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K-Means Clustering in Python - ML From Scratch 12

Implement a K-Means algorithm using only built-in Python modules and numpy, and learn about the math behind this popular ML algorithm.


In this Machine Learning from Scratch Tutorial, we are going to implement a K-Means algorithm using only built-in Python modules and numpy. We will also learn about the concept and the math behind this popular ML algorithm.

All algorithms from this course can be found on GitHub together with example tests.

Implementation

import numpy as np
import matplotlib.pyplot as plt

np.random.seed(42)

def euclidean_distance(x1, x2):
    return np.sqrt(np.sum((x1 - x2)**2))

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)]
        # the centers (mean feature vector) for each cluster
        self.centroids = []

    def predict(self, X):
        self.X = X
        self.n_samples, self.n_features = X.shape

        # initialize 
        random_sample_idxs = np.random.choice(self.n_samples, self.K, replace=False)
        self.centroids = [self.X[idx] for idx in random_sample_idxs]

        # Optimize clusters
        for _ in range(self.max_iters):
            # Assign samples to closest centroids (create clusters)
            self.clusters = self._create_clusters(self.centroids)

            if self.plot_steps:
                self.plot()

            # Calculate new centroids from the clusters
            centroids_old = self.centroids
            self.centroids = self._get_centroids(self.clusters)

            # check if clusters have changed
            if self._is_converged(centroids_old, self.centroids):
                break

            if self.plot_steps:
                self.plot()

        # Classify samples as the index of their clusters
        return self._get_cluster_labels(self.clusters)


    def _get_cluster_labels(self, clusters):
        # each sample will get the label of the cluster it was assigned to
        labels = np.empty(self.n_samples)

        for cluster_idx, cluster in enumerate(clusters):
            for sample_index in cluster:
                labels[sample_index] = cluster_idx
        return labels

    def _create_clusters(self, centroids):
        # Assign the samples to the closest centroids to create clusters
        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):
        # distance of the current sample to each centroid
        distances = [euclidean_distance(sample, point) for point in centroids]
        closest_index = np.argmin(distances)
        return closest_index

    def _get_centroids(self, clusters):
        # assign mean value of clusters to centroids
        centroids = np.zeros((self.K, self.n_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, centroids_old, centroids):
        # distances between each old and new centroids, fol all centroids
        distances = [euclidean_distance(centroids_old[i], 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', linewidth=2)

        plt.show()

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