Extended Grassmann Kernels for Subspace-Based Learning.

Subspace-based learning problems involve data whose elements are linear subspaces of a vector space. To handle such data structures, Grassmann kernels have been proposed and used previously. ... Firstly, we show that the KL distance in the limit yields the Projection kernel on the Grassmann manifold, whereas the Bhattacharyya kernel becomes trivial in the limit and is suboptimal for subspace-based ... The appropriate data space for the subspace-based learning is the Grassmann manifold G(m, D), which is defined as the set of m-dimensional linear subspaces in R D . ...

dblp:conf/nips/HamL08 fatcat:b3dwhbnzojhvfago2e6kfrwvge

We present a biologically motivated manifold learning framework for image set classification inspired by Independent Component Analysis for Grassmann manifolds. ... We propose constructing Grassmann subspaces using Independent Component Analysis for robustness and improved class separation. ... In this paper, we introduce a biologically inspired framework for perceptual subspace learning based on Independent Component Analysis (ICA) for Grassmann manifold construction to promote class discrimination ...

doi:10.1109/icip.2016.7533198 dblp:conf/icip/KumarS16 fatcat:vpe5njldcrchnic5r54b4ecz6i

Secondly, we research into two kinds of disturbance, relevant to the subspace matrix and singular values of bases, with which we extend the Projection kernel on Grassmann manifolds to two new kernels. ... In this paper, we focus on subspace-based learning problems, where data elements are linear subspaces instead of vectors. ... Based on the formulation, we extend the Projection kernel to subspaces with potential disturbance. A. ...

doi:10.1145/3219819.3219959 dblp:conf/kdd/HongCL18 fatcat:3fdt7667onfhba66346flho2e4

Multiple Versions

To leverage the kernel-based methods developed for Euclidean space, several recent methods have been proposed to embed the Grassmann manifold into a high dimensional Hilbert space by exploiting the well ... In video based face recognition, great success has been made by representing videos as linear subspaces, which typically lie in a special type of non-Euclidean space known as Grassmann manifold. ... As a result, kernel learning algorithms (e.g., kernel discriminant analysis [2] ) in vector spaces can be extended to their counterparts on Grassmann manifold. ...

doi:10.1109/cvpr.2015.7298609 dblp:conf/cvpr/HuangWSC15 fatcat:xcnbavicpbfiva3rvhy6ppmuh4

The novelty of this paper is to generalize LRR on Euclidean space onto an LRR model on Grassmann manifold in a uniform kernelized LRR framework. ... In this paper, at a higher level, we intend to cluster subspaces into classes of subspaces. This is naturally described as a clustering problem on Grassmann manifold. ... This algorithm is valid for any kernel functions on Grassmann manifold. ...

arXiv:1601.02124v1 fatcat:mab7mywm3ngkbex72nlmrddqie

In this paper we introduce another kernel for face membership authentication with similarities to the Projection kernel, a Grassmann kernel. ... Experimental results on face membership verification task show the effectiveness of the proposed kernel over the Grassmann kernels and the Grassmann Distance Mutual Subspace Method (GD-MSM). ... Latest techniques involve subspace-based learning methods which are developed under the assumption that data can be modeled as a low-dimensional subspace of the image space instead of vectors [20] . ...

dblp:conf/mva/RelatorHK13 fatcat:lvthw625b5fjhf7rnx7fnvrrfq

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 ... Although the Grassmann manifold is compact, the geodesic distances between Grassmann points are well measured by kernel sparse representations based on linear reconstruction. ... KERNEL SPARSE SUBSPACE CLUSTERING ON GRASSMANN MANIFOLDS Based on the kernel sparse subspace clustering method in [30] , we propose a novel kernel sparse subspace clustering algorithm on Grassmann manifolds ...

doi:10.1109/cyber.2017.8446507 fatcat:zkcue6m6lvd6bh3saqzut7t3xy

We propose a unifying view on the subspace-based learning method by formulating the problems on the Grassmann manifold, which is the set of fixed-dimensional linear subspaces of a Euclidean space. ... In this paper we propose a discriminant learning framework for problems in which data consist of linear subspaces instead of vectors. ... We approach the subspace-based learning problems by formulating the problems on the Grassmann manifold, the set of fixed-dimensional linear subspaces of a Euclidean space. ...

doi:10.1145/1390156.1390204 dblp:conf/icml/HamL08 fatcat:gbqihoyz3bb6ha26h53ionzjqm

Grassmann manifolds are well suited for computer vision problems because they promote smooth surfaces where points are represented as subspaces. ... In this paper we propose Grassmannian Sparse Representations (GSR), a novel subspace learning algorithm that combines the benefits of Grassmann manifolds with sparse representations using least squares ... A recent development based on manifold learning is the representation of image sets as low-dimensional linear subspaces using Grassmann manifolds. ...

doi:10.1109/cvprw.2013.79 dblp:conf/cvpr/AzaryS13 fatcat:x3xnjlqqpvfshpn5ympg67xn6q

We respect the Riemannian ge-ometry of the Grassmann manifold and search for this projection directly from one Grassmann manifold to an-other face-to-face without any additional transformations. ... This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. ... Based on GDA, Graph-embedding Grassmann Discriminant Analysis (GGDA) [14] provides a graph-embedding framework with a new Grassmannian kernel to learn a more discriminatory mapping on Grassmannian manifolds ...

arXiv:1711.06382v1 fatcat:mxtgkuo3zjbblck37bmgimbfue

In order to extend the advantages of the Euclidean based dimensionality reduction methods to the Grassmann Manifold, several methods have been suggested recently which jointly perform dimensionality reduction ... and metric learning on Grassmann manifold to improve performance. ... RELATED WORK The traditional methods of Grassmann manifold dimensionality reduction can be divided into three categories: the subspace based manifold learning methods, the kernel based discriminative learning ...

arXiv:1806.10830v2 fatcat:odvxpnxpc5gy5h3mzkyjpnsrre

Open Access Multiple Versions

In the last few years, there have been growing interests in studying Grassmann manifold to tackle new learning problems. ... Many relevant problems involve subspace-structured features, orthogonality constrained or low-rank constrained objective functions, or subspace distances. ... Based on Fig. 3 : 3 General framework for Grassmannian kernelized learning. ...

arXiv:1808.02229v2 fatcat:sfbjajuwjnbgjl5qnz5w2f4gg4

Multiple Versions

These methods are then used to learn class conditional densities for applications such as activity recognition, video based face recognition and shape classification. ... shape analysis, image matching and learning theory. ... Moreover, since the kernel methods learn a probability density function for the shapes on the Grassmann manifold, it outperforms distance based nearest neighbor classifiers using Grassmann arc-length and ...

doi:10.1109/cvpr.2008.4587733 dblp:conf/cvpr/TuragaVC08 fatcat:uhmpcz2heveothg3zazct5nxlq

Grassmann learning facilitates compact characterization by generating linear subspaces and representing them as points on the manifold. ... Domain adaptation methods on Grassmann manifolds are among the most popular, including Geodesic Subspace Sampling and Geodesic Flow Kernel. ... In Section 4 we present a robust approach for subspace generation during Grassmann manifold construction based on " -PCA. ...

doi:10.1109/cvprw.2016.136 dblp:conf/cvpr/KumarS16 fatcat:vrcvf4juxjhmfjw5q4niusvdfi

The novelty of this paper is to generalize LRR on Euclidean space onto an LRR model on Grassmann manifold in a uniform kernelized framework. ... In this paper, at a higher level, we intend to cluster subspaces into classes of subspaces. This is naturally described as a clustering problem on Grassmann manifold. ... Consider two subspaces span(X i ) and span(X j ) as two Grassmann points where X i and X j are given bases. ...

arXiv:1504.01806v1 fatcat:7yrazrxuy5grdczs3hiyhgj22a

Extended Grassmann Kernels for Subspace-Based Learning

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Learning a perceptual manifold for image set classification

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Disturbance Grassmann Kernels for Subspace-Based Learning

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Projection Metric Learning on Grassmann Manifold with Application to Video based Face Recognition

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Kernelized LRR on Grassmann Manifolds for Subspace Clustering [article]

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Mean polynomial kernel for face membership authentication

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Visual Clustering based on Kernel Sparse Representation on Grassmann Manifolds

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Grassmann discriminant analysis

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Grassmannian Sparse Representations and Motion Depth Surfaces for 3D Action Recognition

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Dimensionality Reduction on Grassmannian via Riemannian Optimization: A Generalized Perspective [article]

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Grassmannian Discriminant Maps (GDM) for Manifold Dimensionality Reduction with Application to Image Set Classification [article]

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Grassmannian Learning: Embedding Geometry Awareness in Shallow and Deep Learning [article]

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Statistical analysis on Stiefel and Grassmann manifolds with applications in computer vision

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Robust Domain Adaptation on the L1-Grassmannian Manifold

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Kernelized Low Rank Representation on Grassmann Manifolds [article]

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