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Preserving projection-based methods are good for finding the manifold structure embedded in data. As they use the Euclidean distance as a metric, which is sensitive to noise and outliers in data, nuclear norm-based 2D locality preserving projection (NN-2DLPP) is thus proposed to improve the robustness of 2DLPP. However, NN-2DLPP does not consider the discriminant ability of data. In order to improve the discriminant ability of preserving projection methods, in this paper, we use preserving projection learning with structurally incoherence of data and propose structurally incoherent low-rank 2DLPP (SILR-2DLPP) for image classification. This approach provides a discriminative representation of preserving projection learning by recovering the distinct different classes of the data. SILR-2DLPP searches the optimal subspace and low-rank representation simultaneously. We further extend SILR-2DLPP to a kernel case and propose kernel SILR-2DLPP (KSILR-2DLPP) to obtain a nonlinear representation. The theoretical analysis including the convergence and computational complexity of SILR-2DLPP are presented. To verify the performance of SILR-2DLPP and KSILR-2DLPP, six well-known image databases were used in the experiments. The experimental results show that the proposed methods are superior to the previous preserving projection methods for image classification. [ABSTRACT FROM AUTHOR]

The codebook model has been developed as an effective means for image classification. However, the inherent operation of assigning visual words to image feature vectors in traditional codebook approaches causes serious ambiguities in image classification. In particular, the nearest word may not be the best fit to a feature, and multiple words may be equally appropriate for one specific feature. To resolve these ambiguities, we propose a novel visual codebook model based on the n- dimensional fuzzy geometry ( n -D FG) theory, where all visual words and features are modeled as fuzzy points in the n -D FG space, and appropriate uncertainty is introduced to each fuzzy point to enhance the representation capacity. This n -D FG-codebook model not only inherits advantages from the fuzzy set theory, but also facilitates the analysis and determination of the relationship between visual words and features in geometric form. By explicitly taking into account the ambiguities, we propose a novel measure of similarity between the visual words and fuzzy features. Following the proposed codebook model and the novel similarity measure, we develop two useful image classification algorithms by modifying popular image coding algorithms (i.e. SPM and LLC). Finally, experimental results demonstrate that the classification accuracy of the proposed algorithms is dramatically improved for a standard large-scale image database. For example, with a codebook size of 256, the proposed algorithms achieve similar performance as traditional algorithms with a codebook size of 1024, indicating that the proposed algorithms reduce the computational cost by 75% while achieving almost identical classification accuracy to traditional algorithms. Thus, the proposed algorithms represent a more efficient and appropriate scheme for big image data. [ABSTRACT FROM AUTHOR]