Tensor LRR based subspace clustering

Fu, Yifan; Gao, Junbin; Tien, David; Lin, Zhouchen

doi:10.1109/ijcnn.2014.6889472

Cited by 11 publications

(17 citation statements)

References 26 publications

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“…The measurements can be highly quantized due to the sensing process and the objective is to recover the data [49,50]. A similar idea also applies to low-quality image recovery [15,2]. Images from the same subject can be represented by {rows of an image × columns of an image × different images}.…”

Section: Notation and Preliminariesmentioning

confidence: 99%

“…Practical datasets may contain additional correlations that cannot be captured by low-rank matrices. For instance, if every frame of a video is vectorized so that the video is represented by a matrix, the spatial correlation is not directly characterized by low-rank matrices [15]. In recommendation systems, users' ratings against objects vary under different contexts [16], [1] We use the notations g = O(n), g = Θ(n) if as n goes to infinity, g ≤ c • n, c1 • n ≤ g ≤ c2 • n eventually holds for some positive constants c, c1 and c2 respectively.…”

Section: Introductionmentioning

confidence: 99%

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Tensor Recovery from Noisy and Multi-Level Quantized Measurements

Ren

Wang

Xiong

2020

Preprint

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Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing works on tensor recovery have focused on data losses and random noises. Only a few works consider tensor recovery from quantized measurements but are restricted to binary measurements. This paper, for the first time, addresses the problem of tensor recovery from multi-level quantized measurements by leveraging the low CANDECOMP/PARAFAC (CP) rank property. We study the recovery of both general low-rank tensors and tensors that have tensor singular value decomposition (TSVD) by solving nonconvex optimization problems. We provide the theoretical upper bounds of the recovery error, which diminish to zero when the sizes of dimensions increase to infinity. We further characterize the fundamental limit of any recovery algorithm and show that our recovery error is nearly order-wise optimal. A tensor-based alternating proximal gradient descent algorithm with a convergence guarantee and a TSVD based projected gradient descent algorithm are proposed to solve the nonconvex problems. Our recovery methods can also handle data losses and do not necessarily need the information of the quantization rule. The methods are validated on synthetic data, image datasets, and music recommender datasets.

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Section: Notation and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tensor Recovery from Noisy and Multi-Level Quantized Measurements

Ren

Wang

Xiong

2020

Preprint

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“…That is, TLRR seeks optimal low-rank solutions U n (1 ≤ n < N) of the structured data X using itself as a dictionary [50]. Remark 1: There is a clear link between the LRR and the TLRR in (8).…”

Section: Subspace Clustering Via Tensor Low-rank Representation Amentioning

confidence: 99%

“…Thus, our model (11) aims to find the lowest rank representations along all the spatial modes, and learn a dictionary with its sparse representation over the samples on the feature mode at the same time. Unlike the TLRR model in [50] merely considers multiple space information, our model takes both spatial and feature information into consideration. The advantage of our model over the TLRR model is shown in Fig.…”

Section: Tensor Spatial Low-rank Representation and Feature Sparsementioning

confidence: 99%

“…Thus, a set of hyperspectral images with a 2-D spatial structure can be denoted by an order-3 tensor X ∈ R I 1 ×I 2 ×I 3 , with mode-i (1 ≤ i ≤ 2) denoting the sample's position along its two spatial directions, and the mode-3 denoting the sample feature direction, e.g., a range of wavelengths in the spectral dimension. Fu et al [50] proposed a novel subspace clustering method called tensor low-rank representation (TLRR), where the input data are represented in their original structural form as a tensor. It finds a lowest rank representation for the input tensor, which can be further used to build an affinity matrix.…”

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confidence: 99%

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Tensor LRR and Sparse Coding-Based Subspace Clustering

Gao

Tien

et al. 2016

IEEE Trans. Neural Netw. Learning Syst.

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Subspace clustering groups a set of samples from a union of several linear subspaces into clusters, so that the samples in the same cluster are drawn from the same linear subspace. In the majority of the existing work on subspace clustering, clusters are built based on feature information, while sample correlations in their original spatial structure are simply ignored. Besides, original high-dimensional feature vector contains noisy/redundant information, and the time complexity grows exponentially with the number of dimensions. To address these issues, we propose a tensor low-rank representation (TLRR) and sparse coding-based (TLRRSC) subspace clustering method by simultaneously considering feature information and spatial structures. TLRR seeks the lowest rank representation over original spatial structures along all spatial directions. Sparse coding learns a dictionary along feature spaces, so that each sample can be represented by a few atoms of the learned dictionary. The affinity matrix used for spectral clustering is built from the joint similarities in both spatial and feature spaces. TLRRSC can well capture the global structure and inherent feature information of data and provide a robust subspace segmentation from corrupted data. Experimental results on both synthetic and real-world data sets show that TLRRSC outperforms several established stateof- the-art methods.

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Community detection method based on mixed-norm sparse subspace clustering

Tian

2018

Neurocomputing

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Community or group is an important structure in disciplines such as social networks, biology gene expression, and physics systems. Community detections for different types of networks have attracted considerable interest. However, it is still challenging to find meaningful community structures in various networks. In particular, accurate community description and implementation of effective detection algorithms with huge datasets are still not solved. In this paper, we present a novel community detection algorithm based on the theory of sparse subspace clustering (SSC) with mixed-norm constraints. Inspired by the sparse representation of subspace, each community in a given network can span a subspace in some similarity measure space. If the basis of subspaces can be solved, all of the nodes can be represented as a linear combination of the nodes that span the same subspace. By introducing a novel mixed-norm constraint in SCC, the connections of nodes among different communities are modeled as noise to improve the clustering accuracy. The formulation of the basis of subspaces is derived from the self-representation property of data by using SSC. Then, the alternating directions method of multipliers (ADMM) framework is used to solve the formulation. Finally, communities are detected by subspace clustering method. The proposed method is compared with state-of-the-art algorithms on synthetic networks and real-world networks. The experimental results show the effectiveness of the proposed algorithm in accurately describing the community. The results also show that the mixed-norm SSC is a practical approach for detecting communities in huge datasets.

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Tensor LRR based subspace clustering

Cited by 11 publications

References 26 publications

Tensor Recovery from Noisy and Multi-Level Quantized Measurements

Tensor Recovery from Noisy and Multi-Level Quantized Measurements

Tensor LRR and Sparse Coding-Based Subspace Clustering

Community detection method based on mixed-norm sparse subspace clustering

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