# Low-rank Kernel Learning for Graph-based Clustering

## TL;DR

This paper introduces a novel low-rank kernel learning method for graph-based clustering that iteratively improves the graph and kernel, outperforming traditional multiple kernel learning approaches on benchmark datasets.

## Contribution

It proposes a low-rank kernel learning framework that enhances graph construction by exploiting kernel similarity and iteratively refining the kernel and graph.

## Key findings

- Outperforms existing methods on benchmark datasets
- Effectively captures kernel similarity through low-rank constraints
- Improves clustering accuracy by joint graph and kernel optimization

## Abstract

Constructing the adjacency graph is fundamental to graph-based clustering. Graph learning in kernel space has shown impressive performance on a number of benchmark data sets. However, its performance is largely determined by the chosen kernel matrix. To address this issue, the previous multiple kernel learning algorithm has been applied to learn an optimal kernel from a group of predefined kernels. This approach might be sensitive to noise and limits the representation ability of the consensus kernel. In contrast to existing methods, we propose to learn a low-rank kernel matrix which exploits the similarity nature of the kernel matrix and seeks an optimal kernel from the neighborhood of candidate kernels. By formulating graph construction and kernel learning in a unified framework, the graph and consensus kernel can be iteratively enhanced by each other. Extensive experimental results validate the efficacy of the proposed method.