Graph Construction with Label Information for Semi-Supervised Learning

TL;DR

This paper introduces a novel semi-supervised graph learning method that incorporates label information during graph construction, improving the capture of data structure and enhancing learning performance.

Contribution

It proposes a general framework to embed label information into graph learning, demonstrated with Low-Rank Representation, applicable to various self-representation methods.

Findings

Improved data structure capture in synthetic and real datasets.

Enhanced semi-supervised learning performance.

Convex optimization problem solved efficiently.

Abstract

In the literature, most existing graph-based semi-supervised learning (SSL) methods only use the label information of observed samples in the label propagation stage, while ignoring such valuable information when learning the graph. In this paper, we argue that it is beneficial to consider the label information in the graph learning stage. Specifically, by enforcing the weight of edges between labeled samples of different classes to be zero, we explicitly incorporate the label information into the state-of-the-art graph learning methods, such as the Low-Rank Representation (LRR), and propose a novel semi-supervised graph learning method called Semi-Supervised Low-Rank Representation (SSLRR). This results in a convex optimization problem with linear constraints, which can be solved by the linearized alternating direction method. Though we take LRR as an example, our proposed method is in fact very general and can be applied to any self-representation graph learning methods. Experiment results on both synthetic and real datasets demonstrate that the proposed graph learning method can better capture the global geometric structure of the data, and therefore is more effective for semi-supervised learning tasks.