Spectral Perturbation Meets Incomplete Multi-view Data

Beyond existing multi-view clustering, this paper studies a more realistic clustering scenario, referred to as incomplete multi-view clustering, where a number of data instances are missing in certain views. To tackle this problem, we explore spectral perturbation theory. In this work, we show a strong link between perturbation risk bounds and incomplete multi-view clustering. That is, as the similarity matrix fed into spectral clustering is a quantity bounded in magnitude O(1), we transfer the missing problem from data to similarity and tailor a matrix completion method for incomplete similarity matrix. Moreover, we show that the minimization of perturbation risk bounds among different views maximizes the final fusion result across all views. This provides a solid fusion criteria for multi-view data. We motivate and propose a Perturbation-oriented Incomplete multi-view Clustering (PIC) method. Experimental results demonstrate the effectiveness of the proposed method.Comment: to appear in IJCAI 201

SA-Net: A deep spectral analysis network for image clustering

Although supervised deep representation learning has attracted enormous attentions across areas of pattern recognition and computer vision, little progress has been made towards unsupervised deep representation learning for image clustering. In this paper, we propose a deep spectral analysis network for unsupervised representation learning and image clustering. While spectral analysis is established with solid theoretical foundations and has been widely applied to unsupervised data mining, its essential weakness lies in the fact that it is difficult to construct a proper affinity matrix and determine the involving Laplacian matrix for a given dataset. In this paper, we propose a SA-Net to overcome these weaknesses and achieve improved image clustering by extending the spectral analysis procedure into a deep learning framework with multiple layers. The SA-Net has the capability to learn deep representations and reveal deep correlations among data samples. Compared with the existing spectral analysis, the SA-Net achieves two advantages: (i) Given the fact that one spectral analysis procedure can only deal with one subset of the given dataset, our proposed SA-Net elegantly integrates multiple parallel and consecutive spectral analysis procedures together to enable interactive learning across different units towards a coordinated clustering model; (ii) Our SA-Net can identify the local similarities among different images at patch level and hence achieves a higher level of robustness against occlusions. Extensive experiments on a number of popular datasets support that our proposed SA-Net outperforms 11 benchmarks across a number of image clustering applications.Comment: arXiv admin note: text overlap with arXiv:2009.0523