90 Artificial Adaptive Systems in Medicine, 90-103 Massimo Buscema / Enzo Grossi (Eds.) All rights reserved - © 2009 Bentham Science Publishers Ltd. CHAPTER 10 IFAST: Implicit Function as Squashing Time for EEG Analysis ∗ - Theory Massimo Buscema 1 , Paolo Maria Rossini 2 , Enzo Grossi 3 , Claudio Babiloni 4 Abstract: This chapter presents the innovative use of special types of Artificial Neural Networks assembled in a novel methodology capable of compressing the temporal sequence of EEG data into spatial invariants. The spatial content of the EEG voltage recorded from 19 channels along 60 seconds is extracted by a step- wise procedure using ANNs (SEMEION©). The core of the procedure is that the ANNs do not classify indi- viduals by directly using the EEG data as an input. Rather, the data inputs for the classification are the weights of the connections within a non linear Auto-Associative ANN trained to generate the recorded EEG data. These connection weights represent an optimal model of the peculiar spatial features of the EEG pat- terns at scalp surface. The classification based on these weight is then performed by a supervised ANN. Half of the EEG database is used for the ANN training and the remaining EEG database serves for the automatic classification phase (testing). The best results distinguishing between mild Alzheimer patients and Mild Cognitive Impairment patient were equal to 92.33%. The comparative results obtained with the best method so far described in the literature, based on blind source separation and Wavelet pre-processing, were 80.43% ( p < 0.001). These results confirmed the working hypothesis and represent the basis for research aimed at inte- grating spatial and temporal information content of the EEG. Keywords: IFAST; Spatial invariants; Mild cognitive impairment (MCI), Alzheimer's disease (AD), Elec- troencephalography (EEG), Artificial Neural Networks (ANNs). General Philosophy The core of the procedure is that the ANNs do not classify individuals by directly using the EEG data as an input. Rather, the data inputs for the classification are the weights of the connections within a re- circulation (non- supervised) ANN trained to generate the recorded EEG data. These connection weights rep- resent an optimal model of the peculiar spatial features of the EEG patterns at the scalp surface. The final classification is based on these weights and is performed by a standard supervised ANN. I.F.A.S.T. is an acronym for “Implicit Function as Squashing Time”. It is a method, therefore, that tries to understand the implicit function in a multivariate data series by compressing the temporal sequence of data into spatial invariants. This method is based on three general observations: 1. Any multivariate sequence of signals coming from the same source represents a non-synchronous tempo- ral phenomenon: the behaviour of every channel is the synthesis of the influence of the other channels at previous but not identical times and in different quantities, and of its own activity at that moment. At the same times, the activity of every channel at a certain moment in time is going to influence the behaviour of the others at different times and in different quantities. Therefore, every multivariate sequence of sig- nals coming from the same natural source is a complex asynchronous dynamic system, highly nonlinear, in which each channel’s behaviour is understandable only in relation to all the others. 2. Given a multivariate sequence of signals generating from the same source, the implicit function defining said asynchronous process is the conversion of that same process into a complex hyper-surface, repre- ∗ IFAST is a European patent (application number EP06115223.7; date of receipt: 09.06.2006). Owner: Semeion Research Center, Via Sersale, 117, Rome 00128, Italy. Inventor: Massimo Buscema. The present paper is deeply inspired to a precedent work published in AIM: Buscema M, Rossini P, Babiloni C, Grossi E. The I.F.A.S.T. Model, a novel parallel non-linear EEG analysis technique, distinguishes mild cognitive impairment and Alzheimer’s disease patients with high degree of accu- racy. Artif Intel Med 2007;40(2):127–141. 1 Massimo Buscema, Semeion Research Center, Via Sersale 117, 00128 Rome, Italy. E-mail: m.buscema@semeion.it 2 Paolo Maria Rossini, Ospedale San Giovanni Calibita “Fatebenefratelli”, Isola Tiberina, 00153 Rome, Italy. IRCCS Centro San Giovanni di Dio Fa- tebenefratelli, 25100 Brescia, Italy. Department of Clinical Neurosciences, University of Rome Campus Biomedico, 00155 Rome, Italy. E-mail: pao- lomaria.rossini@afar.it 3 Enzo Grossi, Bracco Medical Department, Via 25 Aprile 4, 20097 S.Donato Milanese, Milan, Italy. E-mail: enzo.grossi@bracco.com 4 Claudio Babiloni, Department of Human Physiology and Pharmacology, University of Rome La Sapienza, 00185 Rome, Italy. E-mail: clau- dio.babiloni@uniroma1.it