Kernel Learning for Extrinsic Classification of Manifold Features

Vemulapalli, Raviteja; Pillai, Jaishanker K.; Chellappa, Rama

doi:10.1109/cvpr.2013.233

Cited by 85 publications

(78 citation statements)

References 24 publications

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“…For example, the set of all reflectance functions produced by Lambertian objects lies in a linear subspace (Basri and Jacobs 2003;Ramamoorthi 2002). Several state-of-the-art methods for matching videos or image sets model given data by subspaces (Hamm and Lee 2008;Harandi et al 2011;Turaga et al 2011;Vemulapalli et al 2013;Sanderson et al 2012;Chen et al 2013). Auto regressive and moving average models, which are typically employed to model dynamics in spatio-temporal processing, can also be expressed by linear subspaces (Turaga et al 2011).…”

Section: Introductionmentioning

confidence: 98%

Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds

et al. 2015

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Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in Euclidean spaces. With the aim of building a bridge between the two realms, we address the problem of sparse coding and dictionary learning in Grassmann manifolds, i.e., the space of linear subspaces. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping. This in turn enables us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we propose an algorithm for learning a Grassmann dictionary, atom by atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann sparse coding and dictionary learning algorithms through embedding into higher dimensional Hilbert spaces. ExperCommunicated by iments on several classification tasks (gender recognition, gesture classification, scene analysis, face recognition, action recognition and dynamic texture classification) show that the proposed approaches achieve considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelized Affine Hull Method and graphembedding Grassmann discriminant analysis.

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Section: Introductionmentioning

confidence: 98%

Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds

et al. 2015

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“…Nevertheless, to choose an appropriate kernel could be challenging. In fact, several works have been devoted to address this [76,148]. When the kernel is poorly chosen it leads to inferior performance [148].…”

Section: Classification On Riemannian Manifoldsmentioning

confidence: 99%

“…Another popular school of thought is to map manifold points onto a Reproducing Kernel Hilbert Space (RKHS) and apply kernel-based classifiers [61,70,76,148]. As Euclidean geometry applies in the RKHS, this can be thought of a decoupling between machine learning and data representation [81].…”

Section: Classification On Riemannian Manifoldsmentioning

confidence: 99%

“…Projection kernel is one of the most popular kernels used over Grassmann manifolds and has been shown to have superior performance with low computation complexity [59,148]. It can be formulated as:…”

Section: Grassmann Manifoldsmentioning

confidence: 99%

“…In fact, several works have been devoted to address this [76,148]. When the kernel is poorly chosen it leads to inferior performance [148]. In addition, kernel methods are generally computationally demanding especially when training data is extremely large [155].…”

Section: Classification On Riemannian Manifoldsmentioning

confidence: 99%

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Fast and accurate image and video analysis on Riemannian manifolds

Zhao¹

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Recent times have seen increasing attention on representing images and videos on Riemannian manifolds. Such representations offer new means of preserving intrinsic data structures, which Euclidean-based representations often fail to capture. Preserving the intrinsic structure can bring superior benefits in terms of richer representations and robustness to variations. However, to intrinsically operate on the manifold incurs expensive computation complexity because of using non-linear operators. Furthermore, it is difficult to extend the existing computer vision techniques which were originally developed in Euclidean space into the manifold. To address these issues, recent research often uses extrinsic approaches such as tangent space projection and kernelised approaches. Unfortunately, these methods are not free of drawbacks in terms of low accuracy and high computational load. To that end, this research studies approaches for analysing manifold features which achieve superior performance from the manifold structures whilst computational complexity can be massively reduced. This thesis illustrates the general steps of manifold approaches for image and video analysis, here called manifold scheme, followed by discussions on the possible ways to reduce the computational complexities. Guided by the manifold scheme, this research further proposes two frameworks to analyse manifold features: random projection on Riemannian manifolds and convex hull on Symmetric Positive Definite manifolds. To solve the problems posed by each framework, we present three solutions. Through experiments on several computer vision tasks, we verified that our proposed methods can massively reduce the computational load, while still achieving competitive performance. In addition, our manifold scheme shows another possible way to reduce the computational load of manifold approaches through the generating manifold model using effective lower-level features with low dimensionality. Thus, this thesis proposes a landmark manifold model generated by effective landmark points for facial emotion recognition, which shows competitive performance with much lower computational complexity compared to state-of-the-art manifold methods. Design of experiments (10%)

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Set-to-Set Distance Metric Learning on SPD Manifolds

Gao

Jia

2018

Pattern Recognition and Computer Vision

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Kernel Learning for Extrinsic Classification of Manifold Features

Cited by 85 publications

References 24 publications

Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds

Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds

Fast and accurate image and video analysis on Riemannian manifolds

Set-to-Set Distance Metric Learning on SPD Manifolds

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