Weight learning ways for multi-view clustering

Learning a group of weights to combine view features forms many popular schemes in multi-view clustering. The learning ways mainly include two classes: explicit and implicit. For the explicit weight learning ways, there are mainly Norm Regularization (NR) and Exponential Decay (ED). In the NR, the p-norm Norm Regularization (pNR) and Negative Entropy (NE) can be adopted. Moreover, Self-paced Learning is also included in the NR. For the implicit weight learning ways, there are mainly q-Root Loss (qRL), Logarithm Self-weighted Loss (LSL) and Capped Self-weighted Loss (CSL) and so on. Further, these implicit weight ways can be extended to a more generalized implicit weight learning framework. The above involved numerous methods are the special case. In this paper, we firstly show the explicit and implicit weight learning ways in which the multiple ways are set. Then, considering the connections among pNR, ED and qRL three paradigms, a Unified Paradigm (UP) which can represent the above three paradigms by setting different constraints is introduced. From the multiple weight learning manners, we can find that pNR, ED, NE, qRL, LSL and CSL six learning paradigms are used to learn view weights. However, the SPL is used to learn sample weights. Next, the weight sparsity, hyper-parameter setting and limiting behavior of these schemes are discussed. Finally, we conduct experiments on seven multi-view data sets. The experimental results support the theoretical analysis.