Adaptive hypergraph structure regularized semi-supervised non-negative matrix factorization for image clustering

Semi-supervised non-negative matrix factorization (SNMF) is a powerful technique used in image clustering. Unlike traditional graphs, hypergraphs can capture higher-order geometric relationships among data samples. However, many existing hypergraph learning methods use a fixed hypergraph structure, which fails to dynamically optimize the hypergraph during the learning process. As a result, these methods may not accurately represent the true relationships between samples. To address this issue, this paper introduces a novel semi-supervised SNMF-based method called Adaptive Hypergraph Structure Regularized Semi-supervised Non-negative Matrix Factorization (AHS-SNMF). This method enhances the capture of high-order similarity between data samples by adaptively adjusting the hypergraph structure and iteratively improving it throughout the learning process. Additionally, we integrate labeled projection matrix with hypergraph regularization to minimize common errors found in traditional clustering methods. This approach strengthens the representation of labeled data in relation to unlabeled data, thereby boosting the model’s robustness and performance. Experimental results from comparative studies on six datasets confirm that the AHS-SNMF method significantly improves performance in semi-supervised learning tasks.