2 June 2015 A new EEG measure using the 1D cluster variation method
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A new information measure, drawing on the 1-D Cluster Variation Method (CVM), describes local pattern distributions (nearest-neighbor and next-nearest neighbor) in a binary 1-D vector in terms of a single interaction enthalpy parameter h for the specific case where the fractions of elements in each of two states are the same (x1=x2=0.5). An example application of this method would be for EEG interpretation in Brain-Computer Interfaces (BCIs), especially in the frontier of invariant biometrics based on distinctive and invariant individual responses to stimuli containing an image of a person with whom there is a strong affiliative response (e.g., to a person’s grandmother). This measure is obtained by mapping EEG observed configuration variables (z1, z2, z3 for next-nearest neighbor triplets) to h using the analytic function giving h in terms of these variables at equilibrium. This mapping results in a small phase space region of resulting h values, which characterizes local pattern distributions in the source data. The 1-D vector with equal fractions of units in each of the two states can be obtained using the method for transforming natural images into a binarized equi-probability ensemble (Saremi & Sejnowski, 2014; Stephens et al., 2013). An intrinsically 2-D data configuration can be mapped to 1-D using the 1-D Peano-Hilbert space-filling curve, which has demonstrated a 20 dB lower baseline using the method compared with other approaches (cf. SPIE ICA etc. by Hsu & Szu, 2014). This CVM-based method has multiple potential applications; one near-term one is optimizing classification of the EEG signals from a COTS 1-D BCI baseball hat. This can result in a convenient 3-D lab-tethered EEG, configured in a 1-D CVM equiprobable binary vector, and potentially useful for Smartphone wireless display. Longer-range applications include interpreting neural assembly activations via high-density implanted soft, cellular-scale electrodes.
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Alianna J. Maren, Alianna J. Maren, Harold H. Szu, Harold H. Szu, } "A new EEG measure using the 1D cluster variation method", Proc. SPIE 9496, Independent Component Analyses, Compressive Sampling, Large Data Analyses (LDA), Neural Networks, Biosystems, and Nanoengineering XIII, 949609 (2 June 2015); doi: 10.1117/12.2184651; https://doi.org/10.1117/12.2184651

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