Structured Graph Learning for Clustering and Semi-supervised Classification

TL;DR

This paper introduces a graph learning framework that captures both local and global data structures, improving clustering and semi-supervised classification performance by ensuring the learned graph has a specified number of connected components.

Contribution

The proposed method uniquely incorporates rank constraints to produce graphs with a fixed number of connected components, enhancing clustering and classification accuracy.

Findings

Outperforms state-of-the-art methods in clustering tasks

Achieves better semi-supervised classification accuracy

Ensures the learned graph has exactly c connected components

Abstract

Graphs have become increasingly popular in modeling structures and interactions in a wide variety of problems during the last decade. Graph-based clustering and semi-supervised classification techniques have shown impressive performance. This paper proposes a graph learning framework to preserve both the local and global structure of data. Specifically, our method uses the self-expressiveness of samples to capture the global structure and adaptive neighbor approach to respect the local structure. Furthermore, most existing graph-based methods conduct clustering and semi-supervised classification on the graph learned from the original data matrix, which doesn't have explicit cluster structure, thus they might not achieve the optimal performance. By considering rank constraint, the achieved graph will have exactly $c$ connected components if there are $c$ clusters or classes. As a byproduct of this, graph learning and label inference are jointly and iteratively implemented in a principled way. Theoretically, we show that our model is equivalent to a combination of kernel k-means and k-means methods under certain condition. Extensive experiments on clustering and semi-supervised classification demonstrate that the proposed method outperforms other state-of-the-art methods.