Abstract
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 σ 2(F), that is, the variance of an F-value from variance analysis. Three test statistics are derived from the so-called F-ratio σ 2(F)/F 2. 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 χ, α-, and δ-power was found.
Highlights
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
As a step towards such a statistical assessment, we present a data resampling approach
Summary
The reduction of a feature vector to an optimized dimensionality is a common problem in the context of signal analysis. F-ratio test statistics have indicated to (a) better retrieve fixed effects by fading away the random parts and (b) allow for an incremental test, that is, testing the effect of the inclusion of additional variables into an existing feature vector. The latter property makes them especially interesting when one tries to reduce the dimension of a feature vector to an optimal size. We show the inclusion of the outcome of these multivariate statistical methods into a selection scheme following a Bayesian heuristic by weighting hypotheses This allows for reliably constructing weights for the measures. It is shown that an optimal combination of the so-called relative unfolding (or Taken’s) χ and two power spectral estimates (α, δ) will allow for a correct classification of at least 81% of the probands, even in absence of active mental tasks
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