# An effective clustering method based on data indeterminacy in neutrosophic set domain

## TL;DR

This paper introduces a novel clustering algorithm using neutrosophic set theory that effectively manages boundary and outlier points by leveraging data indeterminacy, resulting in improved clustering accuracy across various datasets.

## Contribution

The paper proposes a new data indeterminacy measure in neutrosophic set domain and integrates it into a cost function for clustering, enhancing outlier and boundary point handling.

## Key findings

- Outperforms existing clustering methods on multiple datasets
- Accurately assigns outliers to noise cluster
- Effectively handles boundary points with similar membership degrees

## Abstract

In this work, a new clustering algorithm is proposed based on neutrosophic set (NS) theory. The main contribution is to use NS to handle boundary and outlier points as challenging points of clustering methods. In the first step, a new definition of data indeterminacy (indeterminacy set) is proposed in NS domain based on density properties of data. Lower indeterminacy is assigned to data points in dense regions and vice versa. In the second step, indeterminacy set is presented for a proposed cost function in NS domain by considering a set of main clusters and a noisy cluster. In the proposed cost function, two conditions based on distance from cluster centers and value of indeterminacy, are considered for each data point. In the third step, the proposed cost function is minimized by gradient descend methods. Data points are clustered based on their membership degrees. Outlier points are assigned to noise cluster; and boundary points are assigned to main clusters with almost same membership degrees. To show the effectiveness of the proposed method, three types of datasets including diamond, UCI and image datasets are used. Results demonstrate that the proposed cost function handles boundary and outlier points with more accurate membership degrees and outperforms existing state of the art clustering methods in all datasets.