SOM Cognitive Modeling of Autistic and Schizophrenic Traits Using an Oscillating Topological Neighborhood Width Function

SOM Cognitive Modeling of Autistic and Schizophrenic Traits Using an Oscillating Topological Neighborhood Width Function Spyridon Revithis (revithiss@cse.unsw.edu.au) William H. Wilson (billw@cse.unsw.edu.au) Nadine Marcus (nadinem@cse.unsw.edu.au) School of Computer Science and Engineering, University of New South Wales UNSW-Sydney, NSW 2052, Australia Abstract characteristics and a range of powerful properties, particularly relevant to understanding and modeling of cortical brain maps, including approximation of the input space, topological ordering, density matching, and feature selection (Haykin, 1999). This study investigates cognitive modeling aspects of modeling neuro-developmental disorders using SOM neural networks. The first section presents the SOM modeling framework used in this work, and introduces a novel modification in the SOM formation algorithm with significant cognitive modeling implications. In the subsequent two sections, core biological and behavioral characteristics of two mental disorders, autism and schizophrenia, respectively, are modeled using a prototype SOM model. The last section provides a discussion of the computational and theoretical parameters of the SOM modeling employed in the paper. The artificial neural network class of self-organizing maps (SOMs) is a powerful and promising cognitive modeling tool in the study of the brain and its disorders. Under this premise, this paper proposes a novel modification of the standard SOM algorithm in the form of an oscillating Topological Neighborhood (TN) width function. Existing research in neuroscience indicates that SOMs with oscillating TN width could exhibit higher biological plausibility than standard TN width SOMs. In this paper, two neuro-developmental disorders, autism and schizophrenia, are modeled, based on existing neurocomputational theories, using both SOM approaches. The simulation results demonstrate that there is significant equivalence between standard and oscillating TN width SOM modeling in terms of map formation behavior, output and structure. The theoretical and computational arguments presented validate the proposed SOM modification within a cognitive modeling framework. Keywords: Self-Organizing Maps, Cognitive Modeling, Cortical Maps, Autism, Delusions, Schizophrenia. The SOM Modeling Framework Computational modeling offers a powerful way to study cognition and behavior. It has been applied to numerous areas of psychology and provides a more promising framework than those based on verbal models in terms of methodological diversity and applicability potential (Sun, Coward & Zenzen, 2005). An ever-increasing number of computational modeling studies are dedicated to the modeling of cognitive and developmental phenomena using artificial neural networks (Thomas & Karmiloff-Smith, 2003; Polk & Seifert, 2002; Parks, Levine & Long, 1998). Shultz (2003) provides a comparative evaluation of the different computational neural network systems used to model cognitive developmental phenomena. An important class of such modeling networks is the self-organizing feature map; it is based on a Hebbian-type (Hebb, 1949) unsupervised neural learning mechanism and uniquely resembles topographic cortical maps in the brain to which has directly comparable structure and output characteristics (Spitzer, 1995b; Livingstone & Hubel, 1988; Blasdel & Salama, 1986; Merzenich & Kaas, 1980). Willshaw and von der Malsburg (1976) originally proposed the self-organizing neural network to account for the retinotopic mapping problem. Kohonen’s version (2001) -commonly abbreviated to ‘SOM’-, however, possesses significant computational Aspects of SOM Neural Networks A SOM is a non-linear unsupervised-learning computational neural network consisting of two layers. It has the capacity to map an input ‘environmental’ layer, consisting of patterns of fixed but arbitrary dimension, onto a (usually) one or two dimensional lattice ‘representational’ layer. The representation of environmental input in the output layer (called the map) is performed in a topologically ordered fashion, maintaining the non-linear input data distribution, and involves dimensionality reduction. Figure 1 shows an abstract depiction of a two-dimensional SOM; each input layer pattern vector connects fully with the map neurons. Map Introduction Input pattern Figure 1: A two-dimensional SOM.