A game model for semi-supervised subspace clustering with dynamic affinity and label learning

Abstract

With the aid of partial supervised information, semi-supervised subspace clustering methods aim to obtain affinity matrices directly derived from raw data, and then those affinity matrices are utilized to get assignment matrices. These affinity matrices are susceptible to disturbances such as noise and outliers, which could significantly impact their quality. To mitigate this, it becomes essential to dynamically update the affinity matrix using the clustering result, reducing the high dependency on raw data. This paper presents a Game Model for Semi-supervised Subspace Clustering (GMSSC). The first submodule of GMSSC utilizes a Graph Convolutional Network to learn a mapping from raw data to the assignment matrix with the assistance of the affinity matrix. The second submodule constructs a semi-supervised self-expressive model to learn a discriminative affinity matrix. By integrating these submodules into a game model, GMSSC achieves a Nash Equilibrium during adversarial training, resulting in stable and robust affinity and assignment matrices. Additionally, we propose an iterative algorithm based on data-driven and model-driven approaches to solve the model. Experimental results on four open real-world datasets demonstrate that the proposed method not only achieves elegant results but also outperforms state-of-the-art semi-supervised subspace clustering algorithms.