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Joint nuclear-norm nonlinear Manifold Learning and robust Classification by linear embedding

We propose a Joint nuclear norm based nonlinear Manifold Learning through linear embedding with Classification, called JMLC. By including a feature approximation error into the existing nonlinear manifold learning framework to correlate manifold features with embedded features by a linear projection, the learnt projection can handle the outside points efficiently by embedding. Besides, to encode the neighborhood reconstruction error in manifold learning part, we apply a more reliable nuclear norm based distance metric, since nuclear norm is proved to be more reliable than both L1-norm and Frobenius norm. To make learnt nonlinear features be optimal for classification so that the accuracy can be enhanced, we also minimize a robust L2,1-norm based regressive classification error over the embedded manifold features, which ensures the classification process to be robust to noise and outliers in data. Based on performing joint manifold learning and classification alternately, our JMLC can obtain a low-dimensional embedding, a linear projection and a multi-class classifier simultaneously. Extensive results demonstrate the validity of our proposed algorithm for feature extraction and robust classification, compared with other related models.