Low-Rank Sparse Subspace for Spectral Clustering

Zhu, Xiaofeng; Zhang, Shichao; Li, Yonggang; Zhang, Jilian; Yang, Lifeng; Fang, Yue

doi:10.1109/tkde.2018.2858782

Cited by 171 publications

(52 citation statements)

References 38 publications

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“…After optimizing (6), elaborated in Section 2.3, we conduct feature selection [24, 42–44, 53] by discarding the regressors (or the response variables) whose corresponding coefficients in B (or A ) are zeros in the rows. More specifically, according to (12), the sparse rows on A imply that their corresponding columns ( i.e.…”

Section: Methodsmentioning

confidence: 99%

“…This section describes the optimization process of the parameters b , B , and A . Specifically, we iteratively conduct the following three steps until convergence by means of Iteratively Reweighted Least Square (IRLS) [32, 53]: (i) Update b with fixed B and A . (ii) Update B with fixed b and A .…”

Section: Methodsmentioning

confidence: 99%

“…We provide the pseudo algorithm of solving (6) in Algorithm 1. According to [44, 50, 53], the objective function in (6) monotonically decreases after each iteration.…”

Section: Methodsmentioning

confidence: 99%

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Group sparse reduced rank regression for neuroimaging genetic study

2018

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The neuroimaging genetic study usually needs to deal with high dimensionality of both brain imaging data and genetic data, so that often resulting in the issue of curse of dimensionality. In this paper, we propose a group sparse reduced rank regression model to take the relations of both the phenotypes and the genotypes for the neuroimaging genetic study. Specifically, we propose designing a graph sparsity constraint as well as a reduced rank constraint to simultaneously conduct subspace learning and feature selection. The group sparsity constraint conducts feature selection to identify genotypes highly related to neuroimaging data, while the reduced rank constraint considers the relations among neuroimaging data to conduct subspace learning in the feature selection model. Furthermore, an alternative optimization algorithm is proposed to solve the resulting objective function and is proved to achieve fast convergence. Experimental results on the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset showed that the proposed method has superiority on predicting the phenotype data by the genotype data, than the alternative methods under comparison.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Group sparse reduced rank regression for neuroimaging genetic study

2018

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“…That is, SSC enforces C to be sparse, LSR tends to group highly correlated data together, while LRR encourages C to be low rank [47]. Actually, most RBSC algorithms so far are static SC algorithms and actually are variants or extensions of SSC, LSR, LRR, or a combination of them (e.g., LSS [48]). The optimal C * obtained by (3) will then be utilized to build an affinity matrix that is denoted as W. The SC results will be obtained after applying spectral clustering algorithms [49]- [52] to W.…”

Section: B Subspace Clusteringmentioning

confidence: 99%

Dynamic Sparse Subspace Clustering for Evolving High-Dimensional Data Streams

Sui

Liu

et al. 2022

IEEE Trans. Cybern.

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In an era of ubiquitous large-scale evolving data streams, data stream clustering (DSC) has received lots of attention because the scale of the data streams far exceeds the ability of expert human analysts. It has been observed that high-dimensional data are usually distributed in a union of low-dimensional subspaces. In this article, we propose a novel sparse representation-based DSC algorithm, called evolutionary dynamic sparse subspace clustering (EDSSC). It can cope with the time-varying nature of subspaces underlying the evolving data streams, such as subspace emergence, disappearance, and recurrence. The proposed EDSSC consists of two phases: 1) static learning and 2) online clustering. During the first phase, a data structure for storing the statistic summary of data streams, called EDSSC summary, is proposed which can better address the dilemma between the two conflicting goals: 1) saving more points for accuracy of subspace clustering (SC) and 2) discarding more points for the efficiency of DSC. By further proposing an algorithm to estimate the subspace number, the proposed EDSSC does not need to know the number of subspaces. In the second phase, a more suitable index, called the average sparsity concentration index (ASCI), is proposed, which dramatically promotes the clustering accuracy compared to the conventionally utilized SCI index. In addition, the subspace evolution detection model based on the Page-Hinkley test is proposed where the appearing, disappearing, and recurring subspaces can be detected and adapted. Extinct experiments on real-world data streams show that the EDSSC outperforms the state-of-the-art online SC approaches.

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“…Meanwhile some research work proposes to learn and update these graph similarity matrices iteratively to avoid high dimensional and noisy data problem. Reference [19] proposes a Lowrank Sparse Subspace (LSS) clustering method via dynamically learning the affinity matrix from low-dimensional space of the original data. The authors in Ref.…”

Section: Related Workmentioning

confidence: 99%

Feature selection with graph mining technology

Mudiyanselage

Zhang

2019

Big Data Min. Anal.

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Many real world applications have problems with high dimensionality, which existing algorithms cannot overcome. A critical data preprocessing problem is feature selection, whereby its non-scalability negatively influences both the efficiency and performance of big data applications. In this research, we developed a new algorithm to reduce the dimensionality of a problem using graph-based analysis, which retains the physical meaning of the original high-dimensional feature space. Most existing feature-selection methods are based on a strong assumption that features are independent of each other. However, if the feature-selection algorithm does not take into consideration the interdependencies of the feature space, the selected data fail to correctly represent the original data. We developed a new feature-selection method to address this challenge. Our aim in this research was to examine the dependencies between features and select the optimal feature set with respect to the original data structure. Another important factor in our proposed method is that it can perform even in the absence of class labels. This is a more difficult problem that many feature-selection algorithms fail to address. In this case, they only use wrapper techniques that require a learning algorithm to select features. It is important to note that our experimental results indicates, this proposed simple ranking method performs better than other methods, independent of any particular learning algorithm used.

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Low-Rank Sparse Subspace for Spectral Clustering

Cited by 171 publications

References 38 publications

Group sparse reduced rank regression for neuroimaging genetic study

Group sparse reduced rank regression for neuroimaging genetic study

Dynamic Sparse Subspace Clustering for Evolving High-Dimensional Data Streams

Feature selection with graph mining technology

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