Green Space Design Company Team Assignment

Problem Statement

You have been employed as a data scientist at a green space design company. The company uses aerial images to identify points that do not have good green space. In the dataset, the y coordinates of these images are named feature_1 and their x coordinates are named feature_2. The company plans to deploy 5 teams. Your task is to assign one team to each point in a way that minimizes the travel cost of team members.

Solution Approach

1. Read the dataset which contains the (x, y) coordinates of the points requiring green space design.
2. Calculate the Euclidean distance between all pairs of points to determine the cost of travel between them.
3. Use an optimization algorithm like the Hungarian algorithm to find the optimal assignment of points to the 5 teams that minimizes the total travel cost.
4. Add a feature_team_number column to the dataset with the assigned team numbers.
5. Visualize the team assignments on a map using matplotlib.

Installation and Usage

Use the package manager pip to install the required packages:

pip install numpy pandas matplotlib

Run the code.ipynb script in jupyter notebook to see the solution:

jupyter notebook

This will print the team assignments for each point and show a visualization of the assignments.

Output

The output includes:

1. Python code in code.py implementing the solution

2. A visualization of the team assignments like the image below:

3. The dataset with an added feature_team_number column indicating the team assignment for each point.

Solution Explanation

To solve this task, I used the K-means clustering algorithm to group the points into 5 clusters and assign them to teams. The specific steps taken were:

1. Read the dataset rc_task_2.csv which contains the (x, y) coordinates of the points.

2. Visualize the points on a scatter plot using matplotlib to get an sense of how the points are distributed.

3. Define a kmeans_pp function to initialize the K-means centroids using the kmeans++ algorithm. This chooses good initial centroids that are far from each other.

4. Define a kmeans function to run the K-means clustering algorithm. It takes in the data X, number of clusters K, and maximum number of iterations max_iter. It returns the cluster labels for each point and the final centroid locations.

5. Set a random state for reproducibility and extract the (x, y) coordinates from the dataset into an array X.

6. Run K-means clustering with K=5 and max_iter=100. This groups the points into 5 clusters.

7. Visualize the clustering results on a scatter plot, with each cluster represented by a different color. The final centroid locations are marked with 'x'.

8. Add a label column to the dataset indicating the assigned cluster (team) for each point.

9. Export the updated dataset to rc_task_2_labeled.csv.

10. The end result is assigning each point to 1 of 5 teams (clusters) such that the total distance between points in each team is minimized. The team assignments are visualized and provided in the exported dataset.