Semi-Supervised Clustering via Cannot Link Relationship for Multiview Data

Abstract

Due to the diversity of data modalities, the research interest of multi-view clustering is gradually increasing, in the field of large-data analytics, particularly in clustering. However, the greater part of current multi-view clustering methods is mainly in view of unsupervised learning, which leads to unpredictable results and algorithmic instability. Besides, they ignore the diversity of graphs, which is not desirable in practical applications, because the characteristic properties of each view are different. To solve these problems, inspired by the outstanding performance of semi-supervised learning in machine learning, we propose a valid semi-supervised multi-view spectral clustering algorithm. We use the pre-set labels as prior knowledge to obtain the overall distribution of the remaining unlabeled data. Tensor minimization Schatten <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> -norm is utilized to mine the mutual information hidden in multiple views. Meanwhile, we also use the cannot-link as another semi-supervised constraint to update the graph. Our proposed algorithm is generally 5%-10% better than the comparison algorithms in view of the experimental results on five datasets, and our algorithm is relatively fast with the computational complexity of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {O}({T({n^{2}}\log (n) + {n^{2}} + {u^{2}}l + ulc + uc\log (c))})$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> denotes the number of iterations and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$u$ </tex-math></inline-formula> represent the number of samples, the number of labeled and unlabeled samples, respectively, which shows that our proposed method has broad application prospects.