Riemannian Sparse Coding for Positive Definite Matrices

Cherian, Anoop; Sra, Suvrit

doi:10.1007/978-3-319-10578-9_20

Cited by 49 publications

(65 citation statements)

References 30 publications

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“…Here, the state of the art solution of SPD sparse coding proposed in [31] was used. Once the sparse coefficients were determined, the sparse coding classifier proposed in [159] was used as the classifier.…”

Section: Resultsmentioning

confidence: 99%

“…Sparse Coding for SPD manifolds [31], which used the geodesic distance to preserve the manifold structure. However, the use of the matrix addition forces the summation of the weighted SPD points out of the manifold in some cases.…”

Section: Classification On Riemannian Manifoldsmentioning

confidence: 99%

“…(5.13), we refer readers to [31]. Note that, the difference between our work and the work in [31] is that we restrict the sum of w i equals one and the optimization is based on each class.…”

Section: Convex Hull Distance Based On a Confined Set -Mach-2mentioning

confidence: 99%

“…Note that, the difference between our work and the work in [31] is that we restrict the sum of w i equals one and the optimization is based on each class. These two points are the essential requirements of convex hull that gives us much better performance comparing with [31].…”

Section: Convex Hull Distance Based On a Confined Set -Mach-2mentioning

confidence: 99%

“…Following [31], to solve the above optimization problem on this restricted set, we first rewrite the objective function in Eqn. (5.13) by setting…”

Section: Convex Hull Distance Based On a Confined Set -Mach-2mentioning

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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Section: Resultsmentioning

confidence: 99%

Section: Classification On Riemannian Manifoldsmentioning

confidence: 99%

Section: Convex Hull Distance Based On a Confined Set -Mach-2mentioning

confidence: 99%

Section: Convex Hull Distance Based On a Confined Set -Mach-2mentioning

confidence: 99%

“…Following [31], to solve the above optimization problem on this restricted set, we first rewrite the objective function in Eqn. (5.13) by setting…”

Section: Convex Hull Distance Based On a Confined Set -Mach-2mentioning

confidence: 99%

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Fast and accurate image and video analysis on Riemannian manifolds

Zhao¹

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Statistically-Motivated Second-Order Pooling

Salzmann

2018

Computer Vision – ECCV 2018

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Second-order pooling, a.k.a. bilinear pooling, has proven effective for deep learning based visual recognition. However, the resulting second-order networks yield a final representation that is orders of magnitude larger than that of standard, first-order ones, making them memory-intensive and cumbersome to deploy. Here, we introduce a general, parametric compression strategy that can produce more compact representations than existing compression techniques, yet outperform both compressed and uncompressed second-order models. Our approach is motivated by a statistical analysis of the network's activations, relying on operations that lead to a Gaussian-distributed final representation, as inherently used by first-order deep networks. As evidenced by our experiments, this lets us outperform the state-of-the-art first-order and second-order models on several benchmark recognition datasets.

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Geometric Optimization in Machine Learning

Sra

Hosseini

2016

Algorithmic Advances in Riemannian Geometry and Applications

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Riemannian Sparse Coding for Positive Definite Matrices

Cited by 49 publications

References 30 publications

Fast and accurate image and video analysis on Riemannian manifolds

Fast and accurate image and video analysis on Riemannian manifolds

Statistically-Motivated Second-Order Pooling

Geometric Optimization in Machine Learning

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