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Clustering.py
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Clustering.py
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##############################################################
# #
# Mark Hoogendoorn and Burkhardt Funk (2017) #
# Machine Learning for the Quantified Self #
# Springer #
# Chapter 5 #
# #
##############################################################
from sklearn.cluster import KMeans
from Chapter5.DistanceMetrics import InstanceDistanceMetrics
import sklearn
import pandas as pd
import numpy as np
from sklearn.metrics import silhouette_samples, silhouette_score
from Chapter5.DistanceMetrics import PersonDistanceMetricsNoOrdering
from Chapter5.DistanceMetrics import PersonDistanceMetricsOrdering
import random
import scipy
from scipy.cluster.hierarchy import linkage, fcluster
from sklearn.neighbors import DistanceMetric
import pyclust
from nltk.cluster.kmeans import KMeansClusterer
# Implementation of the non hierarchical clustering approaches.
class NonHierarchicalClustering:
# Global parameters for distance functions
p = 1
max_lag = 1
# Identifiers of the various distance and abstraction approaches.
euclidean = 'euclidean'
minkowski = 'minkowski'
manhattan = 'manhattan'
gower = 'gower'
abstraction_mean = 'abstraction_mean'
abstraction_normal = 'abstraction_normal'
abstraction_p = 'abstraction_p'
abstraction_euclidean = 'abstract_euclidean'
abstraction_lag = 'abstract_lag'
abstraction_dtw = 'abstract_dtw'
# Define the gowers distance between arrays to be used in k-means and k-medoids.
def gowers_similarity(self, X, Y=None, Y_norm_squared=None, squared=False):
X = np.matrix(X)
distances = np.zeros(shape=(X.shape[0], Y.shape[0]))
DM = InstanceDistanceMetrics()
# Pairs up the elements in the dataset
for x_row in range(0, X.shape[0]):
data_row1 = pd.DataFrame(X[x_row])
for y_row in range(0, Y.shape[0]):
data_row2 = pd.DataFrame(Y[y_row]).transpose()
# And computer the distance as defined in our distance metrics class.
distances[x_row, y_row] = DM.gowers_similarity(data_row1, data_row2, self.p)
return np.array(distances)
# Use a predefined distance function for the Minkowski distance
def minkowski_distance(self, X, Y=None, Y_norm_squared=None, squared=False):
dist = DistanceMetric.get_metric('minkowski', p=self.p)
return dist.pairwise(X, Y)
# Use a predefined distance function for the Manhattan distance
def manhattan_distance(self, X, Y=None, Y_norm_squared=None, squared=False):
dist = DistanceMetric.get_metric('manhattan')
return dist.pairwise(X, Y)
# Use a predefined distance function for the Euclidean distance
def euclidean_distance(self, X, Y=None, Y_norm_squared=None, squared=False):
dist = DistanceMetric.get_metric('euclidean')
return dist.pairwise(X, Y)
# If we want to compare dataset between persons one approach is to flatten
# each dataset to a single record/instance. This is done based on the approaches
# we have defined in the distance metrics file.
def aggregate_datasets(self, datasets, cols, abstraction_method):
temp_datasets = []
DM = PersonDistanceMetricsNoOrdering()
# Flatten all datasets and add them to the newly formed dataset.
for i in range(0, len(datasets)):
temp_dataset = datasets[i][cols]
temp_datasets.append(temp_dataset)
if abstraction_method == self.abstraction_normal:
return DM.create_instances_normal_distribution(temp_datasets)
else:
return DM.create_instances_mean(temp_datasets)
# Perform k-means over an individual dataset.
def k_means_over_instances(self, dataset, cols, k, distance_metric, max_iters, n_inits, p=1):
# Take the appropriate columns.
temp_dataset = dataset[cols]
# Override the standard distance functions. Store the original first
# sklearn_euclidian_distances = sklearn.cluster.k_means_.euclidean_distances
sklearn_euclidian_distances = sklearn.metrics.pairwise.euclidean_distances
if distance_metric == self.euclidean:
sklearn.metrics.pairwise.euclidean_distances = self.euclidean_distance
elif distance_metric == self.minkowski:
self.p = p
sklearn.metrics.pairwise.euclidean_distances = self.minkowski_distance
elif distance_metric == self.manhattan:
sklearn.metrics.pairwise.euclidean_distances = self.manhattan_distance
elif distance_metric == self.gower:
self.ranges = []
for col in temp_dataset.columns:
self.ranges.append(temp_dataset[col].max() - temp_dataset[col].min())
sklearn.metrics.pairwise.euclidean_distances = self.gower_similarity
# If we do not recognize the option we use the default distance function, which is much
# faster....
# Now apply the k-means algorithm
kmeans = KMeans(n_clusters=k, max_iter=max_iters, n_init=n_inits, random_state=0).fit(temp_dataset)
# Add the labels to the dataset
dataset['cluster'] = kmeans.labels_
# Compute the solhouette and add it as well.
silhouette_avg = silhouette_score(temp_dataset, kmeans.labels_)
silhouette_per_inst = silhouette_samples(temp_dataset, kmeans.labels_)
dataset['silhouette'] = silhouette_per_inst
# Reset the module distance function for further usage
sklearn_euclidian_distances = sklearn_euclidian_distances
return dataset
# We have datasets covering multiple persons. We abstract the datatasets using an approach and create
# clusters of persons.
def k_means_over_datasets(self, datasets, cols, k, abstraction_method, distance_metric, max_iters, n_inits, p=1):
# Convert the datasets to instances
temp_dataset = self.aggregate_datasets(datasets, cols, abstraction_method)
# And simply apply the instance based algorithm.....
return self.k_means_over_instances(temp_dataset, temp_dataset.columns, k, distance_metric, max_iters, n_inits, p)
# For our own k-medoids algorithm we use our own implementation. For this we computer a complete distance matrix
# between points.
def compute_distance_matrix_instances(self, dataset, distance_metric):
# If the distance function is not defined in our distance metrics, we use the standard euclidean distance.
if not (distance_metric in [self.manhattan, self.minkowski, self.gower, self.euclidean]):
distances = sklearn.metrics.pairwise.euclidean_distances(X=dataset, Y=dataset)
return pd.DataFrame(distances, index=range(0, len(dataset.index)), columns=range(0, len(dataset.index)))
# Create an empty pandas dataframe for our distance matrix
distances = pd.DataFrame(index=range(0, len(dataset.index)), columns=range(0, len(dataset.index)))
DM = InstanceDistanceMetrics()
# Define the ranges of the columns if we use the gower distance.
ranges = []
if distance_metric == self.gower:
for col in dataset.columns:
self.ranges.append(dataset[col].max() - dataset[col].min())
# And compute the distances for each pair. Note that we assume the distances to be symmetric.
for i in range(0, len(dataset.index)):
for j in range(i, len(dataset.index)):
if distance_metric == self.manhattan:
distances.iloc[i,j] = self.manhattan_distance(dataset.iloc[i:i+1,:], dataset.iloc[j:j+1,:])
elif distance_metric == self.minkowski:
distances.iloc[i,j] = self.manhattan_distance(dataset.iloc[i:i+1,:], dataset.iloc[j:j+1,:], self.p)
elif distance_metric == self.gower:
distances.iloc[i,j] = self.gower_distance(dataset.iloc[i:i+1,:], dataset.iloc[j:j+1,:])
elif distance_metric == self.euclidean:
distances.iloc[i,j] = self.euclidean_distance(dataset.iloc[i:i+1,:], dataset.iloc[j:j+1,:])
distances.iloc[j,i] = distances.iloc[i,j]
return distances
# We need to implement k-medoids ourselves to accommodate all distance metrics
def k_medoids_over_instances(self, dataset, cols, k, distance_metric, max_iters, n_inits=5, p=1):
# If we set it to default we use the pyclust package...
temp_dataset = dataset[cols]
if distance_metric == 'default':
km = pyclust.KMedoids(n_clusters=k, n_trials=n_inits)
km.fit(temp_dataset.values)
cluster_assignment = km.labels_
else:
self.p = p
cluster_assignment = []
best_silhouette = -1
# Compute all distances
D = self.compute_distance_matrix_instances(temp_dataset, distance_metric)
for it in range(0, n_inits):
# First select k random points as centers:
centers = random.sample(range(0, len(dataset.index)), k)
prev_centers = []
points_to_cluster = []
n_iter = 0
while (n_iter < max_iters) and not (centers == prev_centers):
n_iter += 1
prev_centers = centers
# Assign points to clusters.
points_to_centroid = D[centers].idxmin(axis=1)
new_centers = []
for i in range(0, k):
# And find the new center that minimized the sum of the differences.
best_center = D.loc[points_to_centroid == centers[i], points_to_centroid == centers[i]].sum().idxmin(axis=1)
new_centers.append(best_center)
centers = new_centers
# Convert centroids to cluster numbers:
points_to_centroid = D[centers].idxmin(axis=1)
current_cluster_assignment = []
for i in range(0, len(dataset.index)):
current_cluster_assignment.append(centers.index(points_to_centroid.iloc[i,:]))
silhouette_avg = silhouette_score(temp_dataset, np.array(current_cluster_assignment))
if silhouette_avg > best_silhouette:
cluster_assignment = current_cluster_assignment
best_silhouette = silhouette_avg
# And add the clusters and silhouette scores to the dataset.
dataset['cluster'] = cluster_assignment
silhouette_avg = silhouette_score(temp_dataset, np.array(cluster_assignment))
silhouette_per_inst = silhouette_samples(temp_dataset, np.array(cluster_assignment))
dataset['silhouette'] = silhouette_per_inst
return dataset
# For k-medoids we use all possible distance metrics between datasets as well. For this we
# again need to define a distance matrix between the datasets.
def compute_distance_matrix_datasets(self, datasets, distance_metric):
distances = pd.DataFrame(index=range(0, len(datasets)), columns=range(0, len(datasets)))
DMNoOrdering = PersonDistanceMetricsNoOrdering()
DMOrdering = PersonDistanceMetricsOrdering()
# And compute the distances for each pair. Note that we assume the distances to be symmetric.
for i in range(0, len(datasets)):
for j in range(i, len(datasets)):
if distance_metric == self.abstraction_p:
distances.iloc[i,j] = DMNoOrdering.p_distance(datasets[i], datasets[j])
elif distance_metric == self.abstraction_euclidean:
distances.iloc[i,j] = DMOrdering.euclidean_distance(datasets[i], datasets[j])
elif distance_metric == self.abstraction_lag:
distances.iloc[i,j] = DMOrdering.lag_correlation(datasets[i], datasets[j], self.max_lag)
elif distance_metric == self.abstraction_dtw:
distances.iloc[i,j] = DMOrdering.dynamic_time_warping(datasets[i], datasets[j])
distances.iloc[j,i] = distances.iloc[i,j]
return distances
# Note: distance metric only important in combination with certain abstraction methods as we allow for more
# in k-medoids.
def k_medoids_over_datasets(self, datasets, cols, k, abstraction_method, distance_metric, max_iters, n_inits=5, p=1, max_lag=5):
self.p = p
self.max_lag = max_lag
# If we compare datasets by flattening them, we can simply flatten the dataset and apply the instance based
# variant.
if abstraction_method in [self.abstraction_mean, self.abstraction_normal]:
# Convert the datasets to instances
temp_dataset = self.aggregate_datasets(datasets, cols, abstraction_method)
# And simply apply the instance based algorithm in case of
return self.k_medoids_over_instances(temp_dataset, temp_dataset.columns, k, distance_metric, max_iters, n_inits=n_inits, p=p)
# For the case over datasets we do not have a quality metric, therefore we just look at a single initialization for now (!)
# First select k random points as centers:
centers = random.sample(range(0, len(datasets)), k)
prev_centers = []
points_to_cluster = []
# Compute all distances
D = self.compute_distance_matrix_datasets(datasets, abstraction_method)
n_iter = 0
while (n_iter < max_iters) and not (centers == prev_centers):
n_iter += 1
prev_centers = centers
# Assign points to clusters.
points_to_centroid = D[centers].idxmin(axis=1)
new_centers = []
for i in range(0, k):
# And find the new center that minimized the sum of the differences.
best_center = D.loc[points_to_centroid == centers[i], points_to_centroid == centers[i]].sum().idxmin(axis=1)
new_centers.append(best_center)
centers = new_centers
# Convert centroids to cluster numbers:
points_to_centroid = D[centers].idxmin(axis=1)
cluster_assignment = []
for i in range(0, len(datasets)):
cluster_assignment.append(centers.index(points_to_centroid.iloc[i,:]))
dataset = pd.DataFrame(index=range(0, len(datasets)))
dataset['cluster'] = cluster_assignment
# Silhouette cannot be used here as it used a distance between instances, not datasets.
return dataset
# In this class, we do not implement the Gover distance between instance, all others are included.
# Furthermore, we only implement the agglomerative approach.
class HierarchicalClustering:
link = None
# Perform agglomerative clustering over a single dataset.
def agglomerative_over_instances(self, dataset, cols, max_clusters, distance_metric, use_prev_linkage=False, link_function='single'):
temp_dataset = dataset[cols]
df = NonHierarchicalClustering()
if (not use_prev_linkage) or (self.link is None):
# Perform the clustering process according to the specified distance metric.
if distance_metric == df.manhattan:
self.link = linkage(temp_dataset.values, method=link_function, metric='cityblock')
else:
self.link = linkage(temp_dataset.values, method=link_function, metric='euclidean')
# And assign the clusters given the set maximum. In addition, compute the
cluster_assignment = fcluster(self.link, max_clusters, criterion='maxclust')
dataset['cluster'] = cluster_assignment
silhouette_avg = silhouette_score(temp_dataset, np.array(cluster_assignment))
silhouette_per_inst = silhouette_samples(temp_dataset, np.array(cluster_assignment))
dataset['silhouette'] = silhouette_per_inst
return dataset, self.link
# Perform agglomerative clustering over the datasets by flattening them into a single dataset.
def agglomerative_over_datasets(self, datasets, cols, max_clusters, abstraction_method, distance_metric, use_prev_linkage=False, link_function='single'):
# Convert the datasets to instances
df = NonHierarchicalClustering()
temp_dataset = df.aggregate_datasets(datasets, cols, abstraction_method)
# And simply apply the instance based algorithm...
return self.agglomerative_over_instances(temp_dataset, temp_dataset.columns, max_clusters, distance_metric, use_prev_linkage=use_prev_linkage, link_function=link_function)