Size Constrained Clustering Solver

Implementation of Size Constrained Clustering. Size constrained clustering can be treated as an optimization problem. Details could be found in a set of reference paper.

Installation

Requirement Python >= 3.6, Numpy >= 1.13, Cython >= 0.29

• install from PyPI

pip install size-constrained-clustering

Methods

• Fuzzy C-means Algorithm: Similar to KMeans, but use membership probability, not 0 or 1
• Same Size Contrained KMeans Heuristics: Use Heuristics methods to reach same size clustering
• Same Size Contrained KMeans Inspired by Minimum Cost Flow Problem
• Minimum and Maximum Size Constrained KMeans Inspired by Minimum Cost Flow Problem
• Deterministic Annealling Algorithm: Input target cluster distribution, return correspondent clusters
• Shrinkage Clustering: base algorithm and minimum size constraints

Usage:

# setup
from size_constrained_clustering import fcm, equal, minmax, shrinkage
# by default it is euclidean distance, but can select others
from sklearn.metrics.pairwise import haversine_distances
import numpy as np

Fuzzy C-means

n_samples = 2000
n_clusters = 4
centers = [(-5, -5), (0, 0), (5, 5), (7, 10)]
X, _ = make_blobs(n_samples=n_samples, n_features=2, cluster_std=1.0,
                    centers=centers, shuffle=False, random_state=42)
model = fcm.FCM(n_clusters)
# use other distance function: e.g. haversine distance
# model = fcm.FCM(n_clusters, distance_func=haversine_distances)
model.fit(X)
centers = model.cluster_centers_
labels = model.labels_

Equal Size Constraint

n_samples = 2000
n_clusters = 3
X = np.random.rand(n_samples, 2)
# use minimum cost flow framework to solve
model = equal.SameSizeKMeansMinCostFlow(n_clusters)
# use heuristics method to solve
model = equal.SameSizeKMeansHeuristics(n_clusters)
model.fit(X)
centers = model.cluster_centers_
labels = model.labels_

Cluster size: 667, 667 and 666 in the figure above.

Minimum and Maximum Size Constraint

n_samples = 2000
n_clusters = 3
X = np.random.rand(n_samples, 2)
model = minmax.MinMaxKMeansMinCostFlow(n_clusters, size_min=400,   size_max=800)
model.fit(X)
centers = model.cluster_centers_
labels = model.labels_

Cluster size: 753, 645 and 602 in the figure above.

Deterministic Annealing

n_samples = 2000
n_clusters = 3
X = np.random.rand(n_samples, 2)
# distribution is the distribution of cluster sizes
model = da.DeterministicAnnealing(n_clusters, distribution=[0.1, 0.6, 0.3])
model.fit(X)
centers = model.cluster_centers_
labels = model.labels_

Cluster size: 1200, 600 and 200 in the figure above, corresponding to distribution [0.6, 0.3, 0.1]

Shrinkage Clustering

The result might be not available.

n_samples = 1000
n_clusters = 4
centers = [(-5, -5), (0, 0), (5, 5), (7, 10)]
X, _ = make_blobs(n_samples=n_samples, n_features=2, cluster_std=1.0, centers=centers, shuffle=False, random_state=42)

model = shrinkage.Shrinkage(n_clusters, size_min=100)
model.fit(X)
centers = model.cluster_centers_
labels = model.labels_

Copyright

Copyright (c) 2020 Jing Wang. Released under the MIT License.

Third-party copyright in this distribution is noted where applicable.

Reference

• Clustering with Capacity and Size Constraints: A Deterministic Approach
• Deterministic Annealing, Clustering and Optimization
• Deterministic Annealing, Constrained Clustering, and Opthiieation
• Shrinkage Clustering
• Clustering with size constraints
• Data Clustering with Cluster Size Constraints Using a Modified k-means Algorithm
• KMeans Constrained Clustering Inspired by Minimum Cost Flow Problem
• Same Size Kmeans Heuristics Methods
• Google's Operations Research tools's SimpleMinCostFlow
• Cluster KMeans Constrained