Clustering and projected clustering with adaptive neighbors

Nie, Feiping; Wang, Xiaoqian; Huang, Heng

doi:10.1145/2623330.2623726

Cited by 639 publications

(280 citation statements)

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“…In order to overcome the aforementioned disadvantages, and inspired by Nie, Wang, and Huang (2014), we aim to learn feature weights jointly in the space of weighted features. The main contributions of the paper are threefold:…”

Section: Contributionmentioning

confidence: 99%

“…In order to estimate the geometrical and topological properties of manifold data, we use the probabilistic neighbors proposed in Nie et al (2014) for its simplicity. We determine a neighbors assignment matrix S ij ∈ R n×n , where S ij denotes the probability of the data points x i can be connected to x j as a neighbor, by solving the following problem:…”

Section: Ideas and Algorithmmentioning

confidence: 99%

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Locality preserving score for joint feature weights learning

Yan

Yang

2015

Neural Networks

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Section: Contributionmentioning

confidence: 99%

Section: Ideas and Algorithmmentioning

confidence: 99%

Locality preserving score for joint feature weights learning

Yan

Yang

2015

Neural Networks

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“…Removing unknown additive noises from measured corrupted images has received much attention in the past fifty years [21,22]. Initial noise reduction approaches focus on imposing various smoothness assumptions on the recovered images [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Sparse Double-Geometric Nonlocal Mean image recovery via steerable kernel

Zhang¹,

Li²,

Yang³

et al. 2015

Applied Soft Computing

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“…Solving l 1 optimisation problems is notoriously expensive and a new formulation and an efficient algorithm are provided to make our model tractable. Second, instead of assuming that the graph topology and weights are known a priori and fixed during learning, we propose to learn the graph [1] and integrate the graph learning into the proposed l 1 -norm graph regularised optimisation problem. Extensive experiments were conducted on five benchmark datasets.…”

mentioning

confidence: 99%

Learning Robust Graph Regularisation for Subspace Clustering

Kodirov¹,

Xiang²,

Fu³

et al. 2016

Procedings of the British Machine Vision Conference 2016

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Abstract. Various subspace clustering methods have benefited from introducing a graph regularisation term in their objective functions [2]. In this work, we identify two critical limitations of the graph regularisation term employed in existing subspace clustering models and provide solutions for both of them. First, the squared l 2 -norm used in the existing term is replaced by a l 1 -norm term to make the regularisation term more robust against outlying data samples and noise. Solving l 1 optimisation problems is notoriously expensive and a new formulation and an efficient algorithm are provided to make our model tractable. Second, instead of assuming that the graph topology and weights are known a priori and fixed during learning, we propose to learn the graph [1] and integrate the graph learning into the proposed l 1 -norm graph regularised optimisation problem. Extensive experiments were conducted on five benchmark datasets.Methodology. To address the aforementioned problems, we propose following objective function:where X ∈ R r×N is a data matrix with N rdimensional data feature vectors as columns, D ∈ R r×d is a dictionary with d number of atoms, W is an affinity matrix that captures the topology of the data, A W is a matrix that is obtained by applying eigendecomposition on W, and Y ∈ R d×N is a sparse code matrix. In the following, we give explanation for each term:(1) X − DY 2 F is the reconstruction error term evaluating how well a linear combination of the atoms (columns) of the dictionary D, can approximate the data matrix X.(2) λ 1 Y 1 is a sparsity regularisation term on Y, with a weighting factor λ 1 to favour a small number of atoms to be used for the reconstruction.(3) λ 2 YA W 1 is our proposed robust graph regularisation term. Note that we are using l 1 -norm instead of l 2 -norm weighted by λ 2 .F is the term with proper constraints (W T 1 = 1 and W ≥ 0) for graph learning weighted by λ 2 and λ 3 .The constraints, W T 1 = 1 and W ≥ 0, are there to ensure the validity of the learned graph, while the constraint d i 2 ≤ 1 (d i is a column of D with i = 1, ... , r) enforces the learned dictionary atoms to be compact.Remark. Terms (3) and (4) are robust graph regularisation and graph learning terms, while first two terms, (1) and (2) constitute the conventional objective function of dictionary learning.Optimisation. To solve the objective Eq. (1), we develop an algorithm based on ADMM.

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Clustering and projected clustering with adaptive neighbors

Cited by 639 publications

References 10 publications

Locality preserving score for joint feature weights learning

Locality preserving score for joint feature weights learning

Sparse Double-Geometric Nonlocal Mean image recovery via steerable kernel

Learning Robust Graph Regularisation for Subspace Clustering

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