notebooks/Lec17-LIVE/Lec17-LIVE.ipynb

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    "# Lecture 17 LIVE\n",
    "\n",
    "Topics for Today\n",
    "- Recap on Pandas Dataframes\n",
    "- PCA on the Wine Data Set\n",
    "\n",
    "![wine-glasses](wine-glasses.jpg)"
   ]
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    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "wine_names = ['Class', 'Alcohol', 'Malic acid', 'Ash', 'Alcalinity of ash', 'Magnesium', 'Total phenols', 'Flavanoids', 'Nonflavanoid phenols', 'Proanthocyanins', 'Color intensity', 'Hue', 'OD280/OD315', 'Proline']\n",
    "dataset_url = 'https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data'\n",
    "wine_data = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data', names = wine_names) "
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    "## Checkout the Data\n",
    "\n",
    "Use `wine_data.head()` and `wine_data.shape` to determine the number of samples and features."
   ]
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    "wine_data.shape"
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    "## Drop the Class Column\n",
    "\n",
    "Use `wine_data.drop` to create a new dataframe `data` where the column \"Class\" is removed from `wine_data`"
   ]
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    "## Mean Centering the Data\n",
    "\n",
    "Use the `data.mean()` command to compute `mean` of `data`\n",
    "\n",
    "Define a new dataframe `B=data - mean`"
   ]
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    "## Exploratory Data Analysis\n",
    "\n",
    "Use the `B.corr()` command to find correlations between features.\n",
    "\n",
    "Identify two features that appear strongly correlated.\n",
    "\n",
    "Use the code `B.plot.scatter(x = 'Feature 1', y = 'Feature 2')` to plot those correlated features on a scatter plot."
   ]
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    "## Find Eigenvalues and Eigenvectors\n",
    "\n",
    "Find the eigenvalues and eigenvectors of $\\frac{1}{177}B^T B$"
   ]
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    "## Percent Variation of Data\n",
    "\n",
    "Write a function that takes in an integer `n` and returns the percent variation in the data explained by the first n eigenvalues.\n",
    "\n",
    "What do you believe is the \"true\" dimension of the data?"
   ]
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    "## Use Scikit-Learn's PCA and Plot\n",
    "\n",
    "Use the code\n",
    "```python\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components=2)\n",
    "pca.fit(data)\n",
    "```\n",
    "\n",
    "To run PCA. \n",
    "\n",
    "Run `pca.components_` and `pca.explained_variance_ratio_` to get percent explained data. **Do these agree with the answers from above?**"
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    "### Create New DataFrame from Transformed Data\n",
    "\n",
    "Use the code\n",
    "```python\n",
    "wine_pca = pca.transform(data)\n",
    "wine_pca_df = pd.DataFrame(data = wine_pca, columns = ['PC1', 'PC2'])\n",
    "```\n",
    "\n",
    "To create a new data frame from the transformed data. Use the code above to create a scatter plot of the transformed data."
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    "## 3D Plotting Bonus\n",
    "\n",
    "Re-run the above code with 3 components and use the code below to plot the 3D projection.\n",
    "```python\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "x=wine_pca_df['PC1']\n",
    "y=wine_pca_df['PC2']\n",
    "z=wine_pca_df['PC3']\n",
    "\n",
    "ax.scatter(x,y,z)\n",
    "```"
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