850 research outputs found
An Information-geometric Approach to Sensor Management
An information-geometric approach to sensor management is introduced that is
based on following geodesic curves in a manifold of possible sensor
configurations. This perspective arises by observing that, given a parameter
estimation problem to be addressed through management of sensor assets, any
particular sensor configuration corresponds to a Riemannian metric on the
parameter manifold. With this perspective, managing sensors involves navigation
on the space of all Riemannian metrics on the parameter manifold, which is
itself a Riemannian manifold. Existing work assumes the metric on the parameter
manifold is one that, in statistical terms, corresponds to a Jeffreys prior on
the parameter to be estimated. It is observed that informative priors, as arise
in sensor management, can also be accommodated. Given an initial sensor
configuration, the trajectory along which to move in sensor configuration space
to gather most information is seen to be locally defined by the geodesic
structure of this manifold. Further, divergences based on Fisher and Shannon
information lead to the same Riemannian metric and geodesics.Comment: 4 pages, 3 figures, to appear in Proceedings of the IEEE
International Conference on Acoustics, Speech, and Signal Processing, March
201
Blind Demixing for Low-Latency Communication
In the next generation wireless networks, lowlatency communication is
critical to support emerging diversified applications, e.g., Tactile Internet
and Virtual Reality. In this paper, a novel blind demixing approach is
developed to reduce the channel signaling overhead, thereby supporting
low-latency communication. Specifically, we develop a low-rank approach to
recover the original information only based on a single observed vector without
any channel estimation. Unfortunately, this problem turns out to be a highly
intractable non-convex optimization problem due to the multiple non-convex
rankone constraints. To address the unique challenges, the quotient manifold
geometry of product of complex asymmetric rankone matrices is exploited by
equivalently reformulating original complex asymmetric matrices to the
Hermitian positive semidefinite matrices. We further generalize the geometric
concepts of the complex product manifolds via element-wise extension of the
geometric concepts of the individual manifolds. A scalable Riemannian
trust-region algorithm is then developed to solve the blind demixing problem
efficiently with fast convergence rates and low iteration cost. Numerical
results will demonstrate the algorithmic advantages and admirable performance
of the proposed algorithm compared with the state-of-art methods.Comment: 14 pages, accepted by IEEE Transaction on Wireless Communicatio
PyDEC: Software and Algorithms for Discretization of Exterior Calculus
This paper describes the algorithms, features and implementation of PyDEC, a
Python library for computations related to the discretization of exterior
calculus. PyDEC facilitates inquiry into both physical problems on manifolds as
well as purely topological problems on abstract complexes. We describe
efficient algorithms for constructing the operators and objects that arise in
discrete exterior calculus, lowest order finite element exterior calculus and
in related topological problems. Our algorithms are formulated in terms of
high-level matrix operations which extend to arbitrary dimension. As a result,
our implementations map well to the facilities of numerical libraries such as
NumPy and SciPy. The availability of such libraries makes Python suitable for
prototyping numerical methods. We demonstrate how PyDEC is used to solve
physical and topological problems through several concise examples.Comment: Revised as per referee reports. Added information on scalability,
removed redundant text, emphasized the role of matrix based algorithms,
shortened length of pape
Generalized Weiszfeld algorithms for Lq optimization
In many computer vision applications, a desired model of some type is computed by minimizing a cost function based on several measurements. Typically, one may compute the model that minimizes the L₂ cost, that is the sum of squares of measurement errors with respect to the model. However, the Lq solution which minimizes the sum of the qth power of errors usually gives more robust results in the presence of outliers for some values of q, for example, q = 1. The Weiszfeld algorithm is a classic algorithm for finding the geometric L1 mean of a set of points in Euclidean space. It is provably optimal and requires neither differentiation, nor line search. The Weiszfeld algorithm has also been generalized to find the L1 mean of a set of points on a Riemannian manifold of non-negative curvature. This paper shows that the Weiszfeld approach may be extended to a wide variety of problems to find an Lq mean for 1 ≤ q <; 2, while maintaining simplicity and provable convergence. We apply this problem to both single-rotation averaging (under which the algorithm provably finds the global Lq optimum) and multiple rotation averaging (for which no such proof exists). Experimental results of Lq optimization for rotations show the improved reliability and robustness compared to L₂ optimization.This research has been funded by National ICT Australia
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