Layer-wise normalized deep incomplete multiview nonnegative matrix factorization

Abstract

Deep (semi-)nonnegative matrix factorization based models have demonstrated promising performance in the multiview clustering tasks. However, they are all developed upon the assumption that the multiview datasets are complete in all views, and need to be pre-trained layer-by-layer to get reasonable results. Addressing these issues, an algorithm named layer-wise normalized deep incomplete multiview nonnegative matrix factorization (LWNdimNMF) is presented in this paper to tackle the multiview clustering problem with arbitrary missing views. Specifically, a novel layer-wise normalization strategy is developed to constrain the value distribution of the factor matrix in each layer to ensure the numerical stability of the model and make it robust to the initialization. Another benefit of this strategy is that it can effectively depress the objective function value and make the model fit data well. An instance selection alignment is adopted to fuse the incomplete multiple views by aligning the paired instances. To discover the high-order geometrical information in each incomplete view, a hypergraph regularization is incorporated into the proposed model. An effective iterative optimization algorithm based on the multiplicative updating rules is designed to solve the minimizing problem. Extensive experiments are conducted to evaluate the effectiveness of the proposed model by comparing with several state-of-the-art (SOTA) incomplete multiview clustering (IMC) methods on ten real-world multiview datasets. The source code is available at: https://github.com/GuoshengCui/LWNdimNMF.