86 research outputs found
Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds
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 over
the space of linear subspaces, which form Riemannian structures known as
Grassmann manifolds. 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 closed-form solutions 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 Hilbert
spaces.
Experiments 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
graph-embedding Grassmann discriminant analysis.Comment: Appearing in International Journal of Computer Visio
Extrinsic methods for coding and dictionary learning on grassmann manifolds
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. Experiments 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 graph-embedding Grassmann discriminant analysis
Comparative Evaluation of Action Recognition Methods via Riemannian Manifolds, Fisher Vectors and GMMs: Ideal and Challenging Conditions
We present a comparative evaluation of various techniques for action
recognition while keeping as many variables as possible controlled. We employ
two categories of Riemannian manifolds: symmetric positive definite matrices
and linear subspaces. For both categories we use their corresponding nearest
neighbour classifiers, kernels, and recent kernelised sparse representations.
We compare against traditional action recognition techniques based on Gaussian
mixture models and Fisher vectors (FVs). We evaluate these action recognition
techniques under ideal conditions, as well as their sensitivity in more
challenging conditions (variations in scale and translation). Despite recent
advancements for handling manifolds, manifold based techniques obtain the
lowest performance and their kernel representations are more unstable in the
presence of challenging conditions. The FV approach obtains the highest
accuracy under ideal conditions. Moreover, FV best deals with moderate scale
and translation changes
Expanding the Family of Grassmannian Kernels: An Embedding Perspective
Modeling videos and image-sets as linear subspaces has proven beneficial for
many visual recognition tasks. However, it also incurs challenges arising from
the fact that linear subspaces do not obey Euclidean geometry, but lie on a
special type of Riemannian manifolds known as Grassmannian. To leverage the
techniques developed for Euclidean spaces (e.g, support vector machines) with
subspaces, several recent studies have proposed to embed the Grassmannian into
a Hilbert space by making use of a positive definite kernel. Unfortunately,
only two Grassmannian kernels are known, none of which -as we will show- is
universal, which limits their ability to approximate a target function
arbitrarily well. Here, we introduce several positive definite Grassmannian
kernels, including universal ones, and demonstrate their superiority over
previously-known kernels in various tasks, such as classification, clustering,
sparse coding and hashing
Locality Preserving Projections for Grassmann manifold
Learning on Grassmann manifold has become popular in many computer vision
tasks, with the strong capability to extract discriminative information for
imagesets and videos. However, such learning algorithms particularly on
high-dimensional Grassmann manifold always involve with significantly high
computational cost, which seriously limits the applicability of learning on
Grassmann manifold in more wide areas. In this research, we propose an
unsupervised dimensionality reduction algorithm on Grassmann manifold based on
the Locality Preserving Projections (LPP) criterion. LPP is a commonly used
dimensionality reduction algorithm for vector-valued data, aiming to preserve
local structure of data in the dimension-reduced space. The strategy is to
construct a mapping from higher dimensional Grassmann manifold into the one in
a relative low-dimensional with more discriminative capability. The proposed
method can be optimized as a basic eigenvalue problem. The performance of our
proposed method is assessed on several classification and clustering tasks and
the experimental results show its clear advantages over other Grassmann based
algorithms.Comment: Accepted by IJCAI 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
- …