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From Manifold to Manifold: Geometry-Aware Dimensionality Reduction for SPD Matrices
Published on Oct 29, 20142791 Views
Representing images and videos with Symmetric Positive Definite (SPD) matrices and considering the Riemannian geometry of the resulting space has proven beneficial for many recognition tasks. Unfortun
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Chapter list
From Manifold to Manifold: Geometry-Aware Dimensionality Reduction for SPD Matrices00:00
Why SPD Matrices? - 100:13
Why SPD Matrices? - 200:47
Our Goal - 101:02
Our Goal - 201:14
Our Goal - 301:22
The Riemannian Structure of SPD Matrices - 101:33
The Riemannian Structure of SPD Matrices - 201:44
The Riemannian Structure of SPD Matrices - 301:51
The Riemannian Structure of SPD Matrices - 401:58
The Riemannian Structure of SPD Matrices - 502:25
Dimensionality Reduction of Manifold-Valued Data02:51
Our Approach03:40
Riemannian Geometry of SPD Manifolds - 104:10
Riemannian Geometry of SPD Manifolds - 205:03
Riemannian Geometry of SPD Manifolds - 305:14
Riemannian Geometry of SPD Manifolds - 405:23
Mapping to Lower-Dimensional SPD Matrices - 105:39
Mapping to Lower-Dimensional SPD Matrices - 205:51
Mapping to Lower-Dimensional SPD Matrices - 306:05
Anity-Based Dimensionality Reduction - 106:14
Anity-Based Dimensionality Reduction - 206:33
Affinity - 107:05
Affinity - 207:24
Affinity - 307:38
Preventing Degeneracies - 107:46
Preventing Degeneracies - 208:09
Preventing Degeneracies - 308:27
Learning as Optimization on a Grassmann Manifold - 108:44
Learning as Optimization on a Grassmann Manifold - 209:29
Learning as Optimization on a Grassmann Manifold - 309:48
Classi cation Algorithms10:04
Evaluated Methods10:51
Material Recognition11:18
Material Recognition: Results - 112:10
Material Recognition: Results - 212:36
Material Recognition: Results - 312:55
Action Recognition from Mocap Data13:04
Action Recognition: Results - 113:43
Action Recognition: Results - 214:01
Action Recognition: Results - 314:14
Conclusions - 114:24
Conclusions - 214:58