# A general model for plane-based clustering with loss function

## TL;DR

This paper introduces a comprehensive model for plane-based clustering that unifies existing methods and proposes a new loss function, with theoretical guarantees and experimental validation on artificial and real datasets.

## Contribution

The paper presents a general framework encompassing various plane-based clustering methods and introduces a novel loss function for improved data distribution capture.

## Key findings

- The model terminates in finite steps at a local or weak local optimum.
- The new loss function effectively captures data distribution.
- Experimental results verify the method's effectiveness.

## Abstract

In this paper, we propose a general model for plane-based clustering. The general model contains many existing plane-based clustering methods, e.g., k-plane clustering (kPC), proximal plane clustering (PPC), twin support vector clustering (TWSVC) and its extensions. Under this general model, one may obtain an appropriate clustering method for specific purpose. The general model is a procedure corresponding to an optimization problem, where the optimization problem minimizes the total loss of the samples. Thereinto, the loss of a sample derives from both within-cluster and between-cluster. In theory, the termination conditions are discussed, and we prove that the general model terminates in a finite number of steps at a local or weak local optimal point. Furthermore, based on this general model, we propose a plane-based clustering method by introducing a new loss function to capture the data distribution precisely. Experimental results on artificial and public available datasets verify the effectiveness of the proposed method.