Added hard and soft Kmeans clustering with tests

numpy_ml/cluster/README.md

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+# Clustering Models
+The `kmeans.py` module implements:
+
+1. [Hard kmeans clustering](https://user-images.githubusercontent.com/1905599/119421132-de04f700-bcb2-11eb-98cd-4337d0b9496d.png) with fixed assignment of data points to only one cluster at a time.
+2. [Soft kmeans clustering](https://user-images.githubusercontent.com/1905599/119421211-0bea3b80-bcb3-11eb-9e71-a337da8db24d.png) with probabilistic assignment of data points. Each data point has a membership degree in each cluster. The highest probabe cluster could then be assigned as the cluser index of the data. Alternatively, the probability distribution can be used for any other purpose as it captures our uncertaintity of the clustering routine.
+

numpy_ml/cluster/__init__.py

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+from .kmeans import *

numpy_ml/cluster/kmeans.py

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+"""An implementation of kmeans clustering (hard, soft)"""
+
+import numpy as np
+
+class KMeans:
+ def __init__(self, X_train, cluster_method="hard", n_clusters=5, beta = 1.0):
+ r"""
+ Kmean implementation.
+
+ Parameters
+ ----------
+ X_train : array
+ The input matrix with dimensions (number of data x number of attributes).
+
+ cluster_method : {'hard', 'soft'}
+ Whether to cluster using hard or soft clustering. Default is hard.
+
+ n_clusters : int
+ number of clusters.
+
+ beta: float
+ span of a radial basis kernel
+ """
+ self.cluster_method = cluster_method
+ self.X_train = X_train
+ self.n_clusters = n_clusters
+
+ self.centroids = None
+ self.assignments = None
+
+ if self.cluster_method == 'soft':
+ self.beta = beta # Use beta only in soft clustering
+ self.centroids, self.assignments = self._kmeans_soft()
+
+ elif self.cluster_method == 'hard':
+ self.centroids, self.assignments = self._kmeans_hard()
+
+
+ def _is_converged(self, prev, cur):
+ r"""
+ Check for convergence by validating if the centroid or assignments have stopped changing across iterations.
+
+ Parameters:
+ -----------
+ prev : array
+ The input could be the centroids or assignment based on the chosen implemtation details (past iteration).
+ cur : array
+ The input could be the centroids or assignment based on the chosen implemtation details (current iteration).
+
+ Returns
+ -------
+ True: if convergence is reached.
+ False: if convergence is not reached. 
+ """
+ return np.allclose(prev,cur)
+
+
+ def _kmeans_hard(self):
+ r"""
+ hard clustering: The "vanilla" kmean clustering assigns every data point to a single cluster.
+
+ Returns
+ -------
+ centroids : array
+ The centroid matrix with dimensions (number of centroids x number of attributes).
+ assignments : array
+ The assignments vector with dimensions (number of data).
+ """
+ size_of_data = self.X_train.shape[0]
+ centroid_indexes = np.random.choice(size_of_data, self.n_clusters, replace=False)
+ centroids = np.take(self.X_train, centroid_indexes, axis=0)
+ assignments = [-1] * size_of_data
+ n_dims = self.X_train.shape[1]
+ iteration, max_iteration = 0, 100 
+ prev_weight_vec = np.zeros(n_dims)
+ weight_list = [prev_weight_vec, centroids] 
+
+ while not self._is_converged(weight_list[-2], weight_list[-1]) or iteration < max_iteration:
+ centroids = weight_list[-1]
+
+ # update cluster assignments
+ for i, x_val in enumerate(self.X_train):
+ min_distance = 1000000000
+ for k, mu_val in enumerate(centroids):
+
+ dist = np.linalg.norm(x_val - mu_val)
+
+ if dist < min_distance: 
+ min_distance = dist
+ assignments[i] = k
+
+ # update centroids
+ set_labels = range(self.n_clusters)
+ # filter by labels
+ for label in set_labels:
+ filter_indices = np.where(np.array(assignments) == label)[0]
+ count_per_label = len(filter_indices)
+ if count_per_label > 0:
+ filter_xdata = np.take(self.X_train, filter_indices, axis=0)
+ centroids[label, :] = np.mean(filter_xdata, axis=0)
+ weight_list.append(centroids)
+ weight_list.pop(0)
+ iteration = iteration + 1
+ return centroids, assignments
+
+
+ def _kmeans_soft(self):
+ r"""
+ Soft clustering: In this implementation, which is the modification of the kmean hard clustering algorithm, we assigns every data point a degree of membership in the cluster assignment. Hence, we give a probability distribution.
+
+ Parameters:
+ -----------
+ beta: float
+ span of a radial basis kernel
+
+ Returns
+ -------
+ centroids : array
+ The centroid matrix with dimensions (number of centroids x number of attributes).
+ assignments : array
+ The assignments vector with dimensions (number of data x number of centroids). This is the probability distribution of the membership of each data point in the cluster.
+ """
+ size_of_data = self.X_train.shape[0]
+ centroid_indexes = np.random.choice(size_of_data, self.n_clusters, replace=False)
+ centroids = np.take(self.X_train, centroid_indexes, axis=0)
+ assignments = -1 * np.ones((size_of_data, self.n_clusters))
+ n_dims = self.X_train.shape[1]
+ iteration, max_iteration = 0, 100 
+ tol = 0.00001 # prevent division by zero
+ prev_weight_vec = np.zeros(n_dims)
+ weight_list = [prev_weight_vec, centroids] 
+
+ while not self._is_converged(weight_list[-2], weight_list[-1]) or iteration < max_iteration:
+ centroids = weight_list[-1]
+
+ # update cluster assignments
+ for i, x_val in enumerate(self.X_train):
+ for k, mu_val in enumerate(centroids):
+ dist = np.linalg.norm(x_val - mu_val)
+ weight = np.exp(-dist / self.beta)
+ assignments[i][k] = weight
+ # normalize assignment matrix
+ row_sums = assignments.sum(axis=1)
+ assignments = (assignments + tol) / (row_sums[:, np.newaxis] + tol)
+
+ # update centroids
+ set_labels = range(self.n_clusters)
+ # filter by labels
+ for label in set_labels:
+ filter_indices = np.where(np.array(assignments) == label)[0]
+ count_per_label = len(filter_indices)
+ if count_per_label > 0:
+ filter_xdata = np.take(self.X_train, filter_indices, axis=0)
+ # weight by the strength of membership
+ weight_by_label = np.take(assignments[:,label], filter_indices, axis=0)
+ weight_by_label_matrix = weight_by_label.reshape((count_per_label, 1))
+ weighted_filtered_xdata = np.multiply(filter_xdata, weight_by_label_matrix)
+
+ # estimate centroid
+ numerator = np.mean(weighted_filtered_xdata, axis=0) # sum the weighted inputs
+ denominator = np.sum(weight_by_label) # weight contribution across data input
+
+ centroids[label, :] = (numerator + tol) / (denominator + tol)
+ weight_list.append(centroids)
+ weight_list.pop(0)
+ iteration = iteration + 1
+ return centroids, assignments
+
+
+ def get_centroids(self):
+ r"""
+ Get the centroids
+
+ Returns
+ -------
+ centroids : array
+ The centroid matrix with dimensions (number of centroids x number of attributes).
+ """
+ return self.centroids
+
+
+ def get_assignments(self):
+ r"""
+ Get the assignment of data points into their clusters
+
+ Returns
+ -------
+ assignments : array
+ The assignments vector with dimensions (number of data).
+ """
+ assignments = self.assignments
+ if self.cluster_method == 'soft':
+ assignments = np.argmax(self.assignments, axis=1)
+ return assignments
+
+
+ def get_proba(self):
+ r"""
+ Get the probability distribution of clusters assignments
+ Note: only when doing soft-clustering
+
+ Returns
+ -------
+ assignments : array (return None if hard clustering, array otherwise)
+ The assignments vector with dimensions (number of data x number of centroids). This is the probability distribution of the membership of each data point in the cluster.
+ """
+ assignments = None
+ if self.cluster_method == 'soft':
+ assignments = self.assignments
+ return assignments

numpy_ml/tests/test_cluster.py

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+# flake8: noqa
+import numpy as np
+from sklearn import datasets
+from sklearn.cluster import KMeans as origKMeans
+from sklearn.datasets.samples_generator import make_blobs
+from sklearn.metrics.cluster import fowlkes_mallows_score
+from sklearn.metrics import davies_bouldin_score
+from numpy_ml.cluster.kmeans import KMeans
+
+def test_kmeans():
+ seed = 12345
+ np.random.seed(seed)
+ n_clusters=4
+ # loading the dataset
+ orig_num_of_samples, orig_num_of_features = 3000, 300
+ X, y_true = make_blobs(n_samples=orig_num_of_samples, centers=n_clusters, n_features = orig_num_of_features,
+ cluster_std=0.50, random_state=seed)
+
+ # K-Means scikit version (Hard clustering)
+ kmeans = origKMeans(n_clusters=n_clusters, random_state=seed).fit(X)
+ # cluster labels as gold standard
+ gold_labels = kmeans.labels_
+
+ # Test the dimensions of the parameters
+ print ("Hard Clustering")
+ km_hard = KMeans(X, cluster_method="hard", n_clusters=n_clusters)
+
+ num_of_samples, num_of_features = km_hard.get_centroids().shape
+ assert (num_of_samples, num_of_features) in [(orig_num_of_features, n_clusters), (n_clusters, orig_num_of_features)], "mismatch in assignment probability"
+
+ num_of_samples = len(km_hard.get_assignments())
+ assert (num_of_samples == orig_num_of_samples), "mismatch in assignment size"
+
+ # Comparing our clustering algorithm to the Gold standard
+ mallows_score = fowlkes_mallows_score(gold_labels, km_hard.get_assignments())
+ print("Mallow score: {} | values closer to 1 indicates better clustering".format(mallows_score))
+
+ print ("Soft Clustering")
+ # Use the default value for the beta variable
+ km_soft = KMeans(X, cluster_method="soft", n_clusters=n_clusters)
+
+ # Only call during soft clustering
+ num_of_samples, num_of_features = km_soft.get_proba().shape
+ assert (num_of_samples, num_of_features) in [(orig_num_of_samples, n_clusters), (n_clusters, orig_num_of_samples)], "mismatch in assignment probability"
+
+ num_of_samples, num_of_features = km_soft.get_centroids().shape
+ assert (num_of_samples, num_of_features) in [(orig_num_of_features, n_clusters), (n_clusters, orig_num_of_features)], "mismatch in assignment probability"
+
+ num_of_samples = len(km_soft.get_assignments())
+ assert (num_of_samples == orig_num_of_samples), "mismatch in assignment size"
+
+ # Comparing our clustering algorithm to the Gold standard
+ mallows_score = fowlkes_mallows_score(gold_labels, km_soft.get_assignments())
+ print("Mallow score: {} | values closer to 1 indicates better clustering".format(mallows_score))