8,916 research outputs found
High-Rate Vector Quantization for the Neyman-Pearson Detection of Correlated Processes
This paper investigates the effect of quantization on the performance of the
Neyman-Pearson test. It is assumed that a sensing unit observes samples of a
correlated stationary ergodic multivariate process. Each sample is passed
through an N-point quantizer and transmitted to a decision device which
performs a binary hypothesis test. For any false alarm level, it is shown that
the miss probability of the Neyman-Pearson test converges to zero exponentially
as the number of samples tends to infinity, assuming that the observed process
satisfies certain mixing conditions. The main contribution of this paper is to
provide a compact closed-form expression of the error exponent in the high-rate
regime i.e., when the number N of quantization levels tends to infinity,
generalizing previous results of Gupta and Hero to the case of non-independent
observations. If d represents the dimension of one sample, it is proved that
the error exponent converges at rate N^{2/d} to the one obtained in the absence
of quantization. As an application, relevant high-rate quantization strategies
which lead to a large error exponent are determined. Numerical results indicate
that the proposed quantization rule can yield better performance than existing
ones in terms of detection error.Comment: 47 pages, 7 figures, 1 table. To appear in the IEEE Transactions on
Information Theor
Quadratic optimal functional quantization of stochastic processes and numerical applications
In this paper, we present an overview of the recent developments of
functional quantization of stochastic processes, with an emphasis on the
quadratic case. Functional quantization is a way to approximate a process,
viewed as a Hilbert-valued random variable, using a nearest neighbour
projection on a finite codebook. A special emphasis is made on the
computational aspects and the numerical applications, in particular the pricing
of some path-dependent European options.Comment: 41 page
Magnification Control in Self-Organizing Maps and Neural Gas
We consider different ways to control the magnification in self-organizing
maps (SOM) and neural gas (NG). Starting from early approaches of magnification
control in vector quantization, we then concentrate on different approaches for
SOM and NG. We show that three structurally similar approaches can be applied
to both algorithms: localized learning, concave-convex learning, and winner
relaxing learning. Thereby, the approach of concave-convex learning in SOM is
extended to a more general description, whereas the concave-convex learning for
NG is new. In general, the control mechanisms generate only slightly different
behavior comparing both neural algorithms. However, we emphasize that the NG
results are valid for any data dimension, whereas in the SOM case the results
hold only for the one-dimensional case.Comment: 24 pages, 4 figure
Magnification Control in Winner Relaxing Neural Gas
An important goal in neural map learning, which can conveniently be
accomplished by magnification control, is to achieve information optimal coding
in the sense of information theory. In the present contribution we consider the
winner relaxing approach for the neural gas network. Originally, winner
relaxing learning is a slight modification of the self-organizing map learning
rule that allows for adjustment of the magnification behavior by an a priori
chosen control parameter. We transfer this approach to the neural gas
algorithm. The magnification exponent can be calculated analytically for
arbitrary dimension from a continuum theory, and the entropy of the resulting
map is studied numerically conf irming the theoretical prediction. The
influence of a diagonal term, which can be added without impacting the
magnification, is studied numerically. This approach to maps of maximal mutual
information is interesting for applications as the winner relaxing term only
adds computational cost of same order and is easy to implement. In particular,
it is not necessary to estimate the generally unknown data probability density
as in other magnification control approaches.Comment: 14pages, 2 figure
On the effect of quantization on performance at high rates
We study the effect of quantization on the performance of a scalar dynamical system in the high rate regime. We evaluate the LQ cost for two commonly used quantizers: uniform and logarithmic and provide a lower bound on performance of any centroid-based quantizer based on entropy arguments. We also consider the case when the channel drops data packets stochastically
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