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Image Clustering Using Local Discriminant Models and Global Integration

In this paper, we propose a new image clustering algorithm, referred to as clustering using local discriminant models and global integration (LDMGI). To deal with the data points sampled from a nonlinear manifold, for each data point, we construct a local clique comprising this data point and its neighboring data points. Inspired by the Fisher criterion, we use a local discriminant model for each local clique to evaluate the clustering performance of samples within the local clique. To obtain the clustering result, we further propose a unified objective function to globally integrate the local models of all the local cliques. With the unified objective function, spectral relaxation and spectral rotation are used to obtain the binary cluster indicator matrix for all the samples. We show that LDMGI shares a similar objective function with the spectral clustering (SC) algorithms, e.g., normalized cut (NCut). In contrast to NCut in which the Laplacian matrix is directly calculated based upon a Gaussian function, a new Laplacian matrix is learnt in LDMGI by exploiting both manifold structure and local discriminant information. We also prove that K-means and discriminative K-means (DisKmeans) are both special cases of LDMGI. Extensive experiments on several benchmark image datasets demonstrate the effectiveness of LDMGI. We observe in the experiments that LDMGI is more robust to algorithmic parameter, when compared with NCut. Thus, LDMGI is more appealing for the real image clustering applications in which the ground truth is generally not available for tuning algorithmic parameters.