Graph-Embedding Discriminant Analysis on Riemannian Manifolds for Visual Recognition

Shirazi, Sareh; Alavi, Azadeh; Harandi, Mehrtash; Lovell, Brian C.

doi:10.1007/978-1-4614-4457-2_7

Cited by 4 publications

(11 citation statements)

References 31 publications

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“…In this section, we detail the procedure graph embedding discriminant analysis on DPS of SPD manifolds. As such, we propose to employ a method similar to the one discussed in [32], where the difference lies on projecting the SPD matrices into DPS rather than embedding such matrices into RKHS. In the experiment section, we show that the proposed graph embedding discriminant analysis based on DPS outperforms similar methods over RKHS.…”

Section: Graph Embedding Discriminative Analysismentioning

confidence: 99%

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Optimized Kernel-based Projection Space of Riemannian Manifolds

Alavi,

Patel,

Chellappa

2016

Preprint

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Recent advances in computer vision suggest that encoding images through Symmetric Positive Definite (SPD) matrices can lead to increased classification performance. Taking into account manifold geometry is typically done via embedding the manifolds in tangent spaces, or Reproducing Kernel Hilbert Spaces (RKHS). Recently it was shown that projecting such manifolds into a kernel-based random projection space (RPS) leads to higher classification performance. In this paper, we propose to learn an optimized projection, based on building local and global sparse similarity graphs that encode the association of data points to the underlying subspace of each point. To this end, we project SPD matrices into an optimized distance preserving projection space (DPS), which can be followed by any Euclidean-based classification algorithm. Further, we adopt the concept of dictionary learning and sparse coding, and discriminative analysis, for the learned DPS on SPD manifolds. Experiments on face recognition, texture classification, person re-identification, and virus classification demonstrate that the proposed methods outperform state-of-the-art methods on such manifolds.

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Section: Graph Embedding Discriminative Analysismentioning

confidence: 99%

“…We further enhance the discriminative power of the method and extend the comparison of DPS-based with RKHS-based methods on SPD manifolds. Finally, we compare the performance of the proposed methods with other DA, and DL methods [18,32,16] on such manifolds.…”

Section: Introductionmentioning

confidence: 99%

Optimized Kernel-based Projection Space of Riemannian Manifolds

Alavi,

Patel,

Chellappa

2016

Preprint

Self Cite

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“…can be investigated by graphical models. In some problems of data science, the points of data are taken from a Riemannian manifold, for example, neural network [3,10], image and visualization [11,12], etc. The underlying relations among the points in the data could be represented by a graph.…”

Section: Introductionmentioning

confidence: 99%

Isometric embeddings of graphs into Riemannian manifolds

Ren¹

2018

Preprint

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An isometric embedding of a graph into a metric space is an embedding of the vertices such that the smallest number of edges connecting any two vertices equals to the distance in the metric space between the images.In this paper, we study isometric embeddings of graphs into Riemannian manifolds. We give some classifications of graphs that can be isometrically embedded into certain Riemannian manifolds.

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“…Manifolds can be also mapped to a reproducing kernel Hilbert space (RKHS) by using kernels. Kernel analysis on SPD matrices and LS has been used for gesture and action recognition in [60,66,146,161]. SPD matrices are embedded into RKHS via a pseudo kernel in [60].…”

Section: Statistical Modelling Of Video Action Descriptors Via Riemannian Manifoldsmentioning

confidence: 99%

“…An improved Grassmann discriminant analysis based on Grassmann kernels and a graph-embedding framework is presented [146]. Recently, the traditional sparse representation (SR) on vectors has been generalised to sparse representations in SPD matrices and LS [55,59,57,165].…”

Section: Statistical Modelling Of Video Action Descriptors Via Riemannian Manifoldsmentioning

confidence: 99%

Action analysis and video summarisation to efficiently manage and interpret video data

Carvajal¹

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In the last few years we have seen how the volume of video data has exponentially grown. Specialised online sites like YouTube and NetFlix are attracting a considerable amount of audience who are uploading, accessing, and actively interacting with the online sites. Furthermore, millions of video surveillance cameras have been installed around the world. Video cameras are installed to monitor shopping centres, universities, parks, streets, and in general to monitor any public place.

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Graph-Embedding Discriminant Analysis on Riemannian Manifolds for Visual Recognition

Cited by 4 publications

References 31 publications

Optimized Kernel-based Projection Space of Riemannian Manifolds

Optimized Kernel-based Projection Space of Riemannian Manifolds

Isometric embeddings of graphs into Riemannian manifolds

Action analysis and video summarisation to efficiently manage and interpret video data

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