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This paper presents a novel, rank-constrained matrix representation combined with hypergraph spectral analysis to enable the recovery of the original subspace structures of corrupted data. Real-world data are frequently corrupted with both sparse error and noise. Our matrix decomposition model separates the low-rank, sparse error, and noise compone...
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Tensors offer a natural representation for many kinds of data frequently encountered in machine learning. Images, for example, are naturally represented as third order tensors, where the modes correspond to height, width, and channels. In particular, tensor decompositions are noted for their ability to discover multi-dimensional dependencies and pr...
Tensors offer a natural representation for many kinds of data frequently encountered in machine learning. Images, for example, are naturally represented as third order tensors, where the modes correspond to height, width, and channels. Tensor methods are noted for their ability to discover multi-dimensional dependencies, and tensor decompositions i...
Citations
... Subspace clustering method is another effective technique to cluster high-dimensional data by finding clusters from different low-dimensional spaces [15]. Hypergraph-based method maps high-dimensional data to weighted hypergraphs and implements clustering procedure exploiting graph segmentation [16]. Sparse feature-based method clusters high-dimensional data using its sparse feature directly to obtain clustering results effectively and efficiently [17]. ...
Clustering algorithm for binary data is a challenging problem in data mining and machine learning fields. While some efforts have been made to deal with clustering binary data, they lack effective methods to balance clustering quality and efficiency. To this end, we propose a hierarchical clustering algorithm for binary data based on cosine similarity (HABOC) in this paper. Firstly, we assess similarity between data objects with binary attributes using Cosine Similarity (CS). Then, the Cosine Similarity of a Set (CSS) is defined to compute similarity of a set containing multiple objects. Based on CSS, we propose the Cosine Feature Vector of a Set (CFVS) and additivity of CFVS to compress data and merge two clusters directly. We also exploit hierarchical clustering method to implement clustering, in order to avoid the sensitivity to the order of data objects and algorithm parameters. Experimental results on several UCI datasets demonstrate that HABOC outperforms existing binary data clustering algorithms.
... The potential motivation behind our NSM-TGV is that, on one hand, NSM, being an unnatural image prior, is prone to result in an salient edge image with staircase artefacts in flat regions which are to reduce the accuracy of blur kernel estimation; on the other hand, TGV, being a natural image prior, though not applicable to blind deblurring, has the potential of preserving higher-order smoothness in the homogeneous areas. With our NSM-TGV prior, a numerical scheme is derived by use of the operator splitting and ADMM (alternating direction method of multipliers) [21,22], leading to a more accurate, efficient, and robust blind deblurring algorithm. Numerous experimental results on both benchmark data and real-world blurred images prove the competitive or even better performance compared with the state of the art. ...
We focus on blind image deconvolution, which has attracted intensive attentions since Fergus et al.’s influential work in 2006. Among the current literature, the daring idea of imposing the normalized sparsity measure on blind image deblurring is a recent spotlight, which is, nevertheless, far from practical use in terms of estimating accuracy, efficiency, as well as robustness. To boost its performance, we propose a novel method via coupling the normalized sparsity measure with the total generalized variation, which, however, does not fit the blind deblurring problem. By use of operator splitting and alternating direction method of multipliers, a numerical scheme is derived, leading to a more accurate, efficient, and robust blind deblurring algorithm. Numerous blind deblurring results on both benchmark data and real-world blurred images demonstrate the competitive or even better performance compared against the state of the art.
In this paper, we propose a novel data-driven regression model for aerosol optical depth (AOD) retrieval. First, we adopt a low rank representation (LRR) model to learn a powerful representation of the spectral response. Then, graph regularization is incorporated into the LRR model to capture the local structure information and the nonlinear property of the remote-sensing data. Since it is easy to acquire the rich satellite-retrieval results, we use them as a baseline to construct the graph. Finally, the learned feature representation is feeded into support vector machine (SVM) to retrieve AOD. Experiments are conducted on two widely used data sets acquired by different sensors, and the experimental results show that the proposed method can achieve superior performance compared to the physical models and other state-of-the-art empirical models.
