Kernel Spectral Clustering and Applications

Langone, Rocco; Mall, Raghvendra; Alzate, Carlos; Suykens, Johan A. K.

doi:10.1007/978-3-319-24211-8_6

Cited by 25 publications

(19 citation statements)

References 51 publications

(34 reference statements)

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“…By allowing the cluster indicator matrices (H, Z) to be continuous valued the problem is solved by eigenvalue decomposition of the graph Laplacian matrix given in Eqs. (2) and (3) [11,12,21].…”

Section: Graph Cutsmentioning

confidence: 99%

A nonlinear orthogonal non-negative matrix factorization approach to subspace clustering

Tolić

Antulov-Fantulin

Kopriva

2018

Pattern Recognition

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A recent theoretical analysis shows the equivalence between non-negative matrix factorization (NMF) and spectral clustering based approach to subspace clustering. As NMF and many of its variants are essentially linear, we introduce a nonlinear NMF with explicit orthogonality and derive general kernelbased orthogonal multiplicative update rules to solve the subspace clustering problem. In nonlinear orthogonal NMF framework, we propose two subspace clustering algorithms, named kernel-based nonnegative subspace clustering KNSC-Ncut and KNSC-Rcut and establish their connection with spectral normalized cut and ratio cut clustering. We further extend the nonlinear orthogonal NMF framework and introduce a graph regularization to obtain a factorization that respects a local geometric structure of the data after the nonlinear mapping. The proposed NMF-based approach to subspace clustering takes into account the nonlinear nature of the manifold, as well as its intrinsic local geometry, which considerably improves the clustering performance when compared to the several recently proposed state-of-the-art methods.

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Section: Graph Cutsmentioning

confidence: 99%

A nonlinear orthogonal non-negative matrix factorization approach to subspace clustering

Tolić

Antulov-Fantulin

Kopriva

2018

Pattern Recognition

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“…Nevertheless, it is challenging to select an appropriate scaling factor σ [19]. Kernel spectral clustering (KSC) [20] and its variants [21] have also been proposed.…”

Section: Introductionmentioning

confidence: 99%

Clustering with similarity preserving

Kang

Wang

et al. 2019

Neurocomputing

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Graph-based clustering has shown promising performance in many tasks.A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the incorporation of nonlinearity. However, most existing kernel-based graph learning mechanisms is not similarity-preserving, hence leads to sub-optimal performance. To overcome this drawback, we propose a more discriminative graph learning method which can preserve the pairwise similarities between samples in an adaptive manner for the first time. Specifically, we require the learned graph be close to a kernel matrix, which serves as a measure of similarity in raw data. Moreover, the structure is adaptively tuned so that the number of connected components of the graph is exactly equal to the number of clusters. Finally, our method unifies clustering and graph learning which can directly obtain cluster indicators from the graph itself without performing further clustering step. The effectiveness of this approach is examined on both single and multiple kernel learning scenarios in several

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“…Clustering is mainly performed using a (weighted or unweighted) graph describing the similarities between these objects. When the graph nodes are themselves the objects of interest, the problem is known as community detection on graphs [2]; otherwise the construction of the graph adjacency matrix K is based on a kernel operator f and the similarity between items xi and xj is given by Kij = f (xi, xj), often taken under the form Kij = f xi −xj 2 or Kij = f (x T i xj) for some function f [3]. One of the prominent methods for clustering from K, known as spectral procedures [4] consists in performing a Principal Component Analysis (PCA) on the dominant eigenvectors (presumably containing all the useful information about the data) of the symmetric normalized Laplacian matrix L = D − 1 2 KD − 1 2 (with D the degree matrix) 1 .…”

Section: Introductionmentioning

confidence: 99%

Random Matrix Asymptotics of Inner Product Kernel Spectral Clustering

Ali

Kammoun

Couillet

2018

2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We study in this article the asymptotic performance of spectral clustering with inner product kernel for Gaussian mixture models of high dimension with numerous samples. As is now classical in large dimensional spectral analysis, we establish a phase transition phenomenon by which a minimum distance between the class means and covariances is required for clustering to be possible from the dominant eigenvectors. Beyond this phase transition, we evaluate the asymptotic content of the dominant eigenvectors thus allowing for a full characterization of clustering performance. However, a surprising finding is that in some particular scenarios, the phase transition does not occur and clustering can be achieved irrespective of the class means and covariances. This is evidenced here in the case of the mixture of two Gaussian datasets having the same means and arbitrary difference between covariances.

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Kernel Spectral Clustering and Applications

Cited by 25 publications

References 51 publications

A nonlinear orthogonal non-negative matrix factorization approach to subspace clustering

A nonlinear orthogonal non-negative matrix factorization approach to subspace clustering

Clustering with similarity preserving

Random Matrix Asymptotics of Inner Product Kernel Spectral Clustering

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