cvi 0.7.0

A Python package implementing both batch and incremental cluster validity indices (CVIs).

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Table of Contents

• Table of Contents
• Cluster Validity Indices
• Installation
• Usage
  • Quickstart
  • Detailed Usage
  • Remove and Merge
• Implemented CVIs
• History
• Acknowledgements
  • Derivation
  • Authors
  • Related Projects
  • Assets
    • Fonts
    • Icons

Cluster Validity Indices

Say you have a clustering algorithm that clusters a set of samples containing features of some kind and some dimensionality. Great! That was a lot of work, and you should feel accomplished. But how do you know that the algorithm performed well? By definition, you wouldn't have the true label belonging to each sample (if one could even exist in your context), just the label prescribed by your clustering algorithm.

Enter Cluster Validity Indices (CVIs).

CVIs are metrics of cluster partitioning when true cluster labels are unavailable. Each operates on only the information available (i.e., the provided samples of features and the labels prescribed by the clustering algorithm) and produces a metric, a number that goes up or down according to how well the CVI believes the clustering algorithm appears to, well, cluster. Clustering well in this context means correctly partitioning (i.e., separating) the data rather than prescribing too many different clusters (over partitioning) or too few (under partitioning). Every CVI itself also behaves differently in terms of the range and scale of their numbers. Furthermore, each CVI has an original batch implementation and incremental implementation that are equivalent.

The cvi Python package contains a variety of these batch and incremental CVIs.

Installation

The cvi package is listed on PyPI, so you may install the latest version with

pip install cvi

You can also specify a version to install in the usual way with

pip install cvi==v0.7.0

Alternatively, you can manually install a release from the releases page on GitHub.

Usage

Quickstart

Create a CVI object and compute the criterion value in batch with get_cvi:

# Import the library
import cvi
# Create a Calinski-Harabasz (CH) CVI object
my_cvi = cvi.CH()
# Load some data from some clustering algorithm
samples, labels = load_some_clustering_data()
# Compute the final criterion value in batch
criterion_value = my_cvi.get_cvi(samples, labels)

or do it incrementally, also with get_cvi:

# Datasets are numpy arrays
import numpy as np
# Create a container for criterion values
n_samples = len(labels)
criterion_values = np.zeros(n_samples)
# Iterate over the data
for ix in range(n_samples):
    criterion_values = my_cvi.get_cvi(samples[ix, :], labels[ix])

Users can also query the .info property of the CVI objects to obtain relevant scaling and naming information.

>>> print(my_cvi.info)
CVIInfo(name='Calinski-Harabasz', name_short='CH', index_min=0.0, index_max=inf, optimality='max')

Detailed Usage

The cvi package contains a set of implemented CVIs with batch and incremental update methods. Each CVI is a standalone stateful object inheriting from a base class CVI, and all CVI functions are object methods, such as those that update parameters and return the criterion value.

Instantiate a CVI of you choice with the default constructor:

# Import the package
import cvi
# Import numpy for some data handling
import numpy as np

# Instantiate a Calinski-Harabasz (CH) CVI object
my_cvi = cvi.CH()

CVIs are instantiated with their acronyms, with a list of all implemented CVIS being found in the Implemented CVIs section.

A batch of data is assumed to be a numpy array of samples and a numpy vector of integer labels.

# Load some data
samples, labels = my_clustering_alg(some_data)

NOTE:

The cvi package assumes the Numpy row-major convention where rows are individual samples and columns are features. A batch dataset is then [n_samples, n_features] large, and their corresponding labels are [n_samples] large.

You may compute the final criterion value with a batch update all at once with CVI.get_cvi

# Get the final criterion value in batch mode
criterion_value = my_cvi.get_cvi(samples, labels)

or you may get them incrementally with the same method, where you pass instead just a single numpy vector of features and a single integer label. The incremental methods are used automatically based upon the dimensions of the data that is passed.

# Create a container for the criterion value after each sample
n_samples = len(labels)
criterion_values = np.zeros(n_samples)

# Iterate across the data and store the criterion value over time
for ix in range(n_samples):
    sample = samples[ix, :]
    label = labels[ix]
    criterion_values[ix] = my_cvi.get_cvi(sample, label)

NOTE:

After batch initialization, additional samples may be added incrementally by passing a single sample and label to get_cvi.

Remove and Merge

An initialized CVI can remove a previously added sample or merge two existing clusters without retaining and replaying the full dataset:

# Remove a sample from its current cluster.
criterion_value = my_cvi.remove(sample, label)

# Merge every member of source_label into target_label.
criterion_value = my_cvi.merge(target_label, source_label)

Both methods update the object in place and return its new criterion value. Removing the final sample of a cluster deletes that cluster, while merge retains target_label and deletes source_label. The caller is responsible for ensuring that a removed sample belongs to the supplied label.

Add, remove, and merge are supported after either incremental or batch initialization.

Implemented CVIs

The following CVIs have been implemented as of the latest version of cvi:

• CH: Calinski-Harabasz.
• CONN: Prototype-based intra- and inter-cluster connectivity index.
• cSIL: Centroid-based Silhouette index.
• DB: Davies-Bouldin index.
• GD43: Generalized Dunn's Index 43.
• GD53: Generalized Dunn's Index 53.
• PS: Partition Separation.
• rCIP: (Renyi's) representative Cross Information Potential.
• WB: WB-index.
• XB: Xie-Beni index.

History

• 8/18/2022: Initialize project.
• 9/8/2022: First release on PyPi and initiate GitFlow.
• 8/10/2023: v0.5.1 released.
• 5/31/2024: Updated documentation.

Acknowledgements

Derivation

The incremental and batch CVI implementations in this package are largely derived from the following Julia language implementations by the same authors of this package:

• ClusterValidityIndices.jl

Authors

The principal authors of the cvi pacakge are:

• Sasha Petrenko petrenkos@mst.edu
• Nik Melton nmmz76@mst.edu

Related Projects

If this package is missing something that you need, feel free to check out some related Python cluster validity packages:

• validclust
• clusterval

Assets

Fonts

The following font is used in the logo:

• Ethnocentric Font Family

Icons

The icon for the project is taken from:

• Cluster computing icons created by IconBaandar - Flaticon (cluster-5464694)