Download the starter code for this assignment. Then, extract (unzip) the contents anywhere on your computer. In VSCode, navigate to File | Open Folder and select the homework4 folder. Inside the homework4 folder you’ll find a number of folders and files:

The folders:

• data: a directory containing the data your program needs
• results: a directory where your plots will be automatically saved

Python files:

• analysis.py: where you’ll do your analysis for part 2
• answers.txt: where you’ll write your answers for questions in part 2
• kmeans.py: where you’ll write your k-means clustering algorithm for parts 1 and 2
• test_kmeans.py: program to test kmeans.py
• test_analysis.py: code to test analysis.py
• utils.py: helper code for the assignment

Part 1: Implementing K-means clustering

In Part 1, you will design and implement a k-means clustering algorithm. You only need to modify kmeans.py for Part 1. Below is an overview of the data structures data and centroids, which you will need to work with in order to implement the algorithm:

data: A list of data points, where each data point is a list of floats.

Example: data = [[0.34, -0.2, 1.13, 4.3], [5.1, -12.6, -7.0, 1.9], [-15.7, 0.06, -7.1, 11.2]] Here, data contains three data points, where each data point is four-dimensional. In this example, point 1 is [0.34, -0.2, 1.13, 4.3], point 2 is [5.1, -12.6, -7.0, 1.9] and point 3 is [-15.7, 0.06, -7.1, 11.2].

centroids: A dictionary of centroids, where the keys are strings (centroid names) and the values are lists (centroid locations).

Example: centroids = {"centroid1": [1.1, 0.2, -3.1, -0.4], "centroid2": [9.3, 6.1, -4.7, 0.18]}. Here, centroids contain two key-value pairs. You should NOT change the names of the centroids when you later update their locations.

We have provided several test functions that you should use to check your implementation as you go through the assignment. To run the tests, open the terminal (Terminal | New Terminal or control-`) and paste in python test_kmeans.py then press enter/return.

You will only be working in kmeans.py for Part 1. Here is a brief overview of the steps, which are described below:

1. Implement euclidean_distance(), which will calculate the distance between two points.
2. Implement get_closest_centroid(), which allows you to find the closest centroid for a point.
3. Implement assign_points_to_centroids(), which sets the centroid assignment for a point.
4. Implement mean_of_points(), which calculates the mean of a list of points. Also, implement update_centroids(), which will update all of the centroids to the new mean of the points assigned to them.
5. Run the entire algorithm!
6. Check code quality
7. Submit your work!

Calculating Euclidean distances¶

Implement euclidean_distance() using the euclidean distance formula to calculate the distance between two points:

def euclidean_distance(point1, point2):
    """
    Calculate the Euclidean distance between two data points.

    Arguments:
        point1: a non-empty list of floats representing a data point
        point2: a non-empty list of floats representing a data point

    Returns: the Euclidean distance between two data points

    Example:
        Code:
            point1 = [1.1, 1, 1, 0.5]
            point2 = [4, 3.14, 2, 1]
            print(euclidean_distance(point1, point2))
        Output:
            3.7735394525564456
    """

python test_kmeans.py

You should see the following output once you have correctly implemented euclidean_distance():

test_euclidean_distance passed.

If you receive an error that looks like

Exception: euclidean_distance() returned None; have you implemented it?

You should check your implementation of euclidean distance to make sure it actually returns a valid value. The exception message will change to reflect the next un-implemented function as you progress through the assignment.

Assigning data points to closest centroids¶

Implement get_closest_centroid() to find the closest centroid for a data point:

def get_closest_centroid(point, centroids_dict):
    """
    Given a data point, finds the closest centroid. You should use
    the euclidean_distance function (that you previously implemented).

    Arguments:
        point: a list of floats representing a data point
        centroids_dict: a dictionary representing the centroids where the keys
                        are strings (centroid names) and the values are lists
                        of centroid locations

    Returns: a string as the key name of the closest centroid to the data point

    Example:
        Code:
            point = [0, 0, 0, 0]
            centroids_dict = {"centroid1": [1, 1, 1, 1],
                            "centroid2": [2, 2, 2, 2]}
            print(get_closest_centroid(point, centroids_dict))
        Output:
            centroid1
    """

You should see the following output once you have correctly implemented get_closest_centroid():

test_closest_centroid passed.

Again, you will also see an error message for the next test, as you have not implemented those functions yet.

Update assignment of points to centroids¶

Implement assign_points_to_centroids() to assign data points to their closest centroid:

def assign_points_to_centroids(list_of_points, centroids_dict):
    """
    Assign all data points to the closest centroids. You should use
    the get_closest_centroid function (that you previously implemented).

    This function should return a new dictionary, not modify any
    passed in parameters.

    Arguments:
        list_of_points: a list of lists representing all data points
        centroids_dict: a dictionary representing the centroids where the keys
                        are strings (centroid names) and the values are lists
                        of centroid locations

    Returns: a new dictionary whose keys are the centroids' key names and
             values are lists of points that belong to the centroid. If a
             given centroid does not have any data points closest to it,
             do not include the centroid in the returned dictionary

    Example:
        Code:
            list_of_points = [[1.1, 1, 1, 0.5], [4, 3.14, 2, 1], [0, 0, 0, 0]]
            centroids_dict = {"centroid1": [1, 1, 1, 1],
                            "centroid2": [2, 2, 2, 2]}

            print(assign_points_to_centroids(list_of_points, centroids_dict))
        Output:
            {'centroid1': [[1.1, 1, 1, 0.5], [0, 0, 0, 0]],
             'centroid2': [[4, 3.14, 2, 1]]}
    """

If there are no data points assigned to a centroid, then you should not include that centroid in the returned dictionary.

You should see the following output from running test_kmeans.py once you have correctly implemented assign_points_to_centroids():

test_assign_points_to_centroids passed.

Update centroids¶

Implement mean_of_points() to find the average of a cluster:

def mean_of_points(list_of_points):
    """
    Calculate the mean of a given group of data points. You should NOT
    hard-code the dimensionality of the data points).

    Arguments:
        list_of_points: a list of lists representing a group of data points

    Returns: a list of floats as the mean of the given data points

    Example:
        Code:
            list_of_points = [[1.1, 1, 1, 0.5], [4, 3.14, 2, 1], [0, 0, 0, 0]]
            print(mean_of_points(list_of_points))
        Output:
            [1.7, 1.3800000000000001, 1.0, 0.5]
    """

Then, implement the update_centroids() to update the centroid to be the average of the clusters:

def update_centroids(assignment_dict):
    """
    Update centroid locations as the mean of all data points that belong
    to the cluster. You should use the mean_of_points function (that you
    previously implemented).

    This function should return a new dictionary, not modify any
    passed in parameters.

    Arguments:
        assignment_dict: a dictionary whose keys are the centroids' key
                         names and values are lists of points that belong
                         to the centroid. It is the dictionary
                         returned by assign_points_to_centroids function.

    Returns: A new dictionary representing the updated centroids. If a
             given centroid does not have any data points closest to it,
             do not include the centroid in the returned dictionary.

    Example:
        Code:
            assignment_dict = {'centroid1': [[1.1, 1, 1, 0.5], [0, 0, 0, 0]],
                               'centroid2': [[4, 3.14, 2, 1]]}
            print(update_centroids(assignment_dict))
        Output:
          {'centroid1': [0.55, 0.5, 0.5, 0.25],
           'centroid2': [4.0, 3.14, 2.0, 1.0]}
    """

You should see the following output from test_kmeans.py once you have correctly implemented mean_of_points() and update_centroids():

test_mean_of_points passed.
test_update_centroids passed.

At this point, if you completed all parts to the k-means clustering algorithm you should see following output when you run the tests:

Clustering 2D points¶

Now that you have completed all parts needed to run your k-means clustering algorithm, we can now run it on actual data. Below you should see four lines of code that will help to do exactly that. These four will load the 2D data points and the initial centroids we provided in the .csv files. After that, main_2d() will execute the k-means algorithm and write_centroids_tofile() will save the final centroids to a file to save them permanently.

if __name__ == '__main__':
    dataset = '2d'

    data, label = read_data("data/" + dataset + ".csv")
    init_c = load_centroids("data/" + dataset + "_init_centroids.csv")
    final_c = main(data, init_c, dataset)
    write_centroids_with_key(dataset + "final_centroids.csv", final_c)

Now run your program again by typing python kmeans.py in the terminal window. If you are successful, you should see:

K-means converged after 7 steps.

In addition, there should be 7 plots generated, in the results/2D/ folder. If you examine these 7 plots, they should be identical to the steps shown in the the gif shown in the background section of this spec.

Quality¶

Your assignment should pass two checks: flake8 and our code quality guidelines. The code quality guidelines are very thorough.

Submission¶

Submit kmeans.py to Gradescope for Part 1.