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 aforementioned 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 limiting behavior of these paradigms. Furthermore, we show the generality of our technique with examples in Multi-Task Learning and Fuzzy Clustering. Our results may provide insights to understand existing algorithms better and inspire research on new weight learning schemes. Numerical results support our theoretical analysis.