Kernel Sparse Subspace Clustering on Symmetric Positive Definite Manifolds

Yin, Ming; Guo, Yi; Gao, Junbin; He, Zhaoshui; Xie, Shengli

doi:10.1109/cvpr.2016.557

Cited by 90 publications

(40 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Taking i ∈ P\S, j ∈ S for instance, since x j already has a label, x i should belong to the same subspace with x j as |Z ij | + |Z ji | is large enough. is can be achieved by the first part of formula (6). In this case, the index of the nonzero elements of the unknown label g i can be properly correlated to the subspace to which the data belongs.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

See 1 more Smart Citation

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

Zhang

Feng

Xiao

et al. 2021

Mathematical Problems in Engineering

View full text Add to dashboard Cite

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.

show abstract

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…Nowadays, many works proposed the assumption of linear subspace may not always be true for many real high-dimensional data. e proposed data may be better modeled by nonlinear manifolds [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

Feng

Xiao

et al. 2021

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…Based on this idea, Vishal M. Patel and R. Vidal proposed the kernel sparse subspace clustering on Euclidean space in [30]. Similarly, kernel sparse subspace clustering on symmetric positive definite Riemannian manifolds has been proposed by Ming Yin in [31], where the sparse representation of data is obtained without referring to a library. However, to our knowledge, the method of kernel sparse representations of data on the Grassmann manifold without referring to a library has not been concerned up to now.…”

Section: B Sparse Representation On Grassmann Manifoldsmentioning

confidence: 99%

“…To address this problem, the kernel method is widely used recently in [14,21,22,25,26,30,31,33]. Right now, we need to find an appropriate kernel for the Grassmann manifolds.…”

Section: A Gaussian Projection Kernel For Grassmann Manifoldsmentioning

confidence: 99%

Visual Clustering based on Kernel Sparse Representation on Grassmann Manifolds

Liu¹,

Shi²,

Liu³

2017

2017 IEEE 7th Annual International Conference on CYBER Technology in Automation, Control, and Intelligent Systems (CYBER)

View full text Add to dashboard Cite

Image sets and videos can be modeled as subspaces which are actually points on Grassmann manifolds. Clustering of such visual data lying on Grassmann manifolds is a hard issue based on the fact that the state-of-the-art methods are only applied to vector space instead of non-Euclidean geometry. In this paper, we propose a novel algorithm termed as kernel sparse subspace clustering on the Grassmann manifold (GKSSC) which embeds the Grassmann manifold into a Reproducing Kernel Hilbert Space (RKHS) by an appropriate Gaussian projection kernel. This kernel is applied to obtain kernel sparse representations of data on Grassmann manifolds utilizing the self-expressive property and exploiting the intrinsic Riemannian geometry within data. Although the Grassmann manifold is compact, the geodesic distances between Grassmann points are well measured by kernel sparse representations based on linear reconstruction. With the kernel sparse representations, experimental results of clustering accuracy on the prevalent public dataset outperform state-of-the-art algorithms by more than 90 percent and the robustness of our algorithm is demonstrated as well.

show abstract

“…On the other hand, in the area of matrix information geometry, data representation by symmetric positive definite (SPD) matrix has been widely applied in many scientific researches, e.g., pattern recognition [ 12 ], image processing [ 13 ], signal processing [ 14 , 15 ] and machine learning [ 16 ]. More specifically, by constructing SPD matrices, the original information extracted from the sample data is embedded on a specific SPD manifold, which is shown to outperform the Euclidean space operation.…”

Section: Introductionmentioning

confidence: 99%

Matrix Information Geometry for Spectral-Based SPD Matrix Signal Detection with Dimensionality Reduction

Feng

Hua

Zhu

2020

Entropy

View full text Add to dashboard Cite

In this paper, a novel signal detector based on matrix information geometric dimensionality reduction (DR) is proposed, which is inspired from spectrogram processing. By short time Fourier transform (STFT), the received data are represented as a 2-D high-precision spectrogram, from which we can well judge whether the signal exists. Previous similar studies extracted insufficient information from these spectrograms, resulting in unsatisfactory detection performance especially for complex signal detection task at low signal-noise-ratio (SNR). To this end, we use a global descriptor to extract abundant features, then exploit the advantages of matrix information geometry technique by constructing the high-dimensional features as symmetric positive definite (SPD) matrices. In this case, our task for signal detection becomes a binary classification problem lying on an SPD manifold. Promoting the discrimination of heterogeneous samples through information geometric DR technique that is dedicated to SPD manifold, our proposed detector achieves satisfactory signal detection performance in low SNR cases using the K distribution simulation and the real-life sea clutter data, which can be widely used in the field of signal detection.

show abstract

Kernel Sparse Subspace Clustering on Symmetric Positive Definite Manifolds

Cited by 90 publications

References 29 publications

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

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

Visual Clustering based on Kernel Sparse Representation on Grassmann Manifolds

Matrix Information Geometry for Spectral-Based SPD Matrix Signal Detection with Dimensionality Reduction

Contact Info

Product

Resources

About