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4 - Graph Theory Applied to Speech: Insights on Cognitive Deficit Diagnosis and Dream Research
- from Part II - Models of Neural and Cognitive Processing
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- By Natália Bezerra Mota, Brain Institute, Federal University of Rio Grande do Norte, Brazil, Mauro Copelli, Physics Department, Federal University of Pernambuco, Brazil, Sidarta Ribeiro, Brain Institute, Federal University of Rio Grande do Norte, Brazil
- Edited by Thierry Poibeau, Centre National de la Recherche Scientifique (CNRS), Paris, Aline Villavicencio, Universidade Federal do Rio Grande do Sul, Brazil
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- Book:
- Language, Cognition, and Computational Models
- Published online:
- 30 November 2017
- Print publication:
- 25 January 2018, pp 81-98
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Summary
Abstract
In the past ten years, graph theory has been widely employed in the study of natural and technological phenomena. The representation of the relationships among the units of a network allow for a quantitative analysis of its overall structure, beyond what can be understood by considering only a few units. Here we discuss the application of graph theory to psychiatric diagnosis of psychoses and dementias. The aim is to quantify the flow of thoughts of psychiatric patients, as expressed by verbal reports of dream or waking events. This flow of thoughts is hard to measure but is at the roots of psychiatry as well as psychoanalysis. To this end, speech graphs were initially designed with nodes representing lexemes and edges representing the temporal sequence between consecutive words, leading to directed multigraphs. In a subsequent study, individual words were considered as nodes and their temporal sequence as edges; this simplification allowed for the automatization of the process, effected by the free software Speech Graphs. Using this approach, one can calculate local and global attributes that characterize the network structure, such as the total number of nodes and edges, the number of nodes present in the largest connected and the largest strongly connected components, measures of recurrence such as loops of 1, 2, and 3 nodes, parallel and repeated edges, and global measures such as the average degree, density, diameter, average shortest path, and clustering coefficient. Using these network attributes we were able to automatically sort schizophrenia and bipolar patients undergoing psychosis, and also to separate these psychotic patients from subjects without psychosis, with more than 90% sensitivity and specificity. In addition to the use of the method for strictly clinical purposes, we found that differences in the content of the verbal reports correspond to structural differences at the graph level. When reporting a dream, healthy subjects without psychosis and psychotic subjects with bipolar disorder produced more complex graphs than when reporting waking activities of the previous day; this difference was not observed in psychotic subjects with schizophrenia, which produced equally poor reports irrespective of the content. As a consequence, graphs of dream reports were more efficient for the differential diagnosis of psychosis than graphs of daily reports. Based on these results we can conclude that graphs from dream reports are more informative about mental states, echoing the psychoanalytic notion that dreams are a privileged window into thought.
8 - Universal Asymptotics in Committee Machines with Tree Architecture
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- By Mauro Copelli, Limburgs Universitair Centrum B-3590 Diepenbeek, Belgium, Nestor Caticha, Instituto de Física, Universidade de São Paulo Caixa Postal 66318, 05389–970 São Paulo, SP, Brazil
- Edited by David Saad, Aston University
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- Book:
- On-Line Learning in Neural Networks
- Published online:
- 28 January 2010
- Print publication:
- 28 January 1999, pp 165-182
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Summary
Abstract
On-line supervised learning in the general K Tree Committee Machine (TCM) is studied for a uniform distribution of inputs. Examples are corrupted by multiplicative noise in the teacher output. From the differential equations which describe the learning dynamics, the modulation function which optimizes the generalization ability is exactly obtained for any finite K. The asymptotical behavior of the generalization error is shown to be independent of K. Robustness with respect to a misestimation of the noise level is also shown to be independent of K.
Introduction
When looking into the properties of different neural network architectures by studying their performance in different model situations, the main objective, rather than delving into the many differences, is to search for similarities. It is from these similarities that intrinsic properties of learning, that go beyond the particular characteristics of the simple models, may be identified.
In order to develop a program of this nature several studies within the community of Statistical Mechanics of Neural Networks (Watkin, Rau and Biehl, 1993) have been pursued. Among the most important contributions that this approach brings to the study of machine learning is the possibility of dealing with networks of a very large size, that is in the thermodynamic limit (TL) and of introducing efficient techniques to average over the randomness associated to the data. The model scenarios that have been analized arise from combinations of the different learning conditioning factors. These include, among others, unsupervised versus supervised learning, realizable rules or not, learning in the presence of noise or in the more idealized noiseless case, learning in a time dependent or constant environment.