373 research outputs found
Disturbance Grassmann Kernels for Subspace-Based Learning
In this paper, we focus on subspace-based learning problems, where data
elements are linear subspaces instead of vectors. To handle this kind of data,
Grassmann kernels were proposed to measure the space structure and used with
classifiers, e.g., Support Vector Machines (SVMs). However, the existing
discriminative algorithms mostly ignore the instability of subspaces, which
would cause the classifiers misled by disturbed instances. Thus we propose
considering all potential disturbance of subspaces in learning processes to
obtain more robust classifiers. Firstly, we derive the dual optimization of
linear classifiers with disturbance subject to a known distribution, resulting
in a new kernel, Disturbance Grassmann (DG) kernel. 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. Experiments on action data indicate that the proposed kernels
perform better compared to state-of-the-art subspace-based methods, even in a
worse environment.Comment: This paper include 3 figures, 10 pages, and has been accpeted to
SIGKDD'1
Generalized Rank Pooling for Activity Recognition
Most popular deep models for action recognition split video sequences into
short sub-sequences consisting of a few frames; frame-based features are then
pooled for recognizing the activity. Usually, this pooling step discards the
temporal order of the frames, which could otherwise be used for better
recognition. Towards this end, we propose a novel pooling method, generalized
rank pooling (GRP), that takes as input, features from the intermediate layers
of a CNN that is trained on tiny sub-sequences, and produces as output the
parameters of a subspace which (i) provides a low-rank approximation to the
features and (ii) preserves their temporal order. We propose to use these
parameters as a compact representation for the video sequence, which is then
used in a classification setup. We formulate an objective for computing this
subspace as a Riemannian optimization problem on the Grassmann manifold, and
propose an efficient conjugate gradient scheme for solving it. Experiments on
several activity recognition datasets show that our scheme leads to
state-of-the-art performance.Comment: Accepted at IEEE International Conference on Computer Vision and
Pattern Recognition (CVPR), 201
Building Deep Networks on Grassmann Manifolds
Learning representations on Grassmann manifolds is popular in quite a few
visual recognition tasks. In order to enable deep learning on Grassmann
manifolds, this paper proposes a deep network architecture by generalizing the
Euclidean network paradigm to Grassmann manifolds. In particular, we design
full rank mapping layers to transform input Grassmannian data to more desirable
ones, exploit re-orthonormalization layers to normalize the resulting matrices,
study projection pooling layers to reduce the model complexity in the
Grassmannian context, and devise projection mapping layers to respect
Grassmannian geometry and meanwhile achieve Euclidean forms for regular output
layers. To train the Grassmann networks, we exploit a stochastic gradient
descent setting on manifolds of the connection weights, and study a matrix
generalization of backpropagation to update the structured data. The
evaluations on three visual recognition tasks show that our Grassmann networks
have clear advantages over existing Grassmann learning methods, and achieve
results comparable with state-of-the-art approaches.Comment: AAAI'18 pape
Grassmann Learning for Recognition and Classification
Computational performance associated with high-dimensional data is a common challenge for real-world classification and recognition systems. Subspace learning has received considerable attention as a means of finding an efficient low-dimensional representation that leads to better classification and efficient processing. A Grassmann manifold is a space that promotes smooth surfaces, where points represent subspaces and the relationship between points is defined by a mapping of an orthogonal matrix. Grassmann learning involves embedding high dimensional subspaces and kernelizing the embedding onto a projection space where distance computations can be effectively performed. In this dissertation, Grassmann learning and its benefits towards action classification and face recognition in terms of accuracy and performance are investigated and evaluated. Grassmannian Sparse Representation (GSR) and Grassmannian Spectral Regression (GRASP) are proposed as Grassmann inspired subspace learning algorithms. GSR is a novel subspace learning algorithm that combines the benefits of Grassmann manifolds with sparse representations using least squares loss §¤1-norm minimization for improved classification. GRASP is a novel subspace learning algorithm that leverages the benefits of Grassmann manifolds and Spectral Regression in a framework that supports high discrimination between classes and achieves computational benefits by using manifold modeling and avoiding eigen-decomposition. The effectiveness of GSR and GRASP is demonstrated for computationally intensive classification problems: (a) multi-view action classification using the IXMAS Multi-View dataset, the i3DPost Multi-View dataset, and the WVU Multi-View dataset, (b) 3D action classification using the MSRAction3D dataset and MSRGesture3D dataset, and (c) face recognition using the ATT Face Database, Labeled Faces in the Wild (LFW), and the Extended Yale Face Database B (YALE). Additional contributions include the definition of Motion History Surfaces (MHS) and Motion Depth Surfaces (MDS) as descriptors suitable for activity representations in video sequences and 3D depth sequences. An in-depth analysis of Grassmann metrics is applied on high dimensional data with different levels of noise and data distributions which reveals that standardized Grassmann kernels are favorable over geodesic metrics on a Grassmann manifold. Finally, an extensive performance analysis is made that supports Grassmann subspace learning as an effective approach for classification and recognition
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