Robust subspace clustering based on latent low rank representation with non-negative sparse Laplacian constraints

As a successful improvement on Low Rank Representation (LRR), Latent Low Rank Representation (LatLRR) has been one of the state-of-the-art models for subspace clustering due to the capability of discovering the low dimensional subspace structures of data, especially when the data samples are insufficient and/or extremely corrupted. However, the LatLRR method does not consider the nonlinear geometric structures within data, which leads to the loss of the locality information among data in the learning phase. Moreover, the coefficients of the learnt representation matrix can be negative, which lack the interpretability. To solve the above drawbacks of LatLRR, this paper introduces Laplacian, sparsity and non-negativity to LatLRR model and proposes a novel subspace clustering method, termed latent low rank representation with non-negative, sparse and laplacian constraints (NNSLLatLRR), in which we jointly take into account non-negativity, sparsity and laplacian properties of the learnt representation. As a result, the NNSLLatLRR can not only capture the global low dimensional structure and intrinsic non-linear geometric information of the data, but also enhance the interpretability of the learnt representation. Extensive experiments on two face benchmark datasets and a handwritten digit dataset show that our proposed method outperforms existing state-of-the-art subspace clustering methods.

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Multiview Common Subspace Clustering via Coupled Low Rank Representation

ACM Transactions on Intelligent Systems and Technology ◽

10.1145/3465056 ◽

2021 ◽

Vol 12 (4) ◽

pp. 1-25

Author(s):

Stanley Ebhohimhen Abhadiomhen ◽

Zhiyang Wang ◽

Xiangjun Shen ◽

Jianping Fan

Keyword(s):

Common Knowledge ◽

Subspace Clustering ◽

Laplacian Matrix ◽

Low Rank ◽

Connected Components ◽

Similarity Matrix ◽

Benchmark Datasets ◽

Low Rank Representation ◽

Low Dimensional ◽

Shared Structure

Multi-view subspace clustering (MVSC) finds a shared structure in latent low-dimensional subspaces of multi-view data to enhance clustering performance. Nonetheless, we observe that most existing MVSC methods neglect the diversity in multi-view data by considering only the common knowledge to find a shared structure either directly or by merging different similarity matrices learned for each view. In the presence of noise, this predefined shared structure becomes a biased representation of the different views. Thus, in this article, we propose a MVSC method based on coupled low-rank representation to address the above limitation. Our method first obtains a low-rank representation for each view, constrained to be a linear combination of the view-specific representation and the shared representation by simultaneously encouraging the sparsity of view-specific one. Then, it uses the k -block diagonal regularizer to learn a manifold recovery matrix for each view through respective low-rank matrices to recover more manifold structures from them. In this way, the proposed method can find an ideal similarity matrix by approximating clustering projection matrices obtained from the recovery structures. Hence, this similarity matrix denotes our clustering structure with exactly k connected components by applying a rank constraint on the similarity matrix’s relaxed Laplacian matrix to avoid spectral post-processing of the low-dimensional embedding matrix. The core of our idea is such that we introduce dynamic approximation into the low-rank representation to allow the clustering structure and the shared representation to guide each other to learn cleaner low-rank matrices that would lead to a better clustering structure. Therefore, our approach is notably different from existing methods in which the local manifold structure of data is captured in advance. Extensive experiments on six benchmark datasets show that our method outperforms 10 similar state-of-the-art compared methods in six evaluation metrics.

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Cascaded Low Rank and Sparse Representation on Grassmann Manifolds

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2018/382 ◽

2018 ◽

Cited By ~ 2

Author(s):

Boyue Wang ◽

Yongli Hu ◽

Junbin Gao ◽

Yanfeng Sun ◽

Baocai Yin

Keyword(s):

Sparse Representation ◽

State Of The Art ◽

Subspace Clustering ◽

Low Rank ◽

Affinity Matrix ◽

Effective Solution ◽

Clustering Methods ◽

Grassmann Manifolds ◽

Trade Off ◽

Low Rank Representation

Inspired by low rank representation and sparse subspace clustering acquiring success, ones attempt to simultaneously perform low rank and sparse constraints on the affinity matrix to improve the performance. However, it is just a trade-off between these two constraints. In this paper, we propose a novel Cascaded Low Rank and Sparse Representation (CLRSR) method for subspace clustering, which seeks the sparse expression on the former learned low rank latent representation. To make our proposed method suitable to multi-dimension or imageset data, we extend CLRSR onto Grassmann manifolds. An effective solution and its convergence analysis are also provided. The excellent experimental results demonstrate the proposed method is more robust than other state-of-the-art clustering methods on imageset data.

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Zero Shot Learning via Low-rank Embedded Semantic AutoEncoder

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2018/345 ◽

2018 ◽

Cited By ~ 15

Author(s):

Yang Liu ◽

Quanxue Gao ◽

Jin Li ◽

Jungong Han ◽

Ling Shao

Keyword(s):

State Of The Art ◽

Feature Space ◽

Original Data ◽

Semantic Space ◽

Dimensional Subspace ◽

Low Rank ◽

Visual Features ◽

Visual Feature ◽

Benchmark Datasets ◽

Low Dimensional

Zero-shot learning (ZSL) has been widely researched and get successful in machine learning. Most existing ZSL methods aim to accurately recognize objects of unseen classes by learning a shared mapping from the feature space to a semantic space. However, such methods did not investigate in-depth whether the mapping can precisely reconstruct the original visual feature. Motivated by the fact that the data have low intrinsic dimensionality e.g. low-dimensional subspace. In this paper, we formulate a novel framework named Low-rank Embedded Semantic AutoEncoder (LESAE) to jointly seek a low-rank mapping to link visual features with their semantic representations. Taking the encoder-decoder paradigm, the encoder part aims to learn a low-rank mapping from the visual feature to the semantic space, while decoder part manages to reconstruct the original data with the learned mapping. In addition, a non-greedy iterative algorithm is adopted to solve our model. Extensive experiments on six benchmark datasets demonstrate its superiority over several state-of-the-art algorithms.

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Subspace Clustering with Sparsity and Grouping Effect

Mathematical Problems in Engineering ◽

10.1155/2017/4787039 ◽

2017 ◽

Vol 2017 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Binbin Zhang ◽

Weiwei Wang ◽

Xiangchu Feng

Keyword(s):

State Of The Art ◽

Subspace Clustering ◽

The Self ◽

Dimensional Structure ◽

High Dimensional ◽

Affinity Matrix ◽

Grouping Effect ◽

Art Methods ◽

Data Points ◽

Low Dimensional

Subspace clustering aims to group a set of data from a union of subspaces into the subspace from which it was drawn. It has become a popular method for recovering the low-dimensional structure underlying high-dimensional dataset. The state-of-the-art methods construct an affinity matrix based on the self-representation of the dataset and then use a spectral clustering method to obtain the final clustering result. These methods show that sparsity and grouping effect of the affinity matrix are important in recovering the low-dimensional structure. In this work, we propose a weighted sparse penalty and a weighted grouping effect penalty in modeling the self-representation of data points. The experimental results on Extended Yale B, USPS, and Berkeley 500 image segmentation datasets show that the proposed model is more effective than state-of-the-art methods in revealing the subspace structure underlying high-dimensional dataset.

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Weighted Low-Rank Tensor Representation for Multi-View Subspace Clustering

Frontiers in Physics ◽

10.3389/fphy.2020.618224 ◽

2021 ◽

Vol 8 ◽

Author(s):

Shuqin Wang ◽

Yongyong Chen ◽

Fangying Zheng

Keyword(s):

Augmented Lagrangian ◽

State Of The Art ◽

Augmented Lagrangian Method ◽

Subspace Clustering ◽

Low Rank ◽

Multiple Views ◽

Clustering Methods ◽

Tensor Representation ◽

Numerical Studies ◽

Rank Tensor

Multi-view clustering has been deeply explored since the compatible and complementary information among views can be well captured. Recently, the low-rank tensor representation-based methods have effectively improved the clustering performance by exploring high-order correlations between multiple views. However, most of them often express the low-rank structure of the self-representative tensor by the sum of unfolded matrix nuclear norms, which may cause the loss of information in the tensor structure. In addition, the amount of effective information in all views is not consistent, and it is unreasonable to treat their contribution to clustering equally. To address the above issues, we propose a novel weighted low-rank tensor representation (WLRTR) method for multi-view subspace clustering, which encodes the low-rank structure of the representation tensor through Tucker decomposition and weights the core tensor to retain the main information of the views. Under the augmented Lagrangian method framework, an iterative algorithm is designed to solve the WLRTR method. Numerical studies on four real databases have proved that WLRTR is superior to eight state-of-the-art clustering methods.

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Unified Low-Rank Subspace Clustering with Dynamic Hypergraph for Hyperspectral Image

Remote Sensing ◽

10.3390/rs13071372 ◽

2021 ◽

Vol 13 (7) ◽

pp. 1372

Author(s):

Jinhuan Xu ◽

Liang Xiao ◽

Jingxiang Yang

Keyword(s):

Hyperspectral Image ◽

Subspace Clustering ◽

Feature Space ◽

Low Rank ◽

Great Success ◽

Clustering Methods ◽

Hypergraph Learning ◽

Optimal Dynamic ◽

Low Rank Representation ◽

Original Feature

Low-rank representation with hypergraph regularization has achieved great success in hyperspectral imagery, which can explore global structure, and further incorporate local information. Existing hypergraph learning methods only construct the hypergraph by a fixed similarity matrix or are adaptively optimal in original feature space; they do not update the hypergraph in subspace-dimensionality. In addition, the clustering performance obtained by the existing k-means-based clustering methods is unstable as the k-means method is sensitive to the initialization of the cluster centers. In order to address these issues, we propose a novel unified low-rank subspace clustering method with dynamic hypergraph for hyperspectral images (HSIs). In our method, the hypergraph is adaptively learned from the low-rank subspace feature, which can capture a more complex manifold structure effectively. In addition, we introduce a rotation matrix to simultaneously learn continuous and discrete clustering labels without any relaxing information loss. The unified model jointly learns the hypergraph and the discrete clustering labels, in which the subspace feature is adaptively learned by considering the optimal dynamic hypergraph with the self-taught property. The experimental results on real HSIs show that the proposed methods can achieve better performance compared to eight state-of-the-art clustering methods.

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Tensor-SVD Based Graph Learning for Multi-View Subspace Clustering

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v34i04.5807 ◽

2020 ◽

Vol 34 (04) ◽

pp. 3930-3937 ◽

Cited By ~ 1

Author(s):

Quanxue Gao ◽

Wei Xia ◽

Zhizhen Wan ◽

Deyan Xie ◽

Pu Zhang

Keyword(s):

Subspace Clustering ◽

Singular Values ◽

Nuclear Norm ◽

Low Rank ◽

Clustering Methods ◽

Norm Minimization ◽

Illumination Changes ◽

Low Rank Representation ◽

Value Decomposition ◽

Tensor Nuclear Norm

Low-rank representation based on tensor-Singular Value Decomposition (t-SVD) has achieved impressive results for multi-view subspace clustering, but it does not well deal with noise and illumination changes embedded in multi-view data. The major reason is that all the singular values have the same contribution in tensor-nuclear norm based on t-SVD, which does not make sense in the existence of noise and illumination change. To improve the robustness and clustering performance, we study the weighted tensor-nuclear norm based on t-SVD and develop an efficient algorithm to optimize the weighted tensor-nuclear norm minimization (WTNNM) problem. We further apply the WTNNM algorithm to multi-view subspace clustering by exploiting the high order correlations embedded in different views. Extensive experimental results reveal that our WTNNM method is superior to several state-of-the-art multi-view subspace clustering methods in terms of performance.

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Computing Robust Principal Components by A* Search

International Journal of Artificial Intelligence Tools ◽

10.1142/s0218213018600138 ◽

2018 ◽

Vol 27 (07) ◽

pp. 1860013 ◽

Cited By ~ 1

Author(s):

Swair Shah ◽

Baokun He ◽

Crystal Maung ◽

Haim Schweitzer

Keyword(s):

State Of The Art ◽

Principal Component ◽

Low Rank ◽

A Algorithm ◽

Running Time ◽

Current State ◽

Dimensionality Reduction Technique ◽

Related Variant ◽

Low Rank Representation ◽

The Cost

Principal Component Analysis (PCA) is a classical dimensionality reduction technique that computes a low rank representation of the data. Recent studies have shown how to compute this low rank representation from most of the data, excluding a small amount of outlier data. We show how to convert this problem into graph search, and describe an algorithm that solves this problem optimally by applying a variant of the A* algorithm to search for the outliers. The results obtained by our algorithm are optimal in terms of accuracy, and are shown to be more accurate than results obtained by the current state-of-the- art algorithms which are shown not to be optimal. This comes at the cost of running time, which is typically slower than the current state of the art. We also describe a related variant of the A* algorithm that runs much faster than the optimal variant and produces a solution that is guaranteed to be near the optimal. This variant is shown experimentally to be more accurate than the current state-of-the-art and has a comparable running time.

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