429,662 research outputs found
Minimax rank estimation for subspace tracking
Rank estimation is a classical model order selection problem that arises in a
variety of important statistical signal and array processing systems, yet is
addressed relatively infrequently in the extant literature. Here we present
sample covariance asymptotics stemming from random matrix theory, and bring
them to bear on the problem of optimal rank estimation in the context of the
standard array observation model with additive white Gaussian noise. The most
significant of these results demonstrates the existence of a phase transition
threshold, below which eigenvalues and associated eigenvectors of the sample
covariance fail to provide any information on population eigenvalues. We then
develop a decision-theoretic rank estimation framework that leads to a simple
ordered selection rule based on thresholding; in contrast to competing
approaches, however, it admits asymptotic minimax optimality and is free of
tuning parameters. We analyze the asymptotic performance of our rank selection
procedure and conclude with a brief simulation study demonstrating its
practical efficacy in the context of subspace tracking.Comment: 10 pages, 4 figures; final versio
Some remarks on the continuity equation
We describe some relations between the properties of the Cauchy problem for
an ODE and the properties of the Cauchy problem for the associated continuity
equation in the class of measures
Insights from evolutionary psychology into primary affective reactions and advertisement effectiveness
Autonomous monitoring of cliff nesting seabirds using computer vision
In this paper we describe a proposed system for automatic visual monitoring of seabird populations. Image sequences of cliff face nesting sites are captured using time-lapse digital photography. We are developing image processing software which is designed to automatically interpret these images, determine the number of birds present, and monitor activity. We focus primarily on the the development of low-level image processing techniques to support this goal. We first describe our existing work in video processing, and show how it is suitable for this problem domain. Image samples from a particular nest site are presented, and used to describe the associated challenges. We conclude by showing how we intend to develop our work to construct a distributed system capable of simultaneously monitoring a number of sites in the same locality
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