%0 Journal Article
%T F-Ratio Test and Hypothesis Weighting: A Methodology to Optimize Feature Vector Size
%A R. M. D¨¹nki
%A M. Dressel
%J Journal of Biophysics
%D 2011
%I Hindawi Publishing Corporation
%R 10.1155/2011/290617
%X Reducing a feature vector to an optimized dimensionality is a common problem in biomedical signal analysis. This analysis retrieves the characteristics of the time series and its associated measures with an adequate methodology followed by an appropriate statistical assessment of these measures (e.g., spectral power or fractal dimension). As a step towards such a statistical assessment, we present a data resampling approach. The techniques allow estimating , that is, the variance of an F-value from variance analysis. Three test statistics are derived from the so-called F-ratio . A Bayesian formalism assigns weights to hypotheses and their corresponding measures considered (hypothesis weighting). This leads to complete, partial, or noninclusion of these measures into an optimized feature vector. We thus distinguished the EEG of healthy probands from the EEG of patients diagnosed as schizophrenic. A reliable discriminance performance of 81% based on Taken's ¦Ö, -, and -power was found. 1. Introduction The reduction of a feature vector to an optimized dimensionality is a common problem in the context of signal analysis. Consider for example, the assessment of the dynamics of biomedical/biophysical signals (e.g., EEG time series). These may be assessed with either linear (mainly: power spectral) and/or nonlinear (mainly: fractal dimension) analysis methods [1¨C5]. Each of the methods used for analysis of the time series extracts one or several measures out of a signal like peak frequency, band power, correlation dimension, K-entropy, and so forth. Some, but not necessarily all of these measures are supposed to exhibit state-specific information connected to the underlying biological/physiological process. Let us denote a collection of these measures a feature vector. An appropriately weighted collection of these information, specific measures may span an optimal feature vector in the sense that the states may be best separated. The temporal variation of these signals often has to be regarded as being almost stationary over limited segments only and not as being stationary in a strict sense, a property which is sometimes denoted as ¡°quasistationarity¡±. This suggests regarding a specific outcome as being randomly drawn from a distribution of outcomes around a state-specific mean. Hence any inference made on such outcomes must be based on statistics relating the effect of interest to that stochastic variation even when regarding a single individual. If a comparative study is conducted, one has to select samples of probands, and this again introduces sources of
%U http://www.hindawi.com/journals/jbp/2011/290617/