ch11.py

# 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.