VIASCKDE — PyPI README

## Motivation

VIASCKDE Index is 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.

## Installation

    pip install viasckde

## Quick Usage

    from viasckde import viasckde_score

    # X: 2D or n-D data array (numpy-like)
    # labels: array-like cluster labels
    score = viasckde_score(X, labels)
    print("VIASCKDE Score:", score)

## Concept

In non-spherical clusters the distance from a point to its nearest neighbor within the same cluster is often more meaningful than the distance to a cluster centroid. VIASCKDE computes compactness and separation by using distances to the closest points inside and outside a point's cluster, producing an index robust to arbitrary shapes.

Compactness and separation computed at point level (example).

## Parameters

- X: Dataset, `X = {x₁, x₂, …, xₙ} ⊂ ℝᵈ`
- labels: Predicted cluster labels (array-like)
- kernel (optional): KDE kernel, default `'gaussian'`. Options: `'tophat'`, `'epanechnikov'`, `'exponential'`, `'linear'`, `'cosine'`.
- bandwidth (optional): KDE bandwidth (default `0.05`).

Recommended: Gaussian kernel and bandwidth = `0.05` based on experiments.

## Output Range

The VIASCKDE score is in `[-1, +1]`, where +1 is best and -1 is worst.

## Example Visualizations

## Dependencies

VIASCKDE uses Kernel Density Estimation. Install required package:

    pip install KernelDensity

Make sure you have `numpy` and standard scientific stack available (NumPy, SciPy, scikit-learn as needed).

## Citation

If you use VIASCKDE in your research, please cite:

> 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 (adjust if your project uses a different license).