," $ Drama      : int  0 0 0 1 0 0 0 0 0 0 ...\n"," $ Fantasy    : int  1 1 0 0 0 0 0 0 0 0 ...\n"," $ Film-Noir  : int  0 0 0 0 0 0 0 0 0 0 ...\n"," $ Horror     : int  0 0 0 0 0 0 0 0 0 0 ...\n"," $ Musical    : int  0 0 0 0 0 0 0 0 0 0 ...\n"," $ Mystery    : int  0 0 0 0 0 0 0 0 0 0 ...\n"," $ Romance    : int  0 0 1 1 0 0 1 0 0 0 ...\n"," $ Sci-Fi     : int  0 0 0 0 0 0 0 0 0 0 ...\n"," $ Thriller   : int  0 0 0 0 0 1 0 0 0 1 ...\n"," $ War        : int  0 0 0 0 0 0 0 0 0 0 ...\n"," $ Western    : int  0 0 0 0 0 0 0 0 0 0 ...\n"]}],"source":["movie_genre <- as.data.frame(movie_data$genres, stringsAsFactors=FALSE)\n","library(data.table)\n","movie_genre2 <- as.data.frame(tstrsplit(movie_genre[,1], '[|]', \n","                                   type.convert=TRUE), \n","                         stringsAsFactors=FALSE)\n","colnames(movie_genre2) <- c(1:10)\n","list_genre <- c(\"Action\", \"Adventure\", \"Animation\", \"Children\", \n","                \"Comedy\", \"Crime\",\"Documentary\", \"Drama\", \"Fantasy\",\n","                \"Film-Noir\", \"Horror\", \"Musical\", \"Mystery\",\"Romance\",\n","                \"Sci-Fi\", \"Thriller\", \"War\", \"Western\")\n","genre_mat1 <- matrix(0,10330,18)\n","genre_mat1[1,] <- list_genre\n","colnames(genre_mat1) <- list_genre\n","for (index in 1:nrow(movie_genre2)) {\n","  for (col in 1:ncol(movie_genre2)) {\n","    gen_col = which(genre_mat1[1,] == movie_genre2[index,col]) \n","    genre_mat1[index+1,gen_col] <- 1\n","}\n","}\n","genre_mat2 <- as.data.frame(genre_mat1[-1,], stringsAsFactors=FALSE) #remove first row, which was the genre list\n","for (col in 1:ncol(genre_mat2)) {\n","  genre_mat2[,col] <- as.integer(genre_mat2[,col]) #convert from characters to integers\n","} \n","str(genre_mat2)"]},{"cell_type":"code","execution_count":8,"id":"7cd23372","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:25:26.202188Z","iopub.status.busy":"2024-05-16T11:25:26.200463Z","iopub.status.idle":"2024-05-16T11:25:26.243237Z","shell.execute_reply":"2024-05-16T11:25:26.24135Z"},"papermill":{"duration":0.067211,"end_time":"2024-05-16T11:25:26.245933","exception":false,"start_time":"2024-05-16T11:25:26.178722","status":"completed"},"tags":[]},"outputs":[{"data":{"text/html":["<table class=\"dataframe\">\n","<caption>A data.frame: 6 × 20</caption>\n","<thead>\n","\t<tr><th></th><th scope=col>movieId</th><th scope=col>title</th><th scope=col>Action</th><th scope=col>Adventure</th><th scope=col>Animation</th><th scope=col>Children</th><th scope=col>Comedy</th><th scope=col>Crime</th><th scope=col>Documentary</th><th scope=col>Drama</th><th scope=col>Fantasy</th><th scope=col>Film-Noir</th><th scope=col>Horror</th><th scope=col>Musical</th><th scope=col>Mystery</th><th scope=col>Romance</th><th scope=col>Sci-Fi</th><th scope=col>Thriller</th><th scope=col>War</th><th scope=col>Western</th></tr>\n","\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n","</thead>\n","<tbody>\n","\t<tr><th scope=row>1</th><td>1</td><td>Toy Story (1995)                  </td><td>0</td><td>1</td><td>1</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n","\t<tr><th scope=row>2</th><td>2</td><td>Jumanji (1995)                    </td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n","\t<tr><th scope=row>3</th><td>3</td><td>Grumpier Old Men (1995)           </td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n","\t<tr><th scope=row>4</th><td>4</td><td>Waiting to Exhale (1995)          </td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n","\t<tr><th scope=row>5</th><td>5</td><td>Father of the Bride Part II (1995)</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n","\t<tr><th scope=row>6</th><td>6</td><td>Heat (1995)                       </td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n","</tbody>\n","</table>\n"],"text/latex":["A data.frame: 6 × 20\n","\\begin{tabular}{r|llllllllllllllllllll}\n","  & movieId & title & Action & Adventure & Animation & Children & Comedy & Crime & Documentary & Drama & Fantasy & Film-Noir & Horror & Musical & Mystery & Romance & Sci-Fi & Thriller & War & Western\\\\\n","  & <int> & <chr> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int>\\\\\n","\\hline\n","\t1 & 1 & Toy Story (1995)                   & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n","\t2 & 2 & Jumanji (1995)                     & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n","\t3 & 3 & Grumpier Old Men (1995)            & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n","\t4 & 4 & Waiting to Exhale (1995)           & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n","\t5 & 5 & Father of the Bride Part II (1995) & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n","\t6 & 6 & Heat (1995)                        & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n","\\end{tabular}\n"],"text/markdown":["\n","A data.frame: 6 × 20\n","\n","| <!--/--> | movieId &lt;int&gt; | title &lt;chr&gt; | Action &lt;int&gt; | Adventure &lt;int&gt; | Animation &lt;int&gt; | Children &lt;int&gt; | Comedy &lt;int&gt; | Crime &lt;int&gt; | Documentary &lt;int&gt; | Drama &lt;int&gt; | Fantasy &lt;int&gt; | Film-Noir &lt;int&gt; | Horror &lt;int&gt; | Musical &lt;int&gt; | Mystery &lt;int&gt; | Romance &lt;int&gt; | Sci-Fi &lt;int&gt; | Thriller &lt;int&gt; | War &lt;int&gt; | Western &lt;int&gt; |\n","|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n","| 1 | 1 | Toy Story (1995)                   | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |\n","| 2 | 2 | Jumanji (1995)                     | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |\n","| 3 | 3 | Grumpier Old Men (1995)            | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |\n","| 4 | 4 | Waiting to Exhale (1995)           | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |\n","| 5 | 5 | Father of the Bride Part II (1995) | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |\n","| 6 | 6 | Heat (1995)                        | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |\n","\n"],"text/plain":["  movieId title                              Action Adventure Animation\n","1 1       Toy Story (1995)                   0      1         1        \n","2 2       Jumanji (1995)                     0      1         0        \n","3 3       Grumpier Old Men (1995)            0      0         0        \n","4 4       Waiting to Exhale (1995)           0      0         0        \n","5 5       Father of the Bride Part II (1995) 0      0         0        \n","6 6       Heat (1995)                        1      0         0        \n","  Children Comedy Crime Documentary Drama Fantasy Film-Noir Horror Musical\n","1 1        1      0     0           0     1       0         0      0      \n","2 1        0      0     0           0     1       0         0      0      \n","3 0        1      0     0           0     0       0         0      0      \n","4 0        1      0     0           1     0       0         0      0      \n","5 0        1      0     0           0     0       0         0      0      \n","6 0        0      1     0           0     0       0         0      0      \n","  Mystery Romance Sci-Fi Thriller War Western\n","1 0       0       0      0        0   0      \n","2 0       0       0      0        0   0      \n","3 0       1       0      0        0   0      \n","4 0       1       0      0        0   0      \n","5 0       0       0      0        0   0      \n","6 0       0       0      1        0   0      "]},"metadata":{},"output_type":"display_data"}],"source":["# Create a ‘search matrix’ that will allow us to perform an easy search of the films by specifying the genre present in our list.\n","SearchMatrix <- cbind(movie_data[,1:2], genre_mat2[])\n","head(SearchMatrix)"]},{"cell_type":"markdown","id":"1e3a9a79","metadata":{"papermill":{"duration":0.020593,"end_time":"2024-05-16T11:25:26.28749","exception":false,"start_time":"2024-05-16T11:25:26.266897","status":"completed"},"tags":[]},"source":["### For the movie recommendation system to make sense of our ratings through recommended labs, we have to convert our matrix into a sparse matrix. This new matrix is of the class ‘realRatingMatrix’:"]},{"cell_type":"code","execution_count":9,"id":"0e418a4e","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:25:26.332744Z","iopub.status.busy":"2024-05-16T11:25:26.331016Z","iopub.status.idle":"2024-05-16T11:25:29.171239Z","shell.execute_reply":"2024-05-16T11:25:29.169441Z"},"papermill":{"duration":2.866252,"end_time":"2024-05-16T11:25:29.174338","exception":false,"start_time":"2024-05-16T11:25:26.308086","status":"completed"},"tags":[]},"outputs":[{"data":{"text/plain":["668 x 10325 rating matrix of class ‘realRatingMatrix’ with 105339 ratings."]},"metadata":{},"output_type":"display_data"}],"source":["ratingMatrix <- dcast(rating_data, userId~movieId, value.var = \"rating\", na.rm=FALSE)\n","ratingMatrix <- as.matrix(ratingMatrix[,-1]) #remove userIds\n","#Convert rating matrix into a recommenderlab sparse matrix\n","ratingMatrix <- as(ratingMatrix, \"realRatingMatrix\")\n","ratingMatrix"]},{"cell_type":"markdown","id":"4e7a39b6","metadata":{"papermill":{"duration":0.02085,"end_time":"2024-05-16T11:25:29.215951","exception":false,"start_time":"2024-05-16T11:25:29.195101","status":"completed"},"tags":[]},"source":["### Overview of some of the important parameters that provide us with various options for building recommendation systems for movies:"]},{"cell_type":"code","execution_count":10,"id":"a8edfc30","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:25:29.26121Z","iopub.status.busy":"2024-05-16T11:25:29.259572Z","iopub.status.idle":"2024-05-16T11:25:29.288488Z","shell.execute_reply":"2024-05-16T11:25:29.2867Z"},"papermill":{"duration":0.054664,"end_time":"2024-05-16T11:25:29.29123","exception":false,"start_time":"2024-05-16T11:25:29.236566","status":"completed"},"tags":[]},"outputs":[{"data":{"text/html":["<style>\n",".list-inline {list-style: none; margin:0; padding: 0}\n",".list-inline>li {display: inline-block}\n",".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n","</style>\n","<ol class=list-inline><li>'HYBRID_realRatingMatrix'</li><li>'ALS_realRatingMatrix'</li><li>'ALS_implicit_realRatingMatrix'</li><li>'IBCF_realRatingMatrix'</li><li>'LIBMF_realRatingMatrix'</li><li>'POPULAR_realRatingMatrix'</li><li>'RANDOM_realRatingMatrix'</li><li>'RERECOMMEND_realRatingMatrix'</li><li>'SVD_realRatingMatrix'</li><li>'SVDF_realRatingMatrix'</li><li>'UBCF_realRatingMatrix'</li></ol>\n"],"text/latex":["\\begin{enumerate*}\n","\\item 'HYBRID\\_realRatingMatrix'\n","\\item 'ALS\\_realRatingMatrix'\n","\\item 'ALS\\_implicit\\_realRatingMatrix'\n","\\item 'IBCF\\_realRatingMatrix'\n","\\item 'LIBMF\\_realRatingMatrix'\n","\\item 'POPULAR\\_realRatingMatrix'\n","\\item 'RANDOM\\_realRatingMatrix'\n","\\item 'RERECOMMEND\\_realRatingMatrix'\n","\\item 'SVD\\_realRatingMatrix'\n","\\item 'SVDF\\_realRatingMatrix'\n","\\item 'UBCF\\_realRatingMatrix'\n","\\end{enumerate*}\n"],"text/markdown":["1. 'HYBRID_realRatingMatrix'\n","2. 'ALS_realRatingMatrix'\n","3. 'ALS_implicit_realRatingMatrix'\n","4. 'IBCF_realRatingMatrix'\n","5. 'LIBMF_realRatingMatrix'\n","6. 'POPULAR_realRatingMatrix'\n","7. 'RANDOM_realRatingMatrix'\n","8. 'RERECOMMEND_realRatingMatrix'\n","9. 'SVD_realRatingMatrix'\n","10. 'SVDF_realRatingMatrix'\n","11. 'UBCF_realRatingMatrix'\n","\n","\n"],"text/plain":[" [1] \"HYBRID_realRatingMatrix\"       \"ALS_realRatingMatrix\"         \n"," [3] \"ALS_implicit_realRatingMatrix\" \"IBCF_realRatingMatrix\"        \n"," [5] \"LIBMF_realRatingMatrix\"        \"POPULAR_realRatingMatrix\"     \n"," [7] \"RANDOM_realRatingMatrix\"       \"RERECOMMEND_realRatingMatrix\" \n"," [9] \"SVD_realRatingMatrix\"          \"SVDF_realRatingMatrix\"        \n","[11] \"UBCF_realRatingMatrix\"        "]},"metadata":{},"output_type":"display_data"}],"source":["recommendation_model <- recommenderRegistry$get_entries(dataType = \"realRatingMatrix\")\n","names(recommendation_model)"]},{"cell_type":"code","execution_count":11,"id":"7f197a67","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:25:29.337063Z","iopub.status.busy":"2024-05-16T11:25:29.335306Z","iopub.status.idle":"2024-05-16T11:25:29.363367Z","shell.execute_reply":"2024-05-16T11:25:29.361326Z"},"papermill":{"duration":0.053952,"end_time":"2024-05-16T11:25:29.366079","exception":false,"start_time":"2024-05-16T11:25:29.312127","status":"completed"},"tags":[]},"outputs":[{"data":{"text/html":["<dl>\n","\t<dt>$HYBRID_realRatingMatrix</dt>\n","\t\t<dd>'Hybrid recommender that aggegates several recommendation strategies using weighted averages.'</dd>\n","\t<dt>$ALS_realRatingMatrix</dt>\n","\t\t<dd>'Recommender for explicit ratings based on latent factors, calculated by alternating least squares algorithm.'</dd>\n","\t<dt>$ALS_implicit_realRatingMatrix</dt>\n","\t\t<dd>'Recommender for implicit data based on latent factors, calculated by alternating least squares algorithm.'</dd>\n","\t<dt>$IBCF_realRatingMatrix</dt>\n","\t\t<dd>'Recommender based on item-based collaborative filtering.'</dd>\n","\t<dt>$LIBMF_realRatingMatrix</dt>\n","\t\t<dd>'Matrix factorization with LIBMF via package recosystem (https://cran.r-project.org/web/packages/recosystem/vignettes/introduction.html).'</dd>\n","\t<dt>$POPULAR_realRatingMatrix</dt>\n","\t\t<dd>'Recommender based on item popularity.'</dd>\n","\t<dt>$RANDOM_realRatingMatrix</dt>\n","\t\t<dd>'Produce random recommendations (real ratings).'</dd>\n","\t<dt>$RERECOMMEND_realRatingMatrix</dt>\n","\t\t<dd>'Re-recommends highly rated items (real ratings).'</dd>\n","\t<dt>$SVD_realRatingMatrix</dt>\n","\t\t<dd>'Recommender based on SVD approximation with column-mean imputation.'</dd>\n","\t<dt>$SVDF_realRatingMatrix</dt>\n","\t\t<dd>'Recommender based on Funk SVD with gradient descend (https://sifter.org/~simon/journal/20061211.html).'</dd>\n","\t<dt>$UBCF_realRatingMatrix</dt>\n","\t\t<dd>'Recommender based on user-based collaborative filtering.'</dd>\n","</dl>\n"],"text/latex":["\\begin{description}\n","\\item[\\$HYBRID\\_realRatingMatrix] 'Hybrid recommender that aggegates several recommendation strategies using weighted averages.'\n","\\item[\\$ALS\\_realRatingMatrix] 'Recommender for explicit ratings based on latent factors, calculated by alternating least squares algorithm.'\n","\\item[\\$ALS\\_implicit\\_realRatingMatrix] 'Recommender for implicit data based on latent factors, calculated by alternating least squares algorithm.'\n","\\item[\\$IBCF\\_realRatingMatrix] 'Recommender based on item-based collaborative filtering.'\n","\\item[\\$LIBMF\\_realRatingMatrix] 'Matrix factorization with LIBMF via package recosystem (https://cran.r-project.org/web/packages/recosystem/vignettes/introduction.html).'\n","\\item[\\$POPULAR\\_realRatingMatrix] 'Recommender based on item popularity.'\n","\\item[\\$RANDOM\\_realRatingMatrix] 'Produce random recommendations (real ratings).'\n","\\item[\\$RERECOMMEND\\_realRatingMatrix] 'Re-recommends highly rated items (real ratings).'\n","\\item[\\$SVD\\_realRatingMatrix] 'Recommender based on SVD approximation with column-mean imputation.'\n","\\item[\\$SVDF\\_realRatingMatrix] 'Recommender based on Funk SVD with gradient descend (https://sifter.org/\\textasciitilde{}simon/journal/20061211.html).'\n","\\item[\\$UBCF\\_realRatingMatrix] 'Recommender based on user-based collaborative filtering.'\n","\\end{description}\n"],"text/markdown":["$HYBRID_realRatingMatrix\n",":   'Hybrid recommender that aggegates several recommendation strategies using weighted averages.'\n","$ALS_realRatingMatrix\n",":   'Recommender for explicit ratings based on latent factors, calculated by alternating least squares algorithm.'\n","$ALS_implicit_realRatingMatrix\n",":   'Recommender for implicit data based on latent factors, calculated by alternating least squares algorithm.'\n","$IBCF_realRatingMatrix\n",":   'Recommender based on item-based collaborative filtering.'\n","$LIBMF_realRatingMatrix\n",":   'Matrix factorization with LIBMF via package recosystem (https://cran.r-project.org/web/packages/recosystem/vignettes/introduction.html).'\n","$POPULAR_realRatingMatrix\n",":   'Recommender based on item popularity.'\n","$RANDOM_realRatingMatrix\n",":   'Produce random recommendations (real ratings).'\n","$RERECOMMEND_realRatingMatrix\n",":   'Re-recommends highly rated items (real ratings).'\n","$SVD_realRatingMatrix\n",":   'Recommender based on SVD approximation with column-mean imputation.'\n","$SVDF_realRatingMatrix\n",":   'Recommender based on Funk SVD with gradient descend (https://sifter.org/~simon/journal/20061211.html).'\n","$UBCF_realRatingMatrix\n",":   'Recommender based on user-based collaborative filtering.'\n","\n","\n"],"text/plain":["$HYBRID_realRatingMatrix\n","[1] \"Hybrid recommender that aggegates several recommendation strategies using weighted averages.\"\n","\n","$ALS_realRatingMatrix\n","[1] \"Recommender for explicit ratings based on latent factors, calculated by alternating least squares algorithm.\"\n","\n","$ALS_implicit_realRatingMatrix\n","[1] \"Recommender for implicit data based on latent factors, calculated by alternating least squares algorithm.\"\n","\n","$IBCF_realRatingMatrix\n","[1] \"Recommender based on item-based collaborative filtering.\"\n","\n","$LIBMF_realRatingMatrix\n","[1] \"Matrix factorization with LIBMF via package recosystem (https://cran.r-project.org/web/packages/recosystem/vignettes/introduction.html).\"\n","\n","$POPULAR_realRatingMatrix\n","[1] \"Recommender based on item popularity.\"\n","\n","$RANDOM_realRatingMatrix\n","[1] \"Produce random recommendations (real ratings).\"\n","\n","$RERECOMMEND_realRatingMatrix\n","[1] \"Re-recommends highly rated items (real ratings).\"\n","\n","$SVD_realRatingMatrix\n","[1] \"Recommender based on SVD approximation with column-mean imputation.\"\n","\n","$SVDF_realRatingMatrix\n","[1] \"Recommender based on Funk SVD with gradient descend (https://sifter.org/~simon/journal/20061211.html).\"\n","\n","$UBCF_realRatingMatrix\n","[1] \"Recommender based on user-based collaborative filtering.\"\n"]},"metadata":{},"output_type":"display_data"}],"source":["lapply(recommendation_model, \"[[\", \"description\")\n","# lapply() is a function that takes a vector,list or data frame as input and gives the output as list by appplying a certain operation on it."]},{"cell_type":"markdown","id":"80ca0c3b","metadata":{"papermill":{"duration":0.022677,"end_time":"2024-05-16T11:25:29.410215","exception":false,"start_time":"2024-05-16T11:25:29.387538","status":"completed"},"tags":[]},"source":["### Based Collaborative Filtering"]},{"cell_type":"code","execution_count":12,"id":"7e96f566","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:25:29.457272Z","iopub.status.busy":"2024-05-16T11:25:29.455176Z","iopub.status.idle":"2024-05-16T11:25:29.479771Z","shell.execute_reply":"2024-05-16T11:25:29.477523Z"},"papermill":{"duration":0.05081,"end_time":"2024-05-16T11:25:29.48261","exception":false,"start_time":"2024-05-16T11:25:29.4318","status":"completed"},"tags":[]},"outputs":[{"data":{"text/html":["<dl>\n","\t<dt>$k</dt>\n","\t\t<dd>30</dd>\n","\t<dt>$method</dt>\n","\t\t<dd>'cosine'</dd>\n","\t<dt>$normalize</dt>\n","\t\t<dd>'center'</dd>\n","\t<dt>$normalize_sim_matrix</dt>\n","\t\t<dd>FALSE</dd>\n","\t<dt>$alpha</dt>\n","\t\t<dd>0.5</dd>\n","\t<dt>$na_as_zero</dt>\n","\t\t<dd>FALSE</dd>\n","</dl>\n"],"text/latex":["\\begin{description}\n","\\item[\\$k] 30\n","\\item[\\$method] 'cosine'\n","\\item[\\$normalize] 'center'\n","\\item[\\$normalize\\_sim\\_matrix] FALSE\n","\\item[\\$alpha] 0.5\n","\\item[\\$na\\_as\\_zero] FALSE\n","\\end{description}\n"],"text/markdown":["$k\n",":   30\n","$method\n",":   'cosine'\n","$normalize\n",":   'center'\n","$normalize_sim_matrix\n",":   FALSE\n","$alpha\n",":   0.5\n","$na_as_zero\n",":   FALSE\n","\n","\n"],"text/plain":["$k\n","[1] 30\n","\n","$method\n","[1] \"cosine\"\n","\n","$normalize\n","[1] \"center\"\n","\n","$normalize_sim_matrix\n","[1] FALSE\n","\n","$alpha\n","[1] 0.5\n","\n","$na_as_zero\n","[1] FALSE\n"]},"metadata":{},"output_type":"display_data"}],"source":["recommendation_model$IBCF_realRatingMatrix$parameters"]},{"cell_type":"markdown","id":"5181f864","metadata":{"papermill":{"duration":0.021256,"end_time":"2024-05-16T11:25:29.526787","exception":false,"start_time":"2024-05-16T11:25:29.505531","status":"completed"},"tags":[]},"source":["# Exploring Similar Data\n","- Collaborative Filtering involves suggesting movies to the users that are based on collecting preferences from many other users. For example, if user A likes to watch action films and so does user B, then the movies that user B will watch in the future will be recommended to A and vice-versa. Therefore, recommending movies is dependent on creating a relationship of similarity between the two users. With the help of recommended lab, we can compute similarities using various operators like cosine, Pearson as well as Jaccard."]},{"cell_type":"markdown","id":"e7d6b624","metadata":{"papermill":{"duration":0.022067,"end_time":"2024-05-16T11:25:29.570184","exception":false,"start_time":"2024-05-16T11:25:29.548117","status":"completed"},"tags":[]},"source":["## User's Similarities"]},{"cell_type":"code","execution_count":13,"id":"c6ff74d0","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:25:29.61691Z","iopub.status.busy":"2024-05-16T11:25:29.614962Z","iopub.status.idle":"2024-05-16T11:25:29.974853Z","shell.execute_reply":"2024-05-16T11:25:29.972395Z"},"papermill":{"duration":0.386626,"end_time":"2024-05-16T11:25:29.977769","exception":false,"start_time":"2024-05-16T11:25:29.591143","status":"completed"},"tags":[]},"outputs":[{"data":{"text/html":["<table class=\"dataframe\">\n","<caption>A matrix: 4 × 4 of type dbl</caption>\n","<thead>\n","\t<tr><th></th><th scope=col>1</th><th scope=col>2</th><th scope=col>3</th><th scope=col>4</th></tr>\n","</thead>\n","<tbody>\n","\t<tr><th scope=row>1</th><td>       NA</td><td>0.9880430</td><td>0.9820862</td><td>0.9957199</td></tr>\n","\t<tr><th scope=row>2</th><td>0.9880430</td><td>       NA</td><td>0.9962866</td><td>0.9687126</td></tr>\n","\t<tr><th scope=row>3</th><td>0.9820862</td><td>0.9962866</td><td>       NA</td><td>0.9944484</td></tr>\n","\t<tr><th scope=row>4</th><td>0.9957199</td><td>0.9687126</td><td>0.9944484</td><td>       NA</td></tr>\n","</tbody>\n","</table>\n"],"text/latex":["A matrix: 4 × 4 of type dbl\n","\\begin{tabular}{r|llll}\n","  & 1 & 2 & 3 & 4\\\\\n","\\hline\n","\t1 &        NA & 0.9880430 & 0.9820862 & 0.9957199\\\\\n","\t2 & 0.9880430 &        NA & 0.9962866 & 0.9687126\\\\\n","\t3 & 0.9820862 & 0.9962866 &        NA & 0.9944484\\\\\n","\t4 & 0.9957199 & 0.9687126 & 0.9944484 &        NA\\\\\n","\\end{tabular}\n"],"text/markdown":["\n","A matrix: 4 × 4 of type dbl\n","\n","| <!--/--> | 1 | 2 | 3 | 4 |\n","|---|---|---|---|---|\n","| 1 |        NA | 0.9880430 | 0.9820862 | 0.9957199 |\n","| 2 | 0.9880430 |        NA | 0.9962866 | 0.9687126 |\n","| 3 | 0.9820862 | 0.9962866 |        NA | 0.9944484 |\n","| 4 | 0.9957199 | 0.9687126 | 0.9944484 |        NA |\n","\n"],"text/plain":["  1         2         3         4        \n","1        NA 0.9880430 0.9820862 0.9957199\n","2 0.9880430        NA 0.9962866 0.9687126\n","3 0.9820862 0.9962866        NA 0.9944484\n","4 0.9957199 0.9687126 0.9944484        NA"]},"metadata":{},"output_type":"display_data"},{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nhB0AQCSEHQBAJIQdAEAkhB0AQCSEHQBAJIQdAEAkhB0A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rWL5v04e3OusTjv0aFUx/52PqtPp/U791cPf75f0sAAAjS2TjtiFEPocffFb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\nS1USFPlKhgAAAABJRU5ErkJggg=="},"metadata":{"image/png":{"height":420,"width":420}},"output_type":"display_data"}],"source":["similarity_mat <- similarity(ratingMatrix[1:4, ],\n","                               method = \"cosine\",\n","                               which = \"users\")\n","as.matrix(similarity_mat)\n","image(as.matrix(similarity_mat), main = \"User's Similarities\")"]},{"cell_type":"markdown","id":"615428f2","metadata":{"papermill":{"duration":0.022555,"end_time":"2024-05-16T11:25:30.022396","exception":false,"start_time":"2024-05-16T11:25:29.999841","status":"completed"},"tags":[]},"source":["- In the above matrix, each row and column represents a user. We have taken four users and each cell in this matrix represents the similarity that is shared between the two users."]},{"cell_type":"markdown","id":"e54e4474","metadata":{"papermill":{"duration":0.021825,"end_time":"2024-05-16T11:25:30.066045","exception":false,"start_time":"2024-05-16T11:25:30.04422","status":"completed"},"tags":[]},"source":["### Delineate the similarity that is shared between the films:"]},{"cell_type":"markdown","id":"fabddddd","metadata":{"papermill":{"duration":0.022011,"end_time":"2024-05-16T11:25:30.109765","exception":false,"start_time":"2024-05-16T11:25:30.087754","status":"completed"},"tags":[]},"source":["## Movies similarity"]},{"cell_type":"code","execution_count":14,"id":"ec5ae5cb","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:25:30.157445Z","iopub.status.busy":"2024-05-16T11:25:30.155506Z","iopub.status.idle":"2024-05-16T11:25:30.348837Z","shell.execute_reply":"2024-05-16T11:25:30.346289Z"},"papermill":{"duration":0.220598,"end_time":"2024-05-16T11:25:30.351921","exception":false,"start_time":"2024-05-16T11:25:30.131323","status":"completed"},"tags":[]},"outputs":[{"data":{"text/html":["<table class=\"dataframe\">\n","<caption>A matrix: 4 × 4 of type dbl</caption>\n","<thead>\n","\t<tr><th></th><th scope=col>1</th><th scope=col>2</th><th scope=col>3</th><th scope=col>4</th></tr>\n","</thead>\n","<tbody>\n","\t<tr><th scope=row>1</th><td>       NA</td><td>0.9834866</td><td>0.9779671</td><td>0.9550638</td></tr>\n","\t<tr><th scope=row>2</th><td>0.9834866</td><td>       NA</td><td>0.9829378</td><td>0.9706208</td></tr>\n","\t<tr><th scope=row>3</th><td>0.9779671</td><td>0.9829378</td><td>       NA</td><td>0.9932438</td></tr>\n","\t<tr><th scope=row>4</th><td>0.9550638</td><td>0.9706208</td><td>0.9932438</td><td>       NA</td></tr>\n","</tbody>\n","</table>\n"],"text/latex":["A matrix: 4 × 4 of type dbl\n","\\begin{tabular}{r|llll}\n","  & 1 & 2 & 3 & 4\\\\\n","\\hline\n","\t1 &        NA & 0.9834866 & 0.9779671 & 0.9550638\\\\\n","\t2 & 0.9834866 &        NA & 0.9829378 & 0.9706208\\\\\n","\t3 & 0.9779671 & 0.9829378 &        NA & 0.9932438\\\\\n","\t4 & 0.9550638 & 0.9706208 & 0.9932438 &        NA\\\\\n","\\end{tabular}\n"],"text/markdown":["\n","A matrix: 4 × 4 of type dbl\n","\n","| <!--/--> | 1 | 2 | 3 | 4 |\n","|---|---|---|---|---|\n","| 1 |        NA | 0.9834866 | 0.9779671 | 0.9550638 |\n","| 2 | 0.9834866 |        NA | 0.9829378 | 0.9706208 |\n","| 3 | 0.9779671 | 0.9829378 |        NA | 0.9932438 |\n","| 4 | 0.9550638 | 0.9706208 | 0.9932438 |        NA |\n","\n"],"text/plain":["  1         2         3         4        \n","1        NA 0.9834866 0.9779671 0.9550638\n","2 0.9834866        NA 0.9829378 0.9706208\n","3 0.9779671 0.9829378        NA 0.9932438\n","4 0.9550638 0.9706208 0.9932438        NA"]},"metadata":{},"output_type":"display_data"},{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nzvr4DOIFc56f/dp72W37XXrTqPqNF9w7v8nPf+HQHnU3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YQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJ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\nABHCDgAgQtgBAET8BU1dFeM5r8SnAAAAAElFTkSuQmCC"},"metadata":{"image/png":{"height":420,"width":420}},"output_type":"display_data"}],"source":["movie_similarity <- similarity(ratingMatrix[, 1:4], method =\n","                                 \"cosine\", which = \"items\")\n","as.matrix(movie_similarity)\n","image(as.matrix(movie_similarity), main = \"Movies similarity\")"]},{"cell_type":"markdown","id":"4f2f442b","metadata":{"papermill":{"duration":0.022574,"end_time":"2024-05-16T11:25:30.397432","exception":false,"start_time":"2024-05-16T11:25:30.374858","status":"completed"},"tags":[]},"source":["### Extract the most unique ratings:"]},{"cell_type":"code","execution_count":15,"id":"0c443903","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:25:30.489002Z","iopub.status.busy":"2024-05-16T11:25:30.486881Z","iopub.status.idle":"2024-05-16T11:25:31.215117Z","shell.execute_reply":"2024-05-16T11:25:31.212228Z"},"papermill":{"duration":0.757039,"end_time":"2024-05-16T11:25:31.21894","exception":false,"start_time":"2024-05-16T11:25:30.461901","status":"completed"},"tags":[]},"outputs":[{"data":{"text/html":["<style>\n",".list-inline {list-style: none; margin:0; padding: 0}\n",".list-inline>li {display: inline-block}\n",".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n","</style>\n","<ol class=list-inline><li>0</li><li>5</li><li>4</li><li>3</li><li>4.5</li><li>1.5</li><li>2</li><li>3.5</li><li>1</li><li>2.5</li><li>0.5</li></ol>\n"],"text/latex":["\\begin{enumerate*}\n","\\item 0\n","\\item 5\n","\\item 4\n","\\item 3\n","\\item 4.5\n","\\item 1.5\n","\\item 2\n","\\item 3.5\n","\\item 1\n","\\item 2.5\n","\\item 0.5\n","\\end{enumerate*}\n"],"text/markdown":["1. 0\n","2. 5\n","3. 4\n","4. 3\n","5. 4.5\n","6. 1.5\n","7. 2\n","8. 3.5\n","9. 1\n","10. 2.5\n","11. 0.5\n","\n","\n"],"text/plain":[" [1] 0.0 5.0 4.0 3.0 4.5 1.5 2.0 3.5 1.0 2.5 0.5"]},"metadata":{},"output_type":"display_data"}],"source":["rating_values <- as.vector(ratingMatrix@data)\n","unique(rating_values) # extracting unique ratings"]},{"cell_type":"markdown","id":"6d8be71b","metadata":{"papermill":{"duration":0.022957,"end_time":"2024-05-16T11:25:31.264989","exception":false,"start_time":"2024-05-16T11:25:31.242032","status":"completed"},"tags":[]},"source":["### Create a table of ratings that will display the most unique ratings:"]},{"cell_type":"code","execution_count":16,"id":"dd5f112d","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:25:31.316157Z","iopub.status.busy":"2024-05-16T11:25:31.314148Z","iopub.status.idle":"2024-05-16T11:25:36.783043Z","shell.execute_reply":"2024-05-16T11:25:36.780162Z"},"papermill":{"duration":5.498815,"end_time":"2024-05-16T11:25:36.786928","exception":false,"start_time":"2024-05-16T11:25:31.288113","status":"completed"},"tags":[]},"outputs":[{"data":{"text/plain":["rating_values\n","      0     0.5       1     1.5       2     2.5       3     3.5       4     4.5 \n","6791761    1198    3258    1567    7943    5484   21729   12237   28880    8187 \n","      5 \n","  14856 "]},"metadata":{},"output_type":"display_data"}],"source":["Table_of_Ratings <- table(rating_values) # creating a count of movie ratings\n","Table_of_Ratings"]},{"cell_type":"markdown","id":"85b00228","metadata":{"papermill":{"duration":0.023078,"end_time":"2024-05-16T11:25:36.833554","exception":false,"start_time":"2024-05-16T11:25:36.810476","status":"completed"},"tags":[]},"source":["# Most Viewed Movies Visualization\n"," - In this section of the machine learning project, we will explore the most viewed movies in our dataset. We will first count the number of views in a film and then organize them in a table that would group them in descending order."]},{"cell_type":"code","execution_count":17,"id":"88153b44","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:25:36.883713Z","iopub.status.busy":"2024-05-16T11:25:36.882009Z","iopub.status.idle":"2024-05-16T11:26:08.198245Z","shell.execute_reply":"2024-05-16T11:26:08.195391Z"},"papermill":{"duration":31.367307,"end_time":"2024-05-16T11:26:08.224354","exception":false,"start_time":"2024-05-16T11:25:36.857047","status":"completed"},"tags":[]},"outputs":[{"data":{"text/html":["<table class=\"dataframe\">\n","<caption>A data.frame: 6 × 3</caption>\n","<thead>\n","\t<tr><th></th><th scope=col>movie</th><th scope=col>views</th><th scope=col>title</th></tr>\n","\t<tr><th></th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n","</thead>\n","<tbody>\n","\t<tr><th scope=row>296</th><td>296</td><td>325</td><td>Pulp Fiction (1994)                      </td></tr>\n","\t<tr><th scope=row>356</th><td>356</td><td>311</td><td>Forrest Gump (1994)                      </td></tr>\n","\t<tr><th scope=row>318</th><td>318</td><td>308</td><td>Shawshank Redemption, The (1994)         </td></tr>\n","\t<tr><th scope=row>480</th><td>480</td><td>294</td><td>Jurassic Park (1993)                     </td></tr>\n","\t<tr><th scope=row>593</th><td>593</td><td>290</td><td>Silence of the Lambs, The (1991)         </td></tr>\n","\t<tr><th scope=row>260</th><td>260</td><td>273</td><td>Star Wars: Episode IV - A New Hope (1977)</td></tr>\n","</tbody>\n","</table>\n"],"text/latex":["A data.frame: 6 × 3\n","\\begin{tabular}{r|lll}\n","  & movie & views & title\\\\\n","  & <chr> & <int> & <chr>\\\\\n","\\hline\n","\t296 & 296 & 325 & Pulp Fiction (1994)                      \\\\\n","\t356 & 356 & 311 & Forrest Gump (1994)                      \\\\\n","\t318 & 318 & 308 & Shawshank Redemption, The (1994)         \\\\\n","\t480 & 480 & 294 & Jurassic Park (1993)                     \\\\\n","\t593 & 593 & 290 & Silence of the Lambs, The (1991)         \\\\\n","\t260 & 260 & 273 & Star Wars: Episode IV - A New Hope (1977)\\\\\n","\\end{tabular}\n"],"text/markdown":["\n","A data.frame: 6 × 3\n","\n","| <!--/--> | movie &lt;chr&gt; | views &lt;int&gt; | title &lt;chr&gt; |\n","|---|---|---|---|\n","| 296 | 296 | 325 | Pulp Fiction (1994)                       |\n","| 356 | 356 | 311 | Forrest Gump (1994)                       |\n","| 318 | 318 | 308 | Shawshank Redemption, The (1994)          |\n","| 480 | 480 | 294 | Jurassic Park (1993)                      |\n","| 593 | 593 | 290 | Silence of the Lambs, The (1991)          |\n","| 260 | 260 | 273 | Star Wars: Episode IV - A New Hope (1977) |\n","\n"],"text/plain":["    movie views title                                    \n","296 296   325   Pulp Fiction (1994)                      \n","356 356   311   Forrest Gump (1994)                      \n","318 318   308   Shawshank Redemption, The (1994)         \n","480 480   294   Jurassic Park (1993)                     \n","593 593   290   Silence of the Lambs, The (1991)         \n","260 260   273   Star Wars: Episode IV - A New Hope (1977)"]},"metadata":{},"output_type":"display_data"}],"source":["movie_views <- colCounts(ratingMatrix) # count views for each movie\n","table_views <- data.frame(movie = names(movie_views),\n","                          views = movie_views) # create dataframe of views\n","table_views <- table_views[order(table_views$views,\n","                                 decreasing = TRUE), ] # sort by number of views\n","table_views$title <- NA\n","for (index in 1:10325){\n","  table_views[index,3] <- as.character(subset(movie_data,\n","                                         movie_data$movieId == table_views[index,1])$title)\n","}\n","table_views[1:6,]"]},{"cell_type":"markdown","id":"2c726778","metadata":{"papermill":{"duration":0.022831,"end_time":"2024-05-16T11:26:08.270006","exception":false,"start_time":"2024-05-16T11:26:08.247175","status":"completed"},"tags":[]},"source":["### Visualize a bar plot for the total number of views of the top films. We will carry this out using ggplot2:"]},{"cell_type":"code","execution_count":18,"id":"27a64878","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:26:08.321407Z","iopub.status.busy":"2024-05-16T11:26:08.319493Z","iopub.status.idle":"2024-05-16T11:26:08.719024Z","shell.execute_reply":"2024-05-16T11:26:08.716152Z"},"papermill":{"duration":0.428837,"end_time":"2024-05-16T11:26:08.722779","exception":false,"start_time":"2024-05-16T11:26:08.293942","status":"completed"},"tags":[]},"outputs":[{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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nX5Qte3/nTcZsxILpCjQeeGNS0XKCIiLi2rFvy8bb9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84iddnT78g/OJDo0LXvoxPvPzV2/644u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liFt15AYQazrEDAAA6MSUUVDs/2+C1ZHCP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\nxMT/ASEeSmR/RWNJAAAAAElFTkSuQmCC"},"metadata":{"image/png":{"height":420,"width":420}},"output_type":"display_data"}],"source":["ggplot(table_views[1:6, ], aes(x = title, y = views)) +\n","  geom_bar(stat=\"identity\", fill = 'steelblue') +\n","  geom_text(aes(label=views), vjust=-0.3, size=3.5) +\n","  theme(axis.text.x = element_text(angle = 45, hjust = 1)) +\n","  ggtitle(\"Total Views of the Top Films\")"]},{"cell_type":"markdown","id":"a12a30b2","metadata":{"papermill":{"duration":0.024418,"end_time":"2024-05-16T11:26:08.771376","exception":false,"start_time":"2024-05-16T11:26:08.746958","status":"completed"},"tags":[]},"source":["- From the above bar-plot, we observe that Pulp Fiction is the most-watched film followed by Forrest Gump."]},{"cell_type":"markdown","id":"38a13f1c","metadata":{"papermill":{"duration":0.02442,"end_time":"2024-05-16T11:26:08.820381","exception":false,"start_time":"2024-05-16T11:26:08.795961","status":"completed"},"tags":[]},"source":["# Heatmap of Movie Ratings\n","- Visualize a heatmap of the movie ratings. This heatmap will contain the first 25 rows and 25 columns as follows "]},{"cell_type":"code","execution_count":19,"id":"463c9c6b","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:26:08.87373Z","iopub.status.busy":"2024-05-16T11:26:08.871947Z","iopub.status.idle":"2024-05-16T11:26:09.072151Z","shell.execute_reply":"2024-05-16T11:26:09.06929Z"},"papermill":{"duration":0.230402,"end_time":"2024-05-16T11:26:09.075573","exception":false,"start_time":"2024-05-16T11:26:08.845171","status":"completed"},"tags":[]},"outputs":[{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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PLR3Rx9Xr8DgB17/4nBZ6rPHrnLp9XoZ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\nAAAAKvH/WCU3W8g6tf8AAAAASUVORK5CYII="},"metadata":{"image/png":{"height":420,"width":420}},"output_type":"display_data"}],"source":["image(ratingMatrix[1:20, 1:25], axes = FALSE, main = \"Heatmap of the first 25 rows and 25 columns\")"]},{"cell_type":"markdown","id":"302bb8b0","metadata":{"papermill":{"duration":0.025028,"end_time":"2024-05-16T11:26:09.12583","exception":false,"start_time":"2024-05-16T11:26:09.100802","status":"completed"},"tags":[]},"source":["# Performing Data Preparation\n","## We will conduct data preparation in the following three steps:\n","\n","- Selecting useful data.\n","- Normalizing data.\n","- Binarizing the data.\n","\n","### For finding useful data in our dataset, we have set the threshold for the minimum number of users who have rated a film as 50. This is also same for minimum number of views that are per film. This way, we have filtered a list of watched films from least-watched ones."]},{"cell_type":"code","execution_count":20,"id":"658190b7","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:26:09.179816Z","iopub.status.busy":"2024-05-16T11:26:09.178092Z","iopub.status.idle":"2024-05-16T11:26:09.212522Z","shell.execute_reply":"2024-05-16T11:26:09.21011Z"},"papermill":{"duration":0.064856,"end_time":"2024-05-16T11:26:09.215802","exception":false,"start_time":"2024-05-16T11:26:09.150946","status":"completed"},"tags":[]},"outputs":[{"data":{"text/plain":["420 x 447 rating matrix of class ‘realRatingMatrix’ with 38341 ratings."]},"metadata":{},"output_type":"display_data"}],"source":["movie_ratings <- ratingMatrix[rowCounts(ratingMatrix) > 50,\n","                             colCounts(ratingMatrix) > 50]\n","movie_ratings"]},{"cell_type":"markdown","id":"5e7951ed","metadata":{"papermill":{"duration":0.02527,"end_time":"2024-05-16T11:26:09.266309","exception":false,"start_time":"2024-05-16T11:26:09.241039","status":"completed"},"tags":[]},"source":["- From the above output of ‘movie_ratings’, we observe that there are 420 users and 447 films as opposed to the previous 668 users and 10325 films."]},{"cell_type":"markdown","id":"d9bf4f3b","metadata":{"papermill":{"duration":0.025763,"end_time":"2024-05-16T11:26:09.317099","exception":false,"start_time":"2024-05-16T11:26:09.291336","status":"completed"},"tags":[]},"source":["###  We can now delineate our matrix of relevant users as follows:"]},{"cell_type":"code","execution_count":21,"id":"957cd9e4","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:26:09.371262Z","iopub.status.busy":"2024-05-16T11:26:09.369616Z","iopub.status.idle":"2024-05-16T11:26:09.594649Z","shell.execute_reply":"2024-05-16T11:26:09.591319Z"},"papermill":{"duration":0.256315,"end_time":"2024-05-16T11:26:09.59852","exception":false,"start_time":"2024-05-16T11:26:09.342205","status":"completed"},"tags":[]},"outputs":[{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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gBwAAIAmCHQAAgCQIdgAAAJIg2AEAAGjClJ2dq+4a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\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UJqfvOETu8xetay0bOWpVw8dzklzcXL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\nAABAJQh2AAAAKkGwAwAAUIn/B2QHuR+aQRMbAAAAAElFTkSuQmCC"},"metadata":{"image/png":{"height":420,"width":420}},"output_type":"display_data"}],"source":["minimum_movies<- quantile(rowCounts(movie_ratings), 0.98)\n","minimum_users <- quantile(colCounts(movie_ratings), 0.98)\n","image(movie_ratings[rowCounts(movie_ratings) > minimum_movies,\n","                     colCounts(movie_ratings) > minimum_users],\n","main = \"Heatmap of the top users and movies\")"]},{"cell_type":"markdown","id":"07f3d3fd","metadata":{"papermill":{"duration":0.026281,"end_time":"2024-05-16T11:26:09.653178","exception":false,"start_time":"2024-05-16T11:26:09.626897","status":"completed"},"tags":[]},"source":["### Visualize the distribution of the average ratings per user:"]},{"cell_type":"code","execution_count":22,"id":"23651b78","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:26:09.711878Z","iopub.status.busy":"2024-05-16T11:26:09.710071Z","iopub.status.idle":"2024-05-16T11:26:10.143409Z","shell.execute_reply":"2024-05-16T11:26:10.140432Z"},"papermill":{"duration":0.46636,"end_time":"2024-05-16T11:26:10.147042","exception":false,"start_time":"2024-05-16T11:26:09.680682","status":"completed"},"tags":[]},"outputs":[{"name":"stderr","output_type":"stream","text":["Warning message:\n","“\u001b[1m\u001b[22m`qplot()` was deprecated in ggplot2 3.4.0.”\n","\u001b[1m\u001b[22m`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"]},{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nN/j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Ag7AIBICDsAgEgIOwCASAg7AIBI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\nJ6Ldm0xEagAAAABJRU5ErkJggg=="},"metadata":{"image/png":{"height":420,"width":420}},"output_type":"display_data"}],"source":["average_ratings <- rowMeans(movie_ratings)\n","qplot(average_ratings, fill=I(\"steelblue\"), col=I(\"red\")) +\n","  ggtitle(\"Distribution of the average rating per user\")"]},{"cell_type":"markdown","id":"8356955f","metadata":{"papermill":{"duration":0.02677,"end_time":"2024-05-16T11:26:10.200883","exception":false,"start_time":"2024-05-16T11:26:10.174113","status":"completed"},"tags":[]},"source":["# Data Normalization\n","- In the case of some users, there can be high ratings or low ratings provided to all of the watched films. This will act as a bias while implementing our model. In order to remove this, we normalize our data. Normalization is a data preparation procedure to standardize the numerical values in a column to a common scale value. This is done in such a way that there is no distortion in the range of values. Normalization transforms the average value of our rating column to 0. We then plot a heatmap that delineates our normalized ratings."]},{"cell_type":"code","execution_count":23,"id":"4d1cac52","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:26:10.257988Z","iopub.status.busy":"2024-05-16T11:26:10.256275Z","iopub.status.idle":"2024-05-16T11:26:10.431947Z","shell.execute_reply":"2024-05-16T11:26:10.429117Z"},"papermill":{"duration":0.207816,"end_time":"2024-05-16T11:26:10.435377","exception":false,"start_time":"2024-05-16T11:26:10.227561","status":"completed"},"tags":[]},"outputs":[{"data":{"text/html":["0"],"text/latex":["0"],"text/markdown":["0"],"text/plain":["[1] 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Ah2AAAAkiDYAQAASIJgBwAAIAmCHQAAgCQIdgAAAJIg2AEAAEiCYAcAACAJ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\nYII="},"metadata":{"image/png":{"height":420,"width":420}},"output_type":"display_data"}],"source":["normalized_ratings <- normalize(movie_ratings)\n","sum(rowMeans(normalized_ratings) > 0.00001)\n","image(normalized_ratings[rowCounts(normalized_ratings) > minimum_movies,\n","                          colCounts(normalized_ratings) > minimum_users],\n","main = \"Normalized Ratings of the Top Users\")"]},{"cell_type":"markdown","id":"6a23630d","metadata":{"papermill":{"duration":0.027341,"end_time":"2024-05-16T11:26:10.490164","exception":false,"start_time":"2024-05-16T11:26:10.462823","status":"completed"},"tags":[]},"source":["# Performing Data Binarization\n","- Binarizing the data means that we have two discrete values 1 and 0, which will allow our recommendation systems to work more efficiently. We will define a matrix that will consist of 1 if the rating is above 3 otherwise it will be 0."]},{"cell_type":"code","execution_count":24,"id":"1268c3cc","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:26:10.549504Z","iopub.status.busy":"2024-05-16T11:26:10.547344Z","iopub.status.idle":"2024-05-16T11:26:10.745093Z","shell.execute_reply":"2024-05-16T11:26:10.742764Z"},"papermill":{"duration":0.230507,"end_time":"2024-05-16T11:26:10.74812","exception":false,"start_time":"2024-05-16T11:26:10.517613","status":"completed"},"tags":[]},"outputs":[{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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Z2xKywsNGROAACgnAkTJkybNi3qVWlpaaNH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\nAAAA8MT/Adn5ws4y7QAaAAAAAElFTkSuQmCC"},"metadata":{"image/png":{"height":420,"width":420}},"output_type":"display_data"}],"source":["binary_minimum_movies <- quantile(rowCounts(movie_ratings), 0.95)\n","binary_minimum_users <- quantile(colCounts(movie_ratings), 0.95)\n","#movies_watched <- binarize(movie_ratings, minRating = 1)\n","good_rated_films <- binarize(movie_ratings, minRating = 3)\n","image(good_rated_films[rowCounts(movie_ratings) > binary_minimum_movies,\n","colCounts(movie_ratings) > binary_minimum_users],\n","main = \"Heatmap of the top users and movies\")"]},{"cell_type":"markdown","id":"36caf68e","metadata":{"papermill":{"duration":0.028656,"end_time":"2024-05-16T11:26:10.806606","exception":false,"start_time":"2024-05-16T11:26:10.77795","status":"completed"},"tags":[]},"source":["# Collaborative Filtering System\n","- In this section of the project, we will develop our very own Item Based Collaborative Filtering System. This type of collaborative filtering finds similarity in the items based on the people’s ratings of them. The algorithm first builds a similar-items table of the customers who have purchased them into a combination of similar items. This is then fed into the recommendation system.\n","\n","- The similarity between single products and related products can be determined with the following algorithm:\n","    - For each Item i1 present in the product catalog, purchased by customer C.\n","    - And, for each item, i2 was also purchased by customer C.\n","    - Create a record that the customer purchased items i1 and i2.\n","    - Calculate the similarity between i1 and i2.\n","\n","- We will build this filtering system by splitting the dataset into an 80% training set and a 20% test set."]},{"cell_type":"code","execution_count":25,"id":"1d18e3e3","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:26:10.871473Z","iopub.status.busy":"2024-05-16T11:26:10.869283Z","iopub.status.idle":"2024-05-16T11:26:10.912309Z","shell.execute_reply":"2024-05-16T11:26:10.910104Z"},"papermill":{"duration":0.080355,"end_time":"2024-05-16T11:26:10.916551","exception":false,"start_time":"2024-05-16T11:26:10.836196","status":"completed"},"tags":[]},"outputs":[],"source":["sampled_data<- sample(x = c(TRUE, FALSE),\n","                      size = nrow(movie_ratings),\n","                      replace = TRUE,\n","                      prob = c(0.8, 0.2))\n","training_data <- movie_ratings[sampled_data, ]\n","testing_data <- movie_ratings[!sampled_data, ]"]},{"cell_type":"markdown","id":"2e76968c","metadata":{"papermill":{"duration":0.031129,"end_time":"2024-05-16T11:26:10.977475","exception":false,"start_time":"2024-05-16T11:26:10.946346","status":"completed"},"tags":[]},"source":["# Building the Recommendation System\n","- We will now explore the various parameters of our Item Based Collaborative Filter. These parameters are default in nature. In the first step, k denotes the number of items for computing their similarities. Here, k is equal to 30. Therefore, the algorithm will now identify the k most similar items and store their number. We use the cosine method which is the default one but you can also use the Pearson method."]},{"cell_type":"code","execution_count":26,"id":"ff84ab9f","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:26:11.044208Z","iopub.status.busy":"2024-05-16T11:26:11.041957Z","iopub.status.idle":"2024-05-16T11:26:11.072343Z","shell.execute_reply":"2024-05-16T11:26:11.069295Z"},"papermill":{"duration":0.066643,"end_time":"2024-05-16T11:26:11.07588","exception":false,"start_time":"2024-05-16T11:26:11.009237","status":"completed"},"tags":[]},"outputs":[{"data":{"text/html":["<dl>\n","\t<dt>$k</dt>\n","\t\t<dd>30</dd>\n","\t<dt>$method</dt>\n","\t\t<dd>'cosine'</dd>\n","\t<dt>$normalize</dt>\n","\t\t<dd>'center'</dd>\n","\t<dt>$normalize_sim_matrix</dt>\n","\t\t<dd>FALSE</dd>\n","\t<dt>$alpha</dt>\n","\t\t<dd>0.5</dd>\n","\t<dt>$na_as_zero</dt>\n","\t\t<dd>FALSE</dd>\n","</dl>\n"],"text/latex":["\\begin{description}\n","\\item[\\$k] 30\n","\\item[\\$method] 'cosine'\n","\\item[\\$normalize] 'center'\n","\\item[\\$normalize\\_sim\\_matrix] FALSE\n","\\item[\\$alpha] 0.5\n","\\item[\\$na\\_as\\_zero] FALSE\n","\\end{description}\n"],"text/markdown":["$k\n",":   30\n","$method\n",":   'cosine'\n","$normalize\n",":   'center'\n","$normalize_sim_matrix\n",":   FALSE\n","$alpha\n",":   0.5\n","$na_as_zero\n",":   FALSE\n","\n","\n"],"text/plain":["$k\n","[1] 30\n","\n","$method\n","[1] \"cosine\"\n","\n","$normalize\n","[1] \"center\"\n","\n","$normalize_sim_matrix\n","[1] FALSE\n","\n","$alpha\n","[1] 0.5\n","\n","$na_as_zero\n","[1] FALSE\n"]},"metadata":{},"output_type":"display_data"}],"source":["recommendation_system <- recommenderRegistry$get_entries(dataType =\"realRatingMatrix\")\n","recommendation_system$IBCF_realRatingMatrix$parameters"]},{"cell_type":"code","execution_count":27,"id":"2646e25a","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:26:11.139574Z","iopub.status.busy":"2024-05-16T11:26:11.137444Z","iopub.status.idle":"2024-05-16T11:26:11.436923Z","shell.execute_reply":"2024-05-16T11:26:11.434362Z"},"papermill":{"duration":0.33469,"end_time":"2024-05-16T11:26:11.440043","exception":false,"start_time":"2024-05-16T11:26:11.105353","status":"completed"},"tags":[]},"outputs":[{"data":{"text/plain":["Recommender of type ‘IBCF’ for ‘realRatingMatrix’ \n","learned using 345 users."]},"metadata":{},"output_type":"display_data"}],"source":["recommen_model <- Recommender(data = training_data,\n","                          method = \"IBCF\",\n","                          parameter = list(k = 30))\n","recommen_model"]},{"cell_type":"code","execution_count":28,"id":"311f1886","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:26:11.502008Z","iopub.status.busy":"2024-05-16T11:26:11.500203Z","iopub.status.idle":"2024-05-16T11:26:11.521011Z","shell.execute_reply":"2024-05-16T11:26:11.518266Z"},"papermill":{"duration":0.055434,"end_time":"2024-05-16T11:26:11.524519","exception":false,"start_time":"2024-05-16T11:26:11.469085","status":"completed"},"tags":[]},"outputs":[{"data":{"text/html":["'Recommender'"],"text/latex":["'Recommender'"],"text/markdown":["'Recommender'"],"text/plain":["[1] \"Recommender\"\n","attr(,\"package\")\n","[1] \"recommenderlab\""]},"metadata":{},"output_type":"display_data"}],"source":["class(recommen_model)"]},{"cell_type":"markdown","id":"f691e379","metadata":{"papermill":{"duration":0.030289,"end_time":"2024-05-16T11:26:11.584493","exception":false,"start_time":"2024-05-16T11:26:11.554204","status":"completed"},"tags":[]},"source":["### Now explore our data science recommendation system model as follows:\n","\n","- Using the getModel() function, we will retrieve the recommen_model. We will then find the class and dimensions of our similarity matrix that is contained within model_info. Finally, we will generate a heatmap, that will contain the top 20 items and visualize the similarity shared between them."]},{"cell_type":"code","execution_count":29,"id":"c301be04","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:26:11.651433Z","iopub.status.busy":"2024-05-16T11:26:11.649569Z","iopub.status.idle":"2024-05-16T11:26:11.808079Z","shell.execute_reply":"2024-05-16T11:26:11.804195Z"},"papermill":{"duration":0.196972,"end_time":"2024-05-16T11:26:11.812254","exception":false,"start_time":"2024-05-16T11:26:11.615282","status":"completed"},"tags":[]},"outputs":[{"data":{"text/html":["'dgCMatrix'"],"text/latex":["'dgCMatrix'"],"text/markdown":["'dgCMatrix'"],"text/plain":["[1] \"dgCMatrix\"\n","attr(,\"package\")\n","[1] \"Matrix\""]},"metadata":{},"output_type":"display_data"},{"data":{"text/html":["<style>\n",".list-inline {list-style: none; margin:0; padding: 0}\n",".list-inline>li {display: inline-block}\n",".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n","</style>\n","<ol class=list-inline><li>447</li><li>447</li></ol>\n"],"text/latex":["\\begin{enumerate*}\n","\\item 447\n","\\item 447\n","\\end{enumerate*}\n"],"text/markdown":["1. 447\n","2. 447\n","\n","\n"],"text/plain":["[1] 447 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AIiHYAQBEQrADAIiEYAcAEAnBDgAgEoIdAEAkBDsAgEgIdgAAkRDsAAAiIdgB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\nAAAAAElFTkSuQmCC"},"metadata":{"image/png":{"height":420,"width":420}},"output_type":"display_data"}],"source":["model_info <- getModel(recommen_model)\n","class(model_info$sim)\n","dim(model_info$sim)\n","top_items <- 20\n","image(model_info$sim[1:top_items, 1:top_items],\n","   main = \"Heatmap of the first rows and columns\")"]},{"cell_type":"markdown","id":"d88e51a0","metadata":{"papermill":{"duration":0.032378,"end_time":"2024-05-16T11:26:11.876668","exception":false,"start_time":"2024-05-16T11:26:11.84429","status":"completed"},"tags":[]},"source":["### In the next step of ML project, we will carry out the sum of rows and columns with the similarity of the objects above 0. We will visualize the sum of columns through a distribution as follows:"]},{"cell_type":"markdown","id":"e7e61920","metadata":{"papermill":{"duration":0.030649,"end_time":"2024-05-16T11:26:11.938142","exception":false,"start_time":"2024-05-16T11:26:11.907493","status":"completed"},"tags":[]},"source":["# Distribution of the column count"]},{"cell_type":"code","execution_count":30,"id":"c271904c","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:26:12.007123Z","iopub.status.busy":"2024-05-16T11:26:12.004263Z","iopub.status.idle":"2024-05-16T11:26:12.37614Z","shell.execute_reply":"2024-05-16T11:26:12.372858Z"},"papermill":{"duration":0.411234,"end_time":"2024-05-16T11:26:12.379854","exception":false,"start_time":"2024-05-16T11:26:11.96862","status":"completed"},"tags":[]},"outputs":[{"data":{"text/plain":["sum_rows\n"," 30 \n","447 "]},"metadata":{},"output_type":"display_data"},{"name":"stderr","output_type":"stream","text":["\u001b[1m\u001b[22m`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"]},{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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"},"metadata":{"image/png":{"height":420,"width":420}},"output_type":"display_data"}],"source":["sum_rows <- rowSums(model_info$sim > 0)\n","table(sum_rows)\n","sum_cols <- colSums(model_info$sim > 0)\n","qplot(sum_cols, fill=I(\"steelblue\"), col=I(\"red\"))+ ggtitle(\"Distribution of the column count\")"]},{"cell_type":"markdown","id":"7fda4b57","metadata":{"papermill":{"duration":0.032595,"end_time":"2024-05-16T11:26:12.444709","exception":false,"start_time":"2024-05-16T11:26:12.412114","status":"completed"},"tags":[]},"source":["# Build Recommender System on the dataset\n","- We will create a top_recommendations variable which will be initialized to 10, specifying the number of films to each user. We will then use the predict() function that will identify similar items and will rank them appropriately. Here, each rating is used as a weight. Each weight is multiplied with related similarities. Finally, everything is added in the end.:"]},{"cell_type":"code","execution_count":31,"id":"5cea91fb","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:26:12.512408Z","iopub.status.busy":"2024-05-16T11:26:12.510764Z","iopub.status.idle":"2024-05-16T11:26:12.617477Z","shell.execute_reply":"2024-05-16T11:26:12.615536Z"},"papermill":{"duration":0.14399,"end_time":"2024-05-16T11:26:12.620863","exception":false,"start_time":"2024-05-16T11:26:12.476873","status":"completed"},"tags":[]},"outputs":[{"data":{"text/plain":["Recommendations as ‘topNList’ with n = 10 for 75 users. "]},"metadata":{},"output_type":"display_data"}],"source":["top_recommendations <- 10 # the number of items to recommend to each user\n","predicted_recommendations <- predict(object = recommen_model,\n","                          newdata = testing_data,\n","                          n = top_recommendations)\n","predicted_recommendations"]},{"cell_type":"code","execution_count":32,"id":"e8259c83","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:26:12.689645Z","iopub.status.busy":"2024-05-16T11:26:12.688007Z","iopub.status.idle":"2024-05-16T11:26:12.759615Z","shell.execute_reply":"2024-05-16T11:26:12.756939Z"},"papermill":{"duration":0.109467,"end_time":"2024-05-16T11:26:12.763081","exception":false,"start_time":"2024-05-16T11:26:12.653614","status":"completed"},"tags":[]},"outputs":[{"data":{"text/html":["<style>\n",".list-inline {list-style: none; margin:0; padding: 0}\n",".list-inline>li {display: inline-block}\n",".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n","</style>\n","<ol class=list-inline><li>'English Patient, The (1996)'</li><li>'Edward Scissorhands (1990)'</li><li>'Pan\\'s Labyrinth (Laberinto del fauno, El) (2006)'</li><li>'WALL·E (2008)'</li><li>'To Kill a Mockingbird (1962)'</li><li>'Amadeus (1984)'</li><li>'Wizard of Oz, The (1939)'</li><li>'Monty Python\\'s Life of Brian (1979)'</li><li>'Dr. Strangelove or: How I Learned to Stop Worrying and Love the Bomb (1964)'</li><li>'Psycho (1960)'</li></ol>\n"],"text/latex":["\\begin{enumerate*}\n","\\item 'English Patient, The (1996)'\n","\\item 'Edward Scissorhands (1990)'\n","\\item 'Pan\\textbackslash{}'s Labyrinth (Laberinto del fauno, El) (2006)'\n","\\item 'WALL·E (2008)'\n","\\item 'To Kill a Mockingbird (1962)'\n","\\item 'Amadeus (1984)'\n","\\item 'Wizard of Oz, The (1939)'\n","\\item 'Monty Python\\textbackslash{}'s Life of Brian (1979)'\n","\\item 'Dr. Strangelove or: How I Learned to Stop Worrying and Love the Bomb (1964)'\n","\\item 'Psycho (1960)'\n","\\end{enumerate*}\n"],"text/markdown":["1. 'English Patient, The (1996)'\n","2. 'Edward Scissorhands (1990)'\n","3. 'Pan\\'s Labyrinth (Laberinto del fauno, El) (2006)'\n","4. 'WALL·E (2008)'\n","5. 'To Kill a Mockingbird (1962)'\n","6. 'Amadeus (1984)'\n","7. 'Wizard of Oz, The (1939)'\n","8. 'Monty Python\\'s Life of Brian (1979)'\n","9. 'Dr. Strangelove or: How I Learned to Stop Worrying and Love the Bomb (1964)'\n","10. 'Psycho (1960)'\n","\n","\n"],"text/plain":[" [1] \"English Patient, The (1996)\"                                                \n"," [2] \"Edward Scissorhands (1990)\"                                                 \n"," [3] \"Pan's Labyrinth (Laberinto del fauno, El) (2006)\"                           \n"," [4] \"WALL·E (2008)\"                                                              \n"," [5] \"To Kill a Mockingbird (1962)\"                                               \n"," [6] \"Amadeus (1984)\"                                                             \n"," [7] \"Wizard of Oz, The (1939)\"                                                   \n"," [8] \"Monty Python's Life of Brian (1979)\"                                        \n"," [9] \"Dr. Strangelove or: How I Learned to Stop Worrying and Love the Bomb (1964)\"\n","[10] \"Psycho (1960)\"                                                              "]},"metadata":{},"output_type":"display_data"}],"source":["user1 <- predicted_recommendations@items[[1]] # recommendation for the first user\n","movies_user1 <- predicted_recommendations@itemLabels[user1]\n","movies_user2 <- movies_user1\n","for (index in 1:10){\n","  movies_user2[index] <- as.character(subset(movie_data,\n","                                         movie_data$movieId == movies_user1[index])$title)\n","}\n","movies_user2"]},{"cell_type":"code","execution_count":33,"id":"b8700528","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:26:12.83093Z","iopub.status.busy":"2024-05-16T11:26:12.829186Z","iopub.status.idle":"2024-05-16T11:26:12.863228Z","shell.execute_reply":"2024-05-16T11:26:12.860331Z"},"papermill":{"duration":0.071497,"end_time":"2024-05-16T11:26:12.86653","exception":false,"start_time":"2024-05-16T11:26:12.795033","status":"completed"},"tags":[]},"outputs":[{"data":{"text/html":["<table class=\"dataframe\">\n","<caption>A matrix: 10 × 4 of type int</caption>\n","<thead>\n","\t<tr><th scope=col>0</th><th scope=col>1</th><th scope=col>2</th><th scope=col>3</th></tr>\n","</thead>\n","<tbody>\n","\t<tr><td> 1183</td><td>  5</td><td> 300</td><td> 1206</td></tr>\n","\t<tr><td> 2291</td><td> 36</td><td> 474</td><td>48774</td></tr>\n","\t<tr><td>48394</td><td>160</td><td> 497</td><td> 7438</td></tr>\n","\t<tr><td>60069</td><td>235</td><td> 508</td><td> 6874</td></tr>\n","\t<tr><td> 1207</td><td>261</td><td> 529</td><td> 1263</td></tr>\n","\t<tr><td> 1225</td><td>266</td><td> 551</td><td> 1213</td></tr>\n","\t<tr><td>  919</td><td>288</td><td> 745</td><td>  111</td></tr>\n","\t<tr><td> 1080</td><td>357</td><td> 913</td><td>  551</td></tr>\n","\t<tr><td>  750</td><td>364</td><td> 924</td><td>  594</td></tr>\n","\t<tr><td> 1219</td><td>440</td><td>1036</td><td>  920</td></tr>\n","</tbody>\n","</table>\n"],"text/latex":["A matrix: 10 × 4 of type int\n","\\begin{tabular}{llll}\n"," 0 & 1 & 2 & 3\\\\\n","\\hline\n","\t  1183 &   5 &  300 &  1206\\\\\n","\t  2291 &  36 &  474 & 48774\\\\\n","\t 48394 & 160 &  497 &  7438\\\\\n","\t 60069 & 235 &  508 &  6874\\\\\n","\t  1207 & 261 &  529 &  1263\\\\\n","\t  1225 & 266 &  551 &  1213\\\\\n","\t   919 & 288 &  745 &   111\\\\\n","\t  1080 & 357 &  913 &   551\\\\\n","\t   750 & 364 &  924 &   594\\\\\n","\t  1219 & 440 & 1036 &   920\\\\\n","\\end{tabular}\n"],"text/markdown":["\n","A matrix: 10 × 4 of type int\n","\n","| 0 | 1 | 2 | 3 |\n","|---|---|---|---|\n","|  1183 |   5 |  300 |  1206 |\n","|  2291 |  36 |  474 | 48774 |\n","| 48394 | 160 |  497 |  7438 |\n","| 60069 | 235 |  508 |  6874 |\n","|  1207 | 261 |  529 |  1263 |\n","|  1225 | 266 |  551 |  1213 |\n","|   919 | 288 |  745 |   111 |\n","|  1080 | 357 |  913 |   551 |\n","|   750 | 364 |  924 |   594 |\n","|  1219 | 440 | 1036 |   920 |\n","\n"],"text/plain":["      0     1   2    3    \n"," [1,]  1183   5  300  1206\n"," [2,]  2291  36  474 48774\n"," [3,] 48394 160  497  7438\n"," [4,] 60069 235  508  6874\n"," [5,]  1207 261  529  1263\n"," [6,]  1225 266  551  1213\n"," [7,]   919 288  745   111\n"," [8,]  1080 357  913   551\n"," [9,]   750 364  924   594\n","[10,]  1219 440 1036   920"]},"metadata":{},"output_type":"display_data"}],"source":["recommendation_matrix <- sapply(predicted_recommendations@items,\n","                      function(x){ as.integer(colnames(movie_ratings)[x]) }) # matrix with the recommendations for each user\n","#dim(recc_matrix)\n","recommendation_matrix[,1:4]"]},{"cell_type":"markdown","id":"56126149","metadata":{"papermill":{"duration":0.03203,"end_time":"2024-05-16T11:26:12.930739","exception":false,"start_time":"2024-05-16T11:26:12.898709","status":"completed"},"tags":[]},"source":["# Distribution of the Number of Items for IBCF"]},{"cell_type":"code","execution_count":34,"id":"424f98f2","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:26:12.998893Z","iopub.status.busy":"2024-05-16T11:26:12.997165Z","iopub.status.idle":"2024-05-16T11:26:13.314978Z","shell.execute_reply":"2024-05-16T11:26:13.31294Z"},"papermill":{"duration":0.354884,"end_time":"2024-05-16T11:26:13.317818","exception":false,"start_time":"2024-05-16T11:26:12.962934","status":"completed"},"tags":[]},"outputs":[{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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UCy644IADDhh7Hw0NUzZ+LTQ0NMyaNavGO+3u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\nCX1PXPfNx/rqORIAwIxVz7DLP3/jXwdL+++/aeVgY+der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CRRcct3Ju7etXnFy3JmO0u76eFxw21o+RC7Gj6rllVvTNgSFaxgi7v39wn0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\nEEI6Ags7hBBCCCEdgYUdQgghhJCO+B9pDYXHaLb3pAAAAABJRU5ErkJggg=="},"metadata":{"image/png":{"height":420,"width":420}},"output_type":"display_data"}],"source":["number_of_items <- factor(table(recommendation_matrix))\n","\n","chart_title <- \"Distribution of the Number of Items for IBCF\"\n","\n","qplot(number_of_items, fill=I(\"steelblue\"), col=I(\"red\")) + ggtitle(chart_title)"]},{"cell_type":"markdown","id":"f51653ef","metadata":{"papermill":{"duration":0.035207,"end_time":"2024-05-16T11:26:13.389571","exception":false,"start_time":"2024-05-16T11:26:13.354364","status":"completed"},"tags":[]},"source":["# Movie Title, No. of Items"]},{"cell_type":"code","execution_count":35,"id":"409a5874","metadata":{"execution":{"iopub.execute_input":"2024-05-16T11:26:13.46723Z","iopub.status.busy":"2024-05-16T11:26:13.46516Z","iopub.status.idle":"2024-05-16T11:26:13.532904Z","shell.execute_reply":"2024-05-16T11:26:13.530409Z"},"papermill":{"duration":0.108572,"end_time":"2024-05-16T11:26:13.536344","exception":false,"start_time":"2024-05-16T11:26:13.427772","status":"completed"},"tags":[]},"outputs":[{"data":{"text/html":["<table class=\"dataframe\">\n","<caption>A data.frame: 4 × 2</caption>\n","<thead>\n","\t<tr><th></th><th scope=col>Movie Title</th><th scope=col>No. of Items</th></tr>\n","\t<tr><th></th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;fct&gt;</th></tr>\n","</thead>\n","<tbody>\n","\t<tr><th scope=row>529</th><td>Searching for Bobby Fischer (1993)</td><td>14</td></tr>\n","\t<tr><th scope=row>16</th><td>Casino (1995)                     </td><td>11</td></tr>\n","\t<tr><th scope=row>508</th><td>Philadelphia (1993)               </td><td>9 </td></tr>\n","\t<tr><th scope=row>1203</th><td>12 Angry Men (1957)               </td><td>9 </td></tr>\n","</tbody>\n","</table>\n"],"text/latex":["A data.frame: 4 × 2\n","\\begin{tabular}{r|ll}\n","  & Movie Title & No. of Items\\\\\n","  & <chr> & <fct>\\\\\n","\\hline\n","\t529 & Searching for Bobby Fischer (1993) & 14\\\\\n","\t16 & Casino (1995)                      & 11\\\\\n","\t508 & Philadelphia (1993)                & 9 \\\\\n","\t1203 & 12 Angry Men (1957)                & 9 \\\\\n","\\end{tabular}\n"],"text/markdown":["\n","A data.frame: 4 × 2\n","\n","| <!--/--> | Movie Title &lt;chr&gt; | No. of Items &lt;fct&gt; |\n","|---|---|---|\n","| 529 | Searching for Bobby Fischer (1993) | 14 |\n","| 16 | Casino (1995)                      | 11 |\n","| 508 | Philadelphia (1993)                | 9  |\n","| 1203 | 12 Angry Men (1957)                | 9  |\n","\n"],"text/plain":["     Movie Title                        No. of Items\n","529  Searching for Bobby Fischer (1993) 14          \n","16   Casino (1995)                      11          \n","508  Philadelphia (1993)                9           \n","1203 12 Angry Men (1957)                9           "]},"metadata":{},"output_type":"display_data"}],"source":["number_of_items_sorted <- sort(number_of_items, decreasing = TRUE)\n","number_of_items_top <- head(number_of_items_sorted, n = 4)\n","table_top <- data.frame(as.integer(names(number_of_items_top)),\n","number_of_items_top)\n","for(i in 1:4) {\n","table_top[i,1] <- as.character(subset(movie_data,\n","movie_data$movieId == table_top[i,1])$title)\n","}\n","\n","colnames(table_top) <- c(\"Movie Title\", \"No. of Items\")\n","head(table_top)"]}],"metadata":{"kaggle":{"accelerator":"none","dataSources":[{"datasetId":2841880,"sourceId":4900517,"sourceType":"datasetVersion"},{"datasetId":2842023,"sourceId":4900737,"sourceType":"datasetVersion"}],"dockerImageVersionId":30372,"isGpuEnabled":false,"isInternetEnabled":true,"language":"r","sourceType":"notebook"},"kernelspec":{"display_name":"R","language":"R","name":"ir"},"language_info":{"codemirror_mode":"r","file_extension":".r","mimetype":"text/x-r-source","name":"R","pygments_lexer":"r","version":"4.0.5"},"papermill":{"default_parameters":{},"duration":59.058816,"end_time":"2024-05-16T11:26:13.696257","environment_variables":{},"exception":null,"input_path":"__notebook__.ipynb","output_path":"__notebook__.ipynb","parameters":{},"start_time":"2024-05-16T11:25:14.637441","version":"2.4.0"}},"nbformat":4,"nbformat_minor":5}