viasckde 0.1.6

VIASCKDE: internal cluster validity index (KDE-weighted compactness & separation)

VIASCKDE Index

VIASCKDE is a novel internal cluster validity index for arbitrary-shaped clusters based on Kernel Density Estimation (KDE).

---

Motivation

The VIASCKDE Index was proposed in:

"VIASCKDE Index: A Novel Internal Cluster Validity Index for Arbitrary Shaped Clusters Based on Kernel Density Estimation"
by Ali Şenol

The index evaluates clustering quality regardless of cluster shape by computing compactness and separation at the point level instead of relying on cluster centroids. This makes it robust for non-spherical and arbitrarily shaped clusters.

---

Installation

pip install viasckde

Usage

from viasckde import viasckde_score


score = viasckde_score(X, labels)
print("VIASCKDE Score:", score)

VIASCKDE index needs four parameters (two are optional) that are:
    # X: your data array (NumPy-like)
	# labels: predicted cluster labels
    # kernel (optional): selected kernel method, krnl='gaussian' is default kernel. 
But it could be 'tophat', 'epanechnikov', 'exponential', 'linear', or 'cosine'.
    # bandwidth(optional): the bandwidth value of kernel density estimation. b_width=0.05 
is the default value. But it could be changed.

Concept

In non-spherical clusters, the distance from a point to the nearest neighbor in the same cluster is often more meaningful than the distance to the cluster centroid. VIASCKDE computes:

Compactness: distance to the closest point in the same cluster

Separation: distance to the closest point in a different cluster

This point-level computation ensures realistic evaluation of clusters regardless of their shape.

Output Range

VIASCKDE returns a score in [-1, +1]:

+1: best clustering

-1: worst clustering

Citation

Ali Şenol, "VIASCKDE Index: A Novel Internal Cluster Validity Index for Arbitrary-Shaped 
Clusters Based on the Kernel Density Estimation", Computational Intelligence and 
Neuroscience, vol. 2022, Article ID 4059302, 20 pages, 2022. 
https://doi.org/10.1155/2022/4059302

BibTeX

@article{csenol2022viasckde,
  title={VIASCKDE Index: A Novel Internal Cluster Validity Index for Arbitrary-Shaped Clusters Based on the Kernel Density Estimation},
  author={{\c{S}}enol, Ali},
  journal={Computational Intelligence and Neuroscience},
  volume={2022},
  number={1},
  pages={4059302},
  year={2022},
  publisher={Wiley Online Library}
}

License & Author

Author: Assoc. Prof. Dr. Ali Şenol
Computer Engineering Department, Tarsus University

License: MIT