Spectral clustering is an elegant and powerful approach for clustering. However, the underlying eigendecomposition takes cubic time and quadratic space w.r.t. the data set size. These can be reduced by the Nyström method which samples only a subset of columns from the matrix. However, the manipulation and storage of these sampled columns can still be expensive when the data set is large. In this paper, we propose a time-and space-efficient spectral clustering algorithm which can scale to very large data sets. A general procedure to orthogonalize the approximated eigenvectors is also proposed. Extensive spectral clustering experiments on a number of data sets, ranging in size from a few thousands to several millions, demonstrate the accuracy and scalability of the proposed approach. We further apply it to the task of image segmentation. For images with more than 10 millions pixels, this algorithm can obtain the eigenvectors in 1 minute on a single machine.

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Abstract. Visual dictionary learning and base (binary) classifier training are two basic problems for the recently most popular image categorization framework, which is based on the bag-of-visual-terms (BOV) models and multiclass SVM classifiers. In this paper, we study new algorithms to improve performance of this framework from these two aspects. Typically SVM classifiers are trained with dictionaries fixed, and as a result the traditional loss function can only be minimized with respect to hyperplane parameters (w and b). We propose a novel loss function for a binary classifier, which links the hinge-loss term with dictionary learning. By doing so, we can further optimize the loss function with respect to the dictionary parameters. Thus, this framework is able to further increase margins of binary classifiers, and consequently decrease the error bound of the aggregated classifier. On two benchmark dataset, Graz [1] and the fifteen scene category dataset [2], our experiment results significantly outperformed state-of-the-art works.

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Dictionary generation is a core technique of the bag-ofvisual-words (BOV) models