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 (NMF), representation learning, and adaptive reconstruction weight learning into a unified model. Specifically, NAFE performs feature and weight learning over the new robust representations of NMF for more accurate measure and representation. For nonnegative adaptive feature extraction, our NAFE first utilizes the sparsity constrained NMF to obtain the new and robust representations of the original data. To preserve the manifold structures of the learnt new representations, we also incorporate a neighborhood reconstruction error over the weight matrix for joint minimization. Note that to further improve the representation power, the weights are jointly shared in the new low-dimensional nonnegative representation space, low-dimensional nonlinear manifold space, and low-dimensional projective subspace, i.e., local neighborhood information is clearly preserved in different feature spaces so that 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 efficiently. Extensive simulations show that our formulation can deliver state-of-the-art results on several public databases for feature extraction and classification, compared with several related methods.