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
• 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

python pip install cvi

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

python pip install cvi==v0.6.0

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:

```python

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 = loadsomeclustering_data()

Compute the final criterion value in batch

criterionvalue = mycvi.get_cvi(samples, labels) ```

or do it incrementally, also with get_cvi:

```python

Datasets are numpy arrays

import numpy as np

Create a container for criterion values

nsamples = len(labels) criterionvalues = np.zeros(n_samples)

Iterate over the data

for ix in range(nsamples): criterionvalues = mycvi.getcvi(samples[ix, :], labels[ix]) ```

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:

```python

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.

```python

Load some data

samples, labels = myclusteringalg(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

```python

Get the final criterion value in batch mode

criterionvalue = mycvi.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.

```python

Create a container for the criterion value after each sample

nsamples = len(labels) criterionvalues = np.zeros(n_samples)

Iterate across the data and store the criterion value over time

for ix in range(nsamples): sample = samples[ix, :] label = labels[ix] criterionvalues[ix] = mycvi.getcvi(sample, label) ```

NOTE:

Currently only using either batch or incremental methods is supported; switching from batch to incremental updates with the same is not yet implemented.

Implemented CVIs

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

• CH: Calinski-Harabasz
• cSIL: Centroid-based Silhouette
• DB: Davies-Bouldin
• 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.

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)