Below is a step-by-step guide on creating Hierarchical Clustering and Dendrogram from our time series using SciPy. Please note that scikit-learn (a powerful data analysis library built on top of SciPY) also implemented many other clustering algorithms .
First we create synthetic time series for the job. We will construct 6 groups of correlated time series, and we expect that hierarchical clustering will detect these six groups.
import numpy as np import seaborn as sns import pandas as pd from scipy import stats import scipy.cluster.hierarchy as hac import matplotlib.pyplot as plt # # build 6 time series groups for testing, called: a, b, c, d, e, f # num_samples = 61 group_size = 10 # # create the main time series for each group # x = np.linspace(0, 5, num_samples) scale = 4 a = scale * np.sin(x) b = scale * (np.cos(1+x*3) + np.linspace(0, 1, num_samples)) c = scale * (np.sin(2+x*6) + np.linspace(0, -1, num_samples)) d = scale * (np.cos(3+x*9) + np.linspace(0, 4, num_samples)) e = scale * (np.sin(4+x*12) + np.linspace(0, -4, num_samples)) f = scale * np.cos(x) # # from each main series build 'group_size' series # timeSeries = pd.DataFrame() ax = None for arr in [a,b,c,d,e,f]: arr = arr + np.random.rand(group_size, num_samples) + np.random.randn(group_size, 1) df = pd.DataFrame(arr) timeSeries = timeSeries.append(df) # We use seaborn to plot what we have #ax = sns.tsplot(ax=ax, data=df.values, ci=[68, 95]) ax = sns.tsplot(ax=ax, data=df.values, err_style="unit_traces") plt.show()
Now we do the clustering and write it:
# Do the clustering Z = hac.linkage(timeSeries, method='single', metric='correlation') # Plot dendogram plt.figure(figsize=(25, 10)) plt.title('Hierarchical Clustering Dendrogram') plt.xlabel('sample index') plt.ylabel('distance') hac.dendrogram( Z, leaf_rotation=90., # rotates the x axis labels leaf_font_size=8., # font size for the x axis labels ) plt.show()
if we want to decide which correlation to apply or use a different distance metric, then we can provide our own metric function:
# Here we use spearman correlation def my_metric(x, y): r = stats.pearsonr(x, y)[0] return 1 - r # correlation to distance: range 0 to 2 # Do the clustering Z = hac.linkage(timeSeries, method='single', metric=my_metric) # Plot dendogram plt.figure(figsize=(25, 10)) plt.title('Hierarchical Clustering Dendrogram') plt.xlabel('sample index') plt.ylabel('distance') hac.dendrogram( Z, leaf_rotation=90., # rotates the x axis labels leaf_font_size=8., # font size for the x axis labels ) plt.show()
To retrieve clusters, we can use the fcluster function. It can be launched in several ways (check the documentation), but in this example we will indicate it as the target number of desired clusters:
from scipy.cluster.hierarchy import fcluster def print_clusters(timeSeries, Z, k, plot=False): # k Number of clusters I'd like to extract results = fcluster(Z, k, criterion='maxclust') # check the results s = pd.Series(results) clusters = s.unique() for c in clusters: cluster_indeces = s[s==c].index print("Cluster %d number of entries %d" % (c, len(cluster_indeces))) if plot: timeSeries.T.iloc[:,cluster_indeces].plot() plt.show() print_clusters(timeSeries, Z, 6, plot=False)
Output:
Cluster 2 number of entries 10 Cluster 5 number of entries 10 Cluster 3 number of entries 10 Cluster 6 number of entries 10 Cluster 1 number of entries 10 Cluster 4 number of entries 10