Abstract: When some data labels are known, the non-negative matrix factorization ( NMF ) method canbe extended to a semi-supervised learning apprach , which enhances the discriminative power of the newdata representation and improves clustering perfommance. In this paper, we propose a graph regularizeddiscriminative non-negative matrix factorization method based on low-dimensional representation scaling(SGDNMF'). The core idea is to scale the low-dimensional representations of labeled data points and align them with the vectors encoding their labels. We formulate the mathematical model for this method.provide an iterative updating algorithm for solving the model, and analyze the convergence of the algo.rithm. We conduet clustering experiments on three real-world datasets and compare it with other state-of.the-art methods. The experimental results demonstrate the feasibility and efficieney of our method.

Key words: semi-supervised learning, clustering, non-negative matrix factorization, diseriminative con-straints