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| from sklearn.metrics import silhouette_samples | |
| from sklearn.cluster import KMeans | |
| import matplotlib.pyplot as plt | |
| import numpy as np | |
| ## quantification of clustering quality via silhouette metric | |
| def quantification_clustering_quality(X:np.array, y_km:np.array, verbose:bool = False)->np.array: | |
| """ | |
| Quantification of clustering quality via silhouette metric. | |
| X -- Array of features used to estimate the clustering. | |
| y_km -- Labels returned by the clustering method to be evaluated. | |
| verbose -- Display or not extra information (default, False). | |
| return -- Array of statistics (mean, std) for each cluster and total. | |
| """ | |
| # clusters labels | |
| cluster_labels = np.unique(y_km) | |
| # number of clusters | |
| n_clusters = cluster_labels.shape[0] | |
| # estimate silhouette values (for all records) | |
| silhouette_vals = silhouette_samples(X, y_km, metric='euclidean') | |
| # initialize | |
| statistics = list() | |
| # loop of cluster labels | |
| for i, c in enumerate(cluster_labels): | |
| # collect silhouette values per cluster | |
| c_silhouette_vals = silhouette_vals[y_km == c] | |
| # estimate statistics for each cluster | |
| statistics.append([f"C{c}", np.mean(c_silhouette_vals), np.std(c_silhouette_vals)]) | |
| # display | |
| if verbose: | |
| print(f"C{c}", np.mean(c_silhouette_vals), np.std(c_silhouette_vals)) | |
| # final statistics | |
| statistics.append([f"ALL", np.mean(silhouette_vals), np.std(silhouette_vals)]) | |
| # display | |
| if verbose: | |
| print(f"ALL", np.mean(silhouette_vals), np.std(silhouette_vals)) | |
| # to df and return | |
| return statistics | |
| ## estimate the optimal number of clusters for k-Means algorithm | |
| def estimate_optimal_num_clusters_kmeans(X:np.array, max_num_clusters:int = 10, with_plot:bool = False)->int: | |
| """ | |
| Estimate the optimal number of clusters for k-Means algorithm. | |
| X -- Array of features used to estimate the clustering. | |
| max_num_clusters -- Maximum number of clusters to be tested. | |
| with_plot -- Plot or not extra information (default, False). | |
| return -- The most optimal number of clusters. | |
| """ | |
| # number of clusters to be tested | |
| num_clusters_to_test = np.arange(2, max_num_clusters + 1, 1) | |
| # initialize | |
| metrics = np.array([]) | |
| # loop of number of clusters | |
| for nc in num_clusters_to_test: | |
| ## k-means clustering definition, fit and prediction | |
| km = KMeans(n_clusters=nc , init='k-means++', n_init=10, max_iter=300, tol=1e-04, random_state=0) | |
| y_km = km.fit_predict(X) | |
| ## cluster cuantification | |
| metric = quantification_clustering_quality(X, y_km)[-1][1] | |
| # append | |
| metrics = np.append(metrics, metric) | |
| # clean | |
| del metric, km, y_km | |
| # sort num of cluster according to metric values | |
| num_clusters_sorted_according_metric = num_clusters_to_test[np.argsort(metrics)[::-1]] | |
| # get the most optimal | |
| num_cluster_optimal = num_clusters_sorted_according_metric[0] | |
| # with plot if it is required | |
| if with_plot: | |
| ## plot | |
| plt.plot(num_clusters_to_test, metrics, color = "grey") | |
| plt.scatter(num_clusters_to_test, metrics, | |
| c='white', marker='o', edgecolor='black', s=25) | |
| plt.axvline(num_cluster_optimal, color="red", linestyle="--") | |
| plt.grid() | |
| plt.tight_layout() | |
| plt.title(f"Optimal Number of Clusters = {num_cluster_optimal}") | |
| plt.xlabel("Number of clusters") | |
| plt.ylabel('Silhouette coefficient') | |
| plt.show() | |
| # return | |
| return num_cluster_optimal |
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