# coding: utf-8 from sklearn.datasets import make_blobs import matplotlib.pyplot as plt from sklearn.cluster import KMeans import numpy as np from matplotlib import cm from sklearn.metrics import silhouette_samples import pandas as pd from scipy.spatial.distance import pdist, squareform from scipy.cluster.hierarchy import linkage from scipy.cluster.hierarchy import dendrogram # from scipy.cluster.hierarchy import set_link_color_palette from sklearn.cluster import AgglomerativeClustering from sklearn.datasets import make_moons from sklearn.cluster import DBSCAN # *Python Machine Learning 3rd Edition* by [Sebastian Raschka](https://sebastianraschka.com), Packt Publishing Ltd. 2019 # # Code Repository: https://github.com/rasbt/python-machine-learning-book-3rd-edition # # Code License: [MIT License](https://github.com/rasbt/python-machine-learning-book-3rd-edition/blob/master/LICENSE.txt) # # Python Machine Learning - Code Examples # # Chapter 11 - Working with Unlabeled Data – Clustering Analysis # Note that the optional watermark extension is a small IPython notebook plugin that I developed to make the code reproducible. You can just skip the following line(s). # *The use of `watermark` is optional. You can install this Jupyter extension via* # # conda install watermark -c conda-forge # # or # # pip install watermark # # *For more information, please see: https://github.com/rasbt/watermark.* # ### Overview # - [Grouping objects by similarity using k-means](#Grouping-objects-by-similarity-using-k-means) # - [K-means clustering using scikit-learn](#K-means-clustering-using-scikit-learn) # - [A smarter way of placing the initial cluster centroids using k-means++](#A-smarter-way-of-placing-the-initial-cluster-centroids-using-k-means++) # - [Hard versus soft clustering](#Hard-versus-soft-clustering) # - [Using the elbow method to find the optimal number of clusters](#Using-the-elbow-method-to-find-the-optimal-number-of-clusters) # - [Quantifying the quality of clustering via silhouette plots](#Quantifying-the-quality-of-clustering-via-silhouette-plots) # - [Organizing clusters as a hierarchical tree](#Organizing-clusters-as-a-hierarchical-tree) # - [Grouping clusters in bottom-up fashion](#Grouping-clusters-in-bottom-up-fashion) # - [Performing hierarchical clustering on a distance matrix](#Performing-hierarchical-clustering-on-a-distance-matrix) # - [Attaching dendrograms to a heat map](#Attaching-dendrograms-to-a-heat-map) # - [Applying agglomerative clustering via scikit-learn](#Applying-agglomerative-clustering-via-scikit-learn) # - [Locating regions of high density via DBSCAN](#Locating-regions-of-high-density-via-DBSCAN) # - [Summary](#Summary) # # Grouping objects by similarity using k-means # ## K-means clustering using scikit-learn X, y = make_blobs(n_samples=150, n_features=2, centers=3, cluster_std=0.5, shuffle=True, random_state=0) plt.scatter(X[:, 0], X[:, 1], c='white', marker='o', edgecolor='black', s=50) plt.grid() plt.tight_layout() #plt.savefig('images/11_01.png', dpi=300) plt.show() km = KMeans(n_clusters=3, init='random', n_init=10, max_iter=300, tol=1e-04, random_state=0) y_km = km.fit_predict(X) plt.scatter(X[y_km == 0, 0], X[y_km == 0, 1], s=50, c='lightgreen', marker='s', edgecolor='black', label='Cluster 1') plt.scatter(X[y_km == 1, 0], X[y_km == 1, 1], s=50, c='orange', marker='o', edgecolor='black', label='Cluster 2') plt.scatter(X[y_km == 2, 0], X[y_km == 2, 1], s=50, c='lightblue', marker='v', edgecolor='black', label='Cluster 3') plt.scatter(km.cluster_centers_[:, 0], km.cluster_centers_[:, 1], s=250, marker='*', c='red', edgecolor='black', label='Centroids') plt.legend(scatterpoints=1) plt.grid() plt.tight_layout() #plt.savefig('images/11_02.png', dpi=300) plt.show() # ## A smarter way of placing the initial cluster centroids using k-means++ # ... # ## Hard versus soft clustering # ... # ## Using the elbow method to find the optimal number of clusters print('Distortion: %.2f' % km.inertia_) distortions = [] for i in range(1, 11): km = KMeans(n_clusters=i, init='k-means++', n_init=10, max_iter=300, random_state=0) km.fit(X) distortions.append(km.inertia_) plt.plot(range(1, 11), distortions, marker='o') plt.xlabel('Number of clusters') plt.ylabel('Distortion') plt.tight_layout() #plt.savefig('images/11_03.png', dpi=300) plt.show() # ## Quantifying the quality of clustering via silhouette plots km = KMeans(n_clusters=3, init='k-means++', n_init=10, max_iter=300, tol=1e-04, random_state=0) y_km = km.fit_predict(X) cluster_labels = np.unique(y_km) n_clusters = cluster_labels.shape[0] silhouette_vals = silhouette_samples(X, y_km, metric='euclidean') y_ax_lower, y_ax_upper = 0, 0 yticks = [] for i, c in enumerate(cluster_labels): c_silhouette_vals = silhouette_vals[y_km == c] c_silhouette_vals.sort() y_ax_upper += len(c_silhouette_vals) color = cm.jet(float(i) / n_clusters) plt.barh(range(y_ax_lower, y_ax_upper), c_silhouette_vals, height=1.0, edgecolor='none', color=color) yticks.append((y_ax_lower + y_ax_upper) / 2.) y_ax_lower += len(c_silhouette_vals) silhouette_avg = np.mean(silhouette_vals) plt.axvline(silhouette_avg, color="red", linestyle="--") plt.yticks(yticks, cluster_labels + 1) plt.ylabel('Cluster') plt.xlabel('Silhouette coefficient') plt.tight_layout() #plt.savefig('images/11_04.png', dpi=300) plt.show() # Comparison to "bad" clustering: km = KMeans(n_clusters=2, init='k-means++', n_init=10, max_iter=300, tol=1e-04, random_state=0) y_km = km.fit_predict(X) plt.scatter(X[y_km == 0, 0], X[y_km == 0, 1], s=50, c='lightgreen', edgecolor='black', marker='s', label='Cluster 1') plt.scatter(X[y_km == 1, 0], X[y_km == 1, 1], s=50, c='orange', edgecolor='black', marker='o', label='Cluster 2') plt.scatter(km.cluster_centers_[:, 0], km.cluster_centers_[:, 1], s=250, marker='*', c='red', label='Centroids') plt.legend() plt.grid() plt.tight_layout() #plt.savefig('images/11_05.png', dpi=300) plt.show() cluster_labels = np.unique(y_km) n_clusters = cluster_labels.shape[0] silhouette_vals = silhouette_samples(X, y_km, metric='euclidean') y_ax_lower, y_ax_upper = 0, 0 yticks = [] for i, c in enumerate(cluster_labels): c_silhouette_vals = silhouette_vals[y_km == c] c_silhouette_vals.sort() y_ax_upper += len(c_silhouette_vals) color = cm.jet(float(i) / n_clusters) plt.barh(range(y_ax_lower, y_ax_upper), c_silhouette_vals, height=1.0, edgecolor='none', color=color) yticks.append((y_ax_lower + y_ax_upper) / 2.) y_ax_lower += len(c_silhouette_vals) silhouette_avg = np.mean(silhouette_vals) plt.axvline(silhouette_avg, color="red", linestyle="--") plt.yticks(yticks, cluster_labels + 1) plt.ylabel('Cluster') plt.xlabel('Silhouette coefficient') plt.tight_layout() #plt.savefig('images/11_06.png', dpi=300) plt.show() # # Organizing clusters as a hierarchical tree # ## Grouping clusters in bottom-up fashion np.random.seed(123) variables = ['X', 'Y', 'Z'] labels = ['ID_0', 'ID_1', 'ID_2', 'ID_3', 'ID_4'] X = np.random.random_sample([5, 3])*10 df = pd.DataFrame(X, columns=variables, index=labels) df # ## Performing hierarchical clustering on a distance matrix row_dist = pd.DataFrame(squareform(pdist(df, metric='euclidean')), columns=labels, index=labels) row_dist # We can either pass a condensed distance matrix (upper triangular) from the `pdist` function, or we can pass the "original" data array and define the `metric='euclidean'` argument in `linkage`. However, we should not pass the squareform distance matrix, which would yield different distance values although the overall clustering could be the same. # 1. incorrect approach: Squareform distance matrix row_clusters = linkage(row_dist, method='complete', metric='euclidean') pd.DataFrame(row_clusters, columns=['row label 1', 'row label 2', 'distance', 'no. of items in clust.'], index=['cluster %d' % (i + 1) for i in range(row_clusters.shape[0])]) # 2. correct approach: Condensed distance matrix row_clusters = linkage(pdist(df, metric='euclidean'), method='complete') pd.DataFrame(row_clusters, columns=['row label 1', 'row label 2', 'distance', 'no. of items in clust.'], index=['cluster %d' % (i + 1) for i in range(row_clusters.shape[0])]) # 3. correct approach: Input matrix row_clusters = linkage(df.values, method='complete', metric='euclidean') pd.DataFrame(row_clusters, columns=['row label 1', 'row label 2', 'distance', 'no. of items in clust.'], index=['cluster %d' % (i + 1) for i in range(row_clusters.shape[0])]) # make dendrogram black (part 1/2) # set_link_color_palette(['black']) row_dendr = dendrogram(row_clusters, labels=labels, # make dendrogram black (part 2/2) # color_threshold=np.inf ) plt.tight_layout() plt.ylabel('Euclidean distance') #plt.savefig('images/11_11.png', dpi=300, # bbox_inches='tight') plt.show() # ## Attaching dendrograms to a heat map # plot row dendrogram fig = plt.figure(figsize=(8, 8), facecolor='white') axd = fig.add_axes([0.09, 0.1, 0.2, 0.6]) # note: for matplotlib < v1.5.1, please use orientation='right' row_dendr = dendrogram(row_clusters, orientation='left') # reorder data with respect to clustering df_rowclust = df.iloc[row_dendr['leaves'][::-1]] axd.set_xticks([]) axd.set_yticks([]) # remove axes spines from dendrogram for i in axd.spines.values(): i.set_visible(False) # plot heatmap axm = fig.add_axes([0.23, 0.1, 0.6, 0.6]) # x-pos, y-pos, width, height cax = axm.matshow(df_rowclust, interpolation='nearest', cmap='hot_r') fig.colorbar(cax) axm.set_xticklabels([''] + list(df_rowclust.columns)) axm.set_yticklabels([''] + list(df_rowclust.index)) #plt.savefig('images/11_12.png', dpi=300) plt.show() # ## Applying agglomerative clustering via scikit-learn ac = AgglomerativeClustering(n_clusters=3, affinity='euclidean', linkage='complete') labels = ac.fit_predict(X) print('Cluster labels: %s' % labels) ac = AgglomerativeClustering(n_clusters=2, affinity='euclidean', linkage='complete') labels = ac.fit_predict(X) print('Cluster labels: %s' % labels) # # Locating regions of high density via DBSCAN X, y = make_moons(n_samples=200, noise=0.05, random_state=0) plt.scatter(X[:, 0], X[:, 1]) plt.tight_layout() #plt.savefig('images/11_14.png', dpi=300) plt.show() # K-means and hierarchical clustering: f, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 3)) km = KMeans(n_clusters=2, random_state=0) y_km = km.fit_predict(X) ax1.scatter(X[y_km == 0, 0], X[y_km == 0, 1], edgecolor='black', c='lightblue', marker='o', s=40, label='cluster 1') ax1.scatter(X[y_km == 1, 0], X[y_km == 1, 1], edgecolor='black', c='red', marker='s', s=40, label='cluster 2') ax1.set_title('K-means clustering') ac = AgglomerativeClustering(n_clusters=2, affinity='euclidean', linkage='complete') y_ac = ac.fit_predict(X) ax2.scatter(X[y_ac == 0, 0], X[y_ac == 0, 1], c='lightblue', edgecolor='black', marker='o', s=40, label='Cluster 1') ax2.scatter(X[y_ac == 1, 0], X[y_ac == 1, 1], c='red', edgecolor='black', marker='s', s=40, label='Cluster 2') ax2.set_title('Agglomerative clustering') plt.legend() plt.tight_layout() #plt.savefig('images/11_15.png', dpi=300) plt.show() # Density-based clustering: db = DBSCAN(eps=0.2, min_samples=5, metric='euclidean') y_db = db.fit_predict(X) plt.scatter(X[y_db == 0, 0], X[y_db == 0, 1], c='lightblue', marker='o', s=40, edgecolor='black', label='Cluster 1') plt.scatter(X[y_db == 1, 0], X[y_db == 1, 1], c='red', marker='s', s=40, edgecolor='black', label='Cluster 2') plt.legend() plt.tight_layout() #plt.savefig('images/11_16.png', dpi=300) plt.show() # # Summary # ... # --- # # Readers may ignore the next cell.