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132 changes: 35 additions & 97 deletions DBCV/DBCV.py
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Original file line number Diff line number Diff line change
Expand Up @@ -7,6 +7,7 @@
Society for Industrial and Applied Mathematics, 2014.
"""

from functools import reduce, partial
import numpy as np
from scipy.spatial.distance import euclidean, cdist
from scipy.sparse.csgraph import minimum_spanning_tree
Expand All @@ -19,10 +20,12 @@ def DBCV(X, labels, dist_function=euclidean):

Args:
X (np.ndarray): ndarray with dimensions [n_samples, n_features]
data to check validity of clustering
data to check validity of clustering, or a precomputed distances
matrix with dimensins [n_samples, n_samples]
labels (np.array): clustering assignments for data X
dist_dunction (func): function to determine distance between objects
func args must be [np.array, np.array] where each array is a point
dist_dunction (func or int): function to determine distance between objects
func args must be [np.array, np.array] where each array is a point.
If X is a precomputed distances matrix, pass an int of number of features.

Returns: cluster_validity (float)
score in range[-1, 1] indicating validity of clustering assignments
Expand All @@ -33,96 +36,50 @@ def DBCV(X, labels, dist_function=euclidean):
return cluster_validity


def _core_dist(point, neighbors, dist_function):
"""
Computes the core distance of a point.
Core distance is the inverse density of an object.

Args:
point (np.array): array of dimensions (n_features,)
point to compute core distance of
neighbors (np.ndarray): array of dimensions (n_neighbors, n_features):
array of all other points in object class
dist_dunction (func): function to determine distance between objects
func args must be [np.array, np.array] where each array is a point

Returns: core_dist (float)
inverse density of point
"""
n_features = np.shape(point)[0]
n_neighbors = np.shape(neighbors)[0]

distance_vector = cdist(point.reshape(1, -1), neighbors)
distance_vector = distance_vector[distance_vector != 0]
numerator = ((1/distance_vector)**n_features).sum()
core_dist = (numerator / (n_neighbors - 1)) ** (-1/n_features)
return core_dist


def _mutual_reachability_dist(point_i, point_j, neighbors_i,
neighbors_j, dist_function):
""".
Computes the mutual reachability distance between points

Args:
point_i (np.array): array of dimensions (n_features,)
point i to compare to point j
point_j (np.array): array of dimensions (n_features,)
point i to compare to point i
neighbors_i (np.ndarray): array of dims (n_neighbors, n_features):
array of all other points in object class of point i
neighbors_j (np.ndarray): array of dims (n_neighbors, n_features):
array of all other points in object class of point j
dist_dunction (func): function to determine distance between objects
func args must be [np.array, np.array] where each array is a point

Returns: mutual_reachability (float)
mutual reachability between points i and j

"""
core_dist_i = _core_dist(point_i, neighbors_i, dist_function)
core_dist_j = _core_dist(point_j, neighbors_j, dist_function)
dist = dist_function(point_i, point_j)
mutual_reachability = np.max([core_dist_i, core_dist_j, dist])
return mutual_reachability


def _mutual_reach_dist_graph(X, labels, dist_function):
"""
Computes the mutual reach distance complete graph.
Graph of all pair-wise mutual reachability distances between points

Args:
X (np.ndarray): ndarray with dimensions [n_samples, n_features]
data to check validity of clustering
data to check validity of clustering or precomputed distances
labels (np.array): clustering assignments for data X
dist_dunction (func): function to determine distance between objects
func args must be [np.array, np.array] where each array is a point
func args must be [np.array, np.array] where each array is a point.
If X is a distance matrix, pass an int of number of features.

Returns: graph (np.ndarray)
array of dimensions (n_samples, n_samples)
Graph of all pair-wise mutual reachability distances between points.

"""
n_samples = np.shape(X)[0]
graph = []
counter = 0
for row in range(n_samples):
graph_row = []
for col in range(n_samples):
point_i = X[row]
point_j = X[col]
class_i = labels[row]
class_j = labels[col]
members_i = _get_label_members(X, labels, class_i)
members_j = _get_label_members(X, labels, class_j)
dist = _mutual_reachability_dist(point_i, point_j,
members_i, members_j,
dist_function)
graph_row.append(dist)
counter += 1
graph.append(graph_row)
graph = np.array(graph)
if isinstance(dist_function, int):
n_samples = np.shape(X)[0]
n_features = dist_function
dists = X
graph = np.empty_like(X)
else:
n_samples = np.shape(X)[0]
n_features = np.shape(X)[1]
dists = cdist(X, X, dist_function)
# If we're calculating the distances ourselves, might as well reuse the array for later
graph = dists

core_dists = np.empty(n_samples)
for label in np.unique(labels):
mask = labels == label
distance_vectors = dists[mask, :][:, mask]
n_neighbors = distance_vectors.shape[0]
z = distance_vectors == 0
distance_vectors[z] = np.nan
numerator = np.nansum((1/distance_vectors)**n_features, axis=1)
cluster_core_dists = (numerator / (n_neighbors - 1)) ** (-1/n_features)
core_dists[mask] = cluster_core_dists

distances = np.broadcast_arrays(dists, core_dists[:, np.newaxis], core_dists[np.newaxis, :])
reduce(partial(np.maximum, out=graph), distances)

return graph


Expand Down Expand Up @@ -238,22 +195,3 @@ def _clustering_validity_index(MST, labels):
cluster_validity = _cluster_validity_index(MST, labels, label)
validity_index += fraction * cluster_validity
return validity_index


def _get_label_members(X, labels, cluster):
"""
Helper function to get samples of a specified cluster.

Args:
X (np.ndarray): ndarray with dimensions [n_samples, n_features]
data to check validity of clustering
labels (np.array): clustering assignments for data X
cluster (int): cluster of interest

Returns: members (np.ndarray)
array of dimensions (n_samples, n_features) of samples of the
specified cluster.
"""
indices = np.where(labels == cluster)[0]
members = X[indices]
return members