113,368 research outputs found
Efficient Clustering on Riemannian Manifolds: A Kernelised Random Projection Approach
Reformulating computer vision problems over Riemannian manifolds has
demonstrated superior performance in various computer vision applications. This
is because visual data often forms a special structure lying on a lower
dimensional space embedded in a higher dimensional space. However, since these
manifolds belong to non-Euclidean topological spaces, exploiting their
structures is computationally expensive, especially when one considers the
clustering analysis of massive amounts of data. To this end, we propose an
efficient framework to address the clustering problem on Riemannian manifolds.
This framework implements random projections for manifold points via kernel
space, which can preserve the geometric structure of the original space, but is
computationally efficient. Here, we introduce three methods that follow our
framework. We then validate our framework on several computer vision
applications by comparing against popular clustering methods on Riemannian
manifolds. Experimental results demonstrate that our framework maintains the
performance of the clustering whilst massively reducing computational
complexity by over two orders of magnitude in some cases
Spectral Clustering with Jensen-type kernels and their multi-point extensions
Motivated by multi-distribution divergences, which originate in information
theory, we propose a notion of `multi-point' kernels, and study their
applications. We study a class of kernels based on Jensen type divergences and
show that these can be extended to measure similarity among multiple points. We
study tensor flattening methods and develop a multi-point (kernel) spectral
clustering (MSC) method. We further emphasize on a special case of the proposed
kernels, which is a multi-point extension of the linear (dot-product) kernel
and show the existence of cubic time tensor flattening algorithm in this case.
Finally, we illustrate the usefulness of our contributions using standard data
sets and image segmentation tasks.Comment: To appear in IEEE Computer Society Conference on Computer Vision and
Pattern Recognitio
Graph kernels between point clouds
Point clouds are sets of points in two or three dimensions. Most kernel
methods for learning on sets of points have not yet dealt with the specific
geometrical invariances and practical constraints associated with point clouds
in computer vision and graphics. In this paper, we present extensions of graph
kernels for point clouds, which allow to use kernel methods for such ob jects
as shapes, line drawings, or any three-dimensional point clouds. In order to
design rich and numerically efficient kernels with as few free parameters as
possible, we use kernels between covariance matrices and their factorizations
on graphical models. We derive polynomial time dynamic programming recursions
and present applications to recognition of handwritten digits and Chinese
characters from few training examples
When Kernel Methods meet Feature Learning: Log-Covariance Network for Action Recognition from Skeletal Data
Human action recognition from skeletal data is a hot research topic and
important in many open domain applications of computer vision, thanks to
recently introduced 3D sensors. In the literature, naive methods simply
transfer off-the-shelf techniques from video to the skeletal representation.
However, the current state-of-the-art is contended between to different
paradigms: kernel-based methods and feature learning with (recurrent) neural
networks. Both approaches show strong performances, yet they exhibit heavy, but
complementary, drawbacks. Motivated by this fact, our work aims at combining
together the best of the two paradigms, by proposing an approach where a
shallow network is fed with a covariance representation. Our intuition is that,
as long as the dynamics is effectively modeled, there is no need for the
classification network to be deep nor recurrent in order to score favorably. We
validate this hypothesis in a broad experimental analysis over 6 publicly
available datasets.Comment: 2017 IEEE Computer Vision and Pattern Recognition (CVPR) Workshop
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