Unsupervised Nonnegative Adaptive Feature Extraction for Data Representation

In this paper, we propose a novel unsupervised Nonnegative Adaptive Feature Extraction (NAFE) algorithm for data representation and classification. The formulation of NAFE integrates the sparsity constrained nonnegative matrix factorization, representation learning and adaptive reconstruction weight learning into a unified model. Specifically, NAFE performs feature and weight learning over the new representations by matrix factorization for more accurate measure and representation. For nonnegative adaptive feature extraction, NAFE firstly uses the sparsity constrained matrix factorization to obtain the new robust representations of the original data. To preserve the manifold structures of new representations, NAFE also incorporates a neighborhood reconstruction error over the weight matrix for joint minimization. Thus, the representation ability can be improved potentially by sharing the weights jointly in the new nonnegative representation subspace, nonlinear manifold subspace and the linear projective subspace, i.e., the neighborhood reconstruction relationship is clearly preserved in different feature subspaces so that more informative representations and features can be jointly obtained. To enable NAFE to extract features from new data, we also include a feature approximation error by a linear projection so that the learnt extractor can obtain features from new data directly. Extensive simulations verified the effectiveness of our method.