Adaptive Transition Probability Matrix Learning for Multiview Spectral Clustering

Yongyong Chen, Xiaolin Xiao, Zhongyun Hua, Yicong Zhou

Abstract: Multiview clustering as an important unsupervised method has been gathering a great deal of attention. However, most multiview clustering methods exploit the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">self-representation property</i> to capture the relationship among data, resulting in high computation cost in calculating the self-representation coefficients. In addition, they usually employ different regularizers to learn the representation tensor or matrix from which a transition probability matrix is constructed in a separate step, such as the one proposed by Wu <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> . Thus, an optimal transition probability matrix cannot be guaranteed. To solve these issues, we propose a unified model for multiview spectral clustering by directly learning an adaptive transition probability matrix (MCA <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> M), rather than an individual representation matrix of each view. Different from the one proposed by Wu <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , MCA <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> M utilizes the one-step strategy to directly learn the transition probability matrix under the robust principal component analysis framework. Unlike existing methods using the absolute symmetrization operation to guarantee the nonnegativity and symmetry of the affinity matrix, the transition probability matrix learned from MCA <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> M is nonnegative and symmetric without any postprocessing. An alternating optimization algorithm is designed based on the efficient alternating direction method of multipliers. Extensive experiments on several real-world databases demonstrate that the proposed method outperforms the state-of-the-art methods.