scholarly journals A Folded Concave Penalty Regularized Subspace Clustering Method to Integrate Affinity and Clustering

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Wenjuan Zhang ◽  
Xiangchu Feng ◽  
Feng Xiao ◽  
Yunmei Chen
Keyword(s):  
Nonzero Element ◽  
Subspace Clustering ◽  
Graph Laplacian ◽  
Low Rank ◽  
Affinity Matrix ◽  
Clustering Methods ◽  
L1 Norm ◽  
L2 Norm ◽  
The Difference ◽  
Block Diagonal

Most sparse or low-rank-based subspace clustering methods divide the processes of getting the affinity matrix and the final clustering result into two independent steps. We propose to integrate the affinity matrix and the data labels into a minimization model. Thus, they can interact and promote each other and finally improve clustering performance. Furthermore, the block diagonal structure of the representation matrix is most preferred for subspace clustering. We define a folded concave penalty (FCP) based norm to approximate rank function and apply it to the combination of label matrix and representation vector. This FCP-based regularization term can enforce the block diagonal structure of the representation matrix effectively. We minimize the difference of l1 norm and l2 norm of the label vector to make it have only one nonzero element since one data only belong to one subspace. The index of that nonzero element is associated with the subspace from which the data come and can be determined by a variant of graph Laplacian regularization. We conduct experiments on several popular datasets. The results show our method has better clustering results than several state-of-the-art methods.

scholarly journals Cascaded Low Rank and Sparse Representation on Grassmann Manifolds

2018 ◽  
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.

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

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.

scholarly journals Sparse and Low-Rank Subspace Data Clustering with Manifold Regularization Learned by Local Linear Embedding

2018 ◽  
Vol 8 (11) ◽  
pp. 2175 ◽  
Author(s):  
Ye Yang ◽  
Yongli Hu ◽  
Fei Wu
Keyword(s):  
Data Clustering ◽  
Spectral Clustering ◽  
Subspace Clustering ◽  
Low Rank ◽  
Clustering Methods ◽  
Local Linear Embedding ◽  
Local Linear ◽  
Non Linear ◽  
Laplacian Graph ◽  
Linear Embedding

Data clustering is an important research topic in data mining and signal processing communications. In all the data clustering methods, the subspace spectral clustering methods based on self expression model, e.g., the Sparse Subspace Clustering (SSC) and the Low Rank Representation (LRR) methods, have attracted a lot of attention and shown good performance. The key step of SSC and LRR is to construct a proper affinity or similarity matrix of data for spectral clustering. Recently, Laplacian graph constraint was introduced into the basic SSC and LRR and obtained considerable improvement. However, the current graph construction methods do not well exploit and reveal the non-linear properties of the clustering data, which is common for high dimensional data. In this paper, we introduce the classic manifold learning method, the Local Linear Embedding (LLE), to learn the non-linear structure underlying the data and use the learned local geometry of manifold as a regularization for SSC and LRR, which results the proposed LLE-SSC and LLE-LRR clustering methods. Additionally, to solve the complex optimization problem involved in the proposed models, an efficient algorithm is also proposed. We test the proposed data clustering methods on several types of public databases. The experimental results show that our methods outperform typical subspace clustering methods with Laplacian graph constraint.

A Novel Low Rank Representation Algorithm for Subspace Clustering

2016 ◽  
Vol 30 (04) ◽  
pp. 1650007 ◽  
Author(s):  
Yuanyuan Chen ◽  
Lei Zhang ◽  
Zhang Yi
Keyword(s):  
Subspace Clustering ◽  
Low Rank ◽  
Affinity Matrix ◽  
Real World Data ◽  
Data Set ◽  
Cluster Data ◽  
Augmented Lagrange Multiplier ◽  
Efficiency And Effectiveness ◽  
Long Time ◽  
Low Rank Representation

Low rank representation (LRR) is widely used to construct a good affinity matrix to cluster data drawn from the union of multiple linear subspaces. However, it is not easy to solve the LRR problem in a closed form, and augmented Lagrange multiplier method (ALM) is usually applied. ALM takes a relative long time dealing with the real-world data. To solve the LRR problem efficiently, we propose an efficient low rank representation (eLRR) algorithm. Given a contaminated data set, we propose a novel way to solve the LRR of the data. We establish a useful theorem which directly gives an approximate solution to our LRR optimization problem. Thus, we can construct a good affinity matrix for subspace clustering. Experimental results with several public databases verify the efficiency and effectiveness of our method.

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

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.

scholarly journals Tensor Completion for Weakly-Dependent Data on Graph for Metro Passenger Flow Prediction

2020 ◽  
Vol 34 (04) ◽  
pp. 4804-4810
Author(s):  
Ziyue Li ◽  
Nurettin Dorukhan Sergin ◽  
Hao Yan ◽  
Chen Zhang ◽  
Fugee Tsung
Keyword(s):  
Tensor Decomposition ◽  
Graph Laplacian ◽  
Efficient Estimation ◽  
Low Rank ◽  
Tensor Completion ◽  
L1 Norm ◽  
Passenger Flow ◽  
Rank Tensor ◽  
Improved Performance ◽  
Weakly Dependent Data

Low-rank tensor decomposition and completion have attracted significant interest from academia given the ubiquity of tensor data. However, low-rank structure is a global property, which will not be fulfilled when the data presents complex and weak dependencies given specific graph structures. One particular application that motivates this study is the spatiotemporal data analysis. As shown in the preliminary study, weakly dependencies can worsen the low-rank tensor completion performance. In this paper, we propose a novel low-rank CANDECOMP / PARAFAC (CP) tensor decomposition and completion framework by introducing the L1-norm penalty and Graph Laplacian penalty to model the weakly dependency on graph. We further propose an efficient optimization algorithm based on the Block Coordinate Descent for efficient estimation. A case study based on the metro passenger flow data in Hong Kong is conducted to demonstrate an improved performance over the regular tensor completion methods.

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

2021 ◽  
pp. 1-15
Author(s):  
Zhixuan xu ◽  
Caikou Chen ◽  
Guojiang Han ◽  
Jun Gao
Keyword(s):  
State Of The Art ◽  
Subspace Clustering ◽  
Dimensional Subspace ◽  
Low Rank ◽  
Dimensional Structure ◽  
Clustering Methods ◽  
Benchmark Datasets ◽  
Handwritten Digit ◽  
Low Rank Representation ◽  
Low Dimensional

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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