# Clustering with Similarity Preserving

## TL;DR

This paper introduces a novel similarity-preserving graph learning method that adaptively constructs graphs aligned with raw data similarities, enhancing clustering accuracy without separate clustering steps.

## Contribution

It proposes the first similarity-preserving, adaptive graph learning approach that unifies clustering and graph construction directly from data.

## Key findings

- Improved clustering accuracy on multiple datasets.
- Effective in both single and multiple kernel learning scenarios.
- Eliminates need for separate clustering algorithms.

## Abstract

Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the incorporation of nonlinearity. However, most existing kernel-based graph learning mechanisms is not similarity-preserving, hence leads to sub-optimal performance. To overcome this drawback, we propose a more discriminative graph learning method which can preserve the pairwise similarities between samples in an adaptive manner for the first time. Specifically, we require the learned graph be close to a kernel matrix, which serves as a measure of similarity in raw data. Moreover, the structure is adaptively tuned so that the number of connected components of the graph is exactly equal to the number of clusters. Finally, our method unifies clustering and graph learning which can directly obtain cluster indicators from the graph itself without performing further clustering step. The effectiveness of this approach is examined on both single and multiple kernel learning scenarios in several datasets.