# General Rough Modeling of Cluster Analysis

arXiv: https://arxiv.org/abs/2106.04683 · HTML: https://mlsanity.com/paper/2106.04683/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 17 references that are in the map.
- First posted on arXiv 2 Jun 2021.

## Built on by (most cited first, 5 of 5)

- [Rough Randomness and its Application](https://mlsanity.com/paper/2304.00005/) (2023)
- [Algebraic Semantics of Generalized RIFs](https://mlsanity.com/paper/2109.12998/) (2021)
- [Granular Generalized Variable Precision Rough Sets and Rational Approximations](https://mlsanity.com/paper/2205.14365/) (2022)
- [Granular Directed Rough Sets, Concept Organization and Soft Clustering](https://mlsanity.com/paper/2208.06623/) (2022)
- [The Representation of Meaningful Precision, and Accuracy](https://mlsanity.com/paper/2410.14721/) (2024)

## Abstract (arXiv)

In this research, a general theoretical framework for clustering is proposed over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering information in any form to be realized in a situation (and therefore in a semantics). It is well-known that of the limited number of proofs in the theory of hard and soft clustering that are known to exist, most involve statistical assumptions. Many methods seem to work because they seem to work in specific empirical practice. A new general rough method of analyzing clusterings is invented, and this opens the subject to clearer conceptions and contamination-free theoretical proofs. Numeric ideas of validation are also proposed to be replaced by those based on general rough approximation. The essence of the approach is explained in brief and supported by an example.