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 fra...
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ISBN:
(纸本)9781509006212
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 L_1-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 L_(2,1)-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.
L1-norm maximization based Discriminant Locality Preserving Projection (DLPP-L1) is shown to be effective and robust to the outliers in given data, but DLPP-L1 is based on the vector space, so it has to convert those ...
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ISBN:
(纸本)9781509006212
L1-norm maximization based Discriminant Locality Preserving Projection (DLPP-L1) is shown to be effective and robust to the outliers in given data, but DLPP-L1 is based on the vector space, so it has to convert those 2D matrices into high-dimensional 1D vectorized representations when handing images. But such transformation usually destroys the topology structures of images pixels, which can decrease performance. We therefore propose to extend DLPP-L1 to the 2D matrix space. A two-dimensional DLPP-L1, termed 2D-DLPP-L1, is technically proposed for image feature extraction. Compared with DLPP-L1 for representation, our proposed 2D-DLPP-L1 can effectively preserve the topology structures among image pixels in addition to inheriting the robustness property against noise and outliers. Extensive simulations on real-world image datasets show that our 2D-DLPP-L1 can deliver enhanced performance over other state-of-the-arts for recognition.
We propose a new transductive label propagation method, termed Adaptive Neighborhood Propagation (Adaptive-NP) by joint L2,1-norm regularized sparse coding, for semi-supervised classification. To make the predicted so...
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ISBN:
(纸本)9781509054749
We propose a new transductive label propagation method, termed Adaptive Neighborhood Propagation (Adaptive-NP) by joint L2,1-norm regularized sparse coding, for semi-supervised classification. To make the predicted soft labels more accurate for predicting the labels of samples and to avoid the tricky process of choosing the optimal neighborhood size or kernel width for graph construction, Adaptive-NP seamlessly integrates sparse coding and neighborhood propagation into a unified framework. That is, the sparse reconstruction error and classification error are combined for joint minimization, which clearly differs from traditional methods that explicitly separate graph construction and label propagation into independent steps, which may result in inaccurate predictions. Note that our Adaptive-NP alternately optimize the sparse codes and soft labels matrices, where the sparse codes are used as adaptive weights for neighborhood propagation at each iteration, so the tricky process of determining neighborhood size or kernel width is avoided. Besides, for enhancing sparse coding, we use the L2,1-norm constraint on the sparse coding coefficients and the reconstruction error at the same time for delivering more accurate and robust representations. Extensive simulations show that our model can deliver state-of-the-art performances on several public datasets for classification.
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