A Unified Weight Learning Paradigm for Multi-view Learning

Learning a set of weights to combine views linearly forms a series of popular schemes in multi-view learning. Three weight learning paradigms, i.e., Norm Regularization (NR), Exponential Decay (ED), and p-th Root Loss (pRL), are widely used in the literature, while the relations between them and the limiting behaviors of them are not well understood yet. In this paper, we present a Unified Paradigm (UP) that contains the aforemen-tioned three popular paradigms as special cases. Specifically, we extend the domain of hyper-parameters of NR from positive to real numbers and show this extension bridges NR, ED, and pRL. Besides, we provide detailed discussion on the weights sparsity, hyper-parameter setting, and counterintuitive lim-iting behavior of these paradigms. Further-more, we show the generality of our technique with examples in Multi-Task Learning and Fuzzy Clustering. Our results may provide in-sights to understand existing algorithms bet-ter and inspire research on new weight learn-ing schemes. Numerical results support our theoretical analysis.