kmeans.py

import numpy as np
import matplotlib.pyplot as plt

np.random.seed(42)


def euclidean_distance(x1, x2):
    return np.sqrt(np.dot(x1 - x2, x1 - x2))


class KMeans:
    def __init__(self, K=5, max_iters=100, plot_steps=False):
        self.K = K
        self.max_iters = max_iters
        self.plot_steps = plot_steps

        # list of sample indices for each cluster
        self.clusters = [[] for _ in range(self.K)]

        # Mean feature vector for each cluster
        self.centroids = []

    def predict(self, X):
        self.X = X
        self.num_samples, self.num_features = X.shape

        # initialize our centroids
        random_sample_indices = np.random.choice(
            self.num_samples, self.K, replace=False
        )
        self.centroids = [self.X[idx] for idx in random_sample_indices]
        # optimization
        for _ in range(self.max_iters):
            # update clusters
            self.clusters = self._create_clusters(self.centroids)
            if self.plot_steps: self.plot()

            # update centroids
            centroids_old = self.centroids
            self.centroids = self._get_centroids(self.clusters)
            if self.plot_steps: self.plot() 

            # check convergence
            if self._is_converged(centroids_old, self.centroids):
                break

        return self._get_cluster_labels(self.clusters)

    def _get_cluster_labels(self, clusters):
        labels = np.empty(self.num_samples)
        for cluster_idx, cluster in enumerate(clusters):
            for sample_idx in cluster:
                labels[sample_idx] = cluster_idx
        return labels

    def _create_clusters(self, centroids):
        clusters = [[] for _ in range(self.K)]

        for idx, sample in enumerate(self.X):
            centroid_idx = self._closest_centroid(sample, centroids)
            clusters[centroid_idx].append(idx)
        return clusters

    def _closest_centroid(self, sample, centroids):
        distances = [euclidean_distance(sample, point) for point in centroids]
        closest_idx = np.argmin(distances)
        return closest_idx

    def _get_centroids(self, clusters):
        centroids = np.zeros((self.K, self.num_features))
        for cluster_idx, cluster in enumerate(clusters):
            cluster_mean = np.mean(self.X[cluster], axis=0)
            centroids[cluster_idx] = cluster_mean
        return centroids

    def _is_converged(self, old_centroids, new_centroids):
        distances = [
            euclidean_distance(old_centroids[i], new_centroids[i])
            for i in range(self.K)
        ]
        return sum(distances) == 0

    def plot(self):
        fig, ax = plt.subplots(figsize=(12,8))

        for i, index in enumerate(self.clusters):
            point = self.X[index].T
            ax.scatter(*point)

        for point in self.centroids:
            ax.scatter(*point, marker='x', color='black', linewidths=2)

        plt.show()