Robust Neighborhood Preserving Projection by Nuclear/L2,1-Norm Regularization for Image Feature Extraction

We propose two nuclear- and L2,1-norm regularized 2D neighborhood preserving projection (2DNPP) methods for extracting representative 2D image features. 2DNPP extracts neighborhood preserving features by minimizing a Frobenius norm-based reconstruction error that is very sensitive noise and outliers in given data. To make the distance metric more reliable and robust, and encode the neighborhood reconstruction error more accurately, we minimize the nuclear- and L2,1-norm-based reconstruction error, respectively and measure it over each image. Technically, we propose two enhanced variants of 2DNPP, nuclear-norm-based 2DNPP and sparse reconstruction-based 2DNPP. Besides, to optimize the projection for more promising feature extraction, we also add the nuclear- and sparse L2,1-norm constraints on it accordingly, where L2,1-norm ensures the projection to be sparse in rows so that discriminative features are learnt in the latent subspace and the nuclear-norm ensures the low-rank property of features by projecting data into their respective subspaces. By fully considering the neighborhood preserving power, using more reliable and robust distance metric, and imposing the low-rank or sparse constraints on projections at the same time, our methods can outperform related state-of-the-arts in a variety of simulation settings.

COST-SENSITIVE MULTI-VIEW LEARNING MACHINE

Multi-view learning aims to effectively learn from data represented by multiple independent sets of attributes, where each set is taken as one view of the original data. In real-world application, each view should be acquired in unequal cost. Taking web-page classification for example, it is cheaper to get the words on itself (view one) than to get the words contained in anchor texts of inbound hyper-links (view two). However, almost all the existing multi-view learning does not consider the cost of acquiring the views or the cost of evaluating them. In this paper, we support that different views should adopt different representations and lead to different acquisition cost. Thus we develop a new view-dependent cost different from the existing both class-dependent cost and example-dependent cost. To this end, we generalize the framework of multi-view learning with the cost-sensitive technique and further propose a Cost-sensitive Multi-View Learning Machine named CMVLM for short. In implementation, we take into account and measure both the acquisition cost and the discriminant scatter of each view. Then through eliminating the useless views with a predefined threshold, we use the reserved views to train the final classifier. The experimental results on a broad range of data sets including the benchmark UCI, image, and bioinformatics data sets validate that the proposed algorithm can effectively reduce the total cost and have a competitive even better classification performance. The contributions of this paper are that: (1) first proposing a view-dependent cost; (2) establishing a cost-sensitive multi-view learning framework; (3) developing a wrapper technique that is universal to most multiple kernel based classifier.