Semi-supervised non-negative matrix factorization with structure preserving for image clustering.

Semi-supervised learning methods have wide applications thanks to the reasonable utilization for a part of label information of data. In recent years, non-negative matrix factorization (NMF) has received considerable attention because of its interpretability and practicality. Based on the advantages of semi-supervised learning and NMF, many semi-supervised NMF methods have been presented. However, these existing semi-supervised NMF methods construct a label matrix only containing elements 1 and 0 to represent the labeled data and further construct a label regularization, which neglects an intrinsic structure of NMF. To address the deficiency, in this paper, we propose a novel semi-supervised NMF method with structure preserving. Specifically, we first construct a new label matrix with weights and further construct a label constraint regularizer to both utilize the label information and maintain the intrinsic structure of NMF. Then, based on the label constraint regularizer, the basis images of labeled data are extracted for monitoring and modifying the basis images learning of all data by establishing a basis regularizer. Finally, incorporating the label constraint regularizer and the basis regularizer into NMF, we propose a new semi-supervised NMF method. To solve the optimization problem, a multiplicative updating algorithm is developed. The proposed method is applied to image clustering to test its performance. Experimental results on eight data sets demonstrate the effectiveness of the proposed method in contrast with state-of-the-art unsupervised and semi-supervised algorithms.