7,805 research outputs found
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
Randomized methods for matrix computations
The purpose of this text is to provide an accessible introduction to a set of
recently developed algorithms for factorizing matrices. These new algorithms
attain high practical speed by reducing the dimensionality of intermediate
computations using randomized projections. The algorithms are particularly
powerful for computing low-rank approximations to very large matrices, but they
can also be used to accelerate algorithms for computing full factorizations of
matrices. A key competitive advantage of the algorithms described is that they
require less communication than traditional deterministic methods
Tyler's Covariance Matrix Estimator in Elliptical Models with Convex Structure
We address structured covariance estimation in elliptical distributions by
assuming that the covariance is a priori known to belong to a given convex set,
e.g., the set of Toeplitz or banded matrices. We consider the General Method of
Moments (GMM) optimization applied to robust Tyler's scatter M-estimator
subject to these convex constraints. Unfortunately, GMM turns out to be
non-convex due to the objective. Instead, we propose a new COCA estimator - a
convex relaxation which can be efficiently solved. We prove that the relaxation
is tight in the unconstrained case for a finite number of samples, and in the
constrained case asymptotically. We then illustrate the advantages of COCA in
synthetic simulations with structured compound Gaussian distributions. In these
examples, COCA outperforms competing methods such as Tyler's estimator and its
projection onto the structure set.Comment: arXiv admin note: text overlap with arXiv:1311.059
Probabilistic Multilevel Clustering via Composite Transportation Distance
We propose a novel probabilistic approach to multilevel clustering problems
based on composite transportation distance, which is a variant of
transportation distance where the underlying metric is Kullback-Leibler
divergence. Our method involves solving a joint optimization problem over
spaces of probability measures to simultaneously discover grouping structures
within groups and among groups. By exploiting the connection of our method to
the problem of finding composite transportation barycenters, we develop fast
and efficient optimization algorithms even for potentially large-scale
multilevel datasets. Finally, we present experimental results with both
synthetic and real data to demonstrate the efficiency and scalability of the
proposed approach.Comment: 25 pages, 3 figure
Exploring multimodal data fusion through joint decompositions with flexible couplings
A Bayesian framework is proposed to define flexible coupling models for joint
tensor decompositions of multiple data sets. Under this framework, a natural
formulation of the data fusion problem is to cast it in terms of a joint
maximum a posteriori (MAP) estimator. Data driven scenarios of joint posterior
distributions are provided, including general Gaussian priors and non Gaussian
coupling priors. We present and discuss implementation issues of algorithms
used to obtain the joint MAP estimator. We also show how this framework can be
adapted to tackle the problem of joint decompositions of large datasets. In the
case of a conditional Gaussian coupling with a linear transformation, we give
theoretical bounds on the data fusion performance using the Bayesian Cramer-Rao
bound. Simulations are reported for hybrid coupling models ranging from simple
additive Gaussian models, to Gamma-type models with positive variables and to
the coupling of data sets which are inherently of different size due to
different resolution of the measurement devices.Comment: 15 pages, 7 figures, revised versio
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