Marco Breda

An improved I-FAST system for the diagnosis of Alzheimer's disease from unprocessed electroencephalograms by using robust invariant features

OBJECTIVE This paper proposes a new, complex algorithm for the blind classification of the original electroencephalogram (EEG) tracing of each subject, without any preliminary pre-processing. The medical need in this field is to reach an early differential diagnosis between subjects affected by mild cognitive impairment (MCI), early Alzheimers disease (AD) and the healthy elderly (CTR) using only the recording and the analysis of few minutes of their EEG. METHODS AND MATERIAL This study analyzed the EEGs of 272 subjects, recorded at Romes Neurology Unit of the Policlinico Campus Bio-Medico. The EEG recordings were performed using 19 electrodes, in a 0.3-70Hz bandpass, positioned according to the International 10-20 System. Many powerful learning machines and algorithms have been proposed during the last 20 years to effectively resolve this complex problem, resulting in different and interesting outcomes. Among these algorithms, a new artificial adaptive system, named implicit function as squashing time (I-FAST), is able to diagnose, with high accuracy, a few minutes of the subjects EEG track; whether it manifests an AD, MCI or CTR condition. An updating of this system, carried out by adding a new algorithm, named multi scale ranked organizing maps (MS-ROM), to the I-FAST system, is presented, in order to classify with greater accuracy the unprocessed EEGs of AD, MCI and control subjects. RESULTS The proposed system has been measured on three independent pattern recognition tasks from unprocessed EEG tracks of a sample of AD subjects, MCI subjects and CTR: (a) AD compared with CTR; (b) AD compared with MCI; (c) CTR compared with MCI. While the values of accuracy of the previous system in distinguishing between AD and MCI were around 92%, the new proposed system reaches values between 94% and 98%. Similarly, the overall accuracy with best artificial neural networks (ANNs) is 98.25% for the distinguishing between CTR and MCI. CONCLUSIONS This new version of I-FAST makes different steps forward: (a) avoidance of pre-processing phase and filtering procedure of EEG data, being the algorithm able to directly process an unprocessed EEG; (b) noise elimination, through the use of a training variant with input selection and testing system, based on naïve Bayes classifier; (c) a more robust classification phase, showing the stability of results on nine well known learning machine algorithms; (d) extraction of spatial invariants of an EEG signal using, in addition to the unsupervised ANN, the principal component analysis and the multi scale entropy, together with the MS-ROM; a more accurate performance in this specific task.

Analyzing the Semantics of Point Spaces through the Topological Weighted Centroid and Other Mathematical Quantities: The Hidden Geometry of the Global Economic Order

For many spatial processes, there is a natural need to find out the point of origin on the basis of the available scatter of observations; think, for instance, of finding out the home base of a criminal given the actual distribution of crime scenes, or the outbreak source of an epidemics. In this article, we build on the topological weighted centroid (TWC) methodology that has been applied in previous research to the reconstruction of space syntax problems, for example, of problems where all relevant entities are of spatial nature so that the relationships between them are inherently spatial and need to be properly reconstructed. In this article, we take this methodology to a new standard by tackling the new and challenging task of analyzing space semantics problems, where entities are characterized by properties of a nonspatial nature and must therefore be properly spatialized. We apply the space semantics version of the TWC methodology to a particularly hard problem: the reconstruction of global political and economic relationships on the basis of a small‐dimensional qualitative dataset. The combination of a small set of spatial and nonspatial sources of information allows us to elucidate some intriguing and counterintuitive properties of the inherent global economic order and, in particular, to highlight its long‐term structural features, which interestingly point toward the idea of longue durée developed by the distinguished French historian Fernand Braudel.

Auto-contractive Maps

This chapter focuses on Auto-Contractive Maps, which is a particularly useful ANN. Moreover, the relationship between Auto-Contractive Map (Auto-CM), which is the main topic of this monograph, its relationship to other ANNs and some illustrative example applications are presented.

Semantics of Point Spaces Through the Topological Weighted Centroid and Other Mathematical Quantities: Theory and Applications

Given a scattering of observations on a map it is natural for one to want to determine the most likely origin of those points, and the origin is typically hidden within data. Using an example to illustrate the point, suppose the police authorities have a map on which is noted the actual distribution of home break-ins. It is natural for the police to want to know the point of origin of those crimes so that they might be able to quickly apprehend the criminals. If the points were those of an outbreak of an epidemic the public health officials would want to know the location of the source of the disease. A new methodology is introduced to solve just this kind of set of problems. It is based on the notion of the Topological Weighted Centroid that permits one to draw powerful inferences about these kinds of center points, even in cases containing very few observations or in which the points are based on a poorly understood underlying data system. Two kinds of problems, based on the degree of spatialization, are addressed: the first kind of problem possesses an inherent spatial semantic in which all of the relevant characteristics of the observed entities are of a spatial nature; the other kind of problem involves those possessing full semantics in which some of the characteristics have a non-spatial nature and must therefore be properly spatialized. The theory is backed up by case studies involving criminal network detection, tracking down the course of an epidemic, and the reconstruction of terrorist attacks relationships on the basis of a small-dimensional qualitative dataset.

Artificial Neural Networks

Artificial Adaptive Systems include Artificial Neural Networks (ANNs or simply neural networks as they are commonly known). The philosophy of neural networks is to extract from data the underlying model that relates this data as an input/output (domain/range) pair. This is quite different from the way most mathematical modeling processes operate. Most mathematical modeling processes normally impose on the given data a model from which the input to output relationship is obtained. For example, a linear model that is a “best fit” in some sense, that relates the input to the output is such a model. What is imposed on the data by artificial neural networks is an a priori architecture rather than an a priori model. From the architecture, a model is extracted. It is clear, from any process that seeks to relate input to output (domain to range), requires a representation of the relationships among data. The advantage of imposing an architecture rather than a data model, is that it allows for the model to adapt. Fundamentally, a neural network is represented by its architecture. Thus, we look at the architecture first followed by a brief introduction of the two types of approaches for implementing the architecture—supervised and unsupervised neural networks. Recall that Auto-CM, which we discuss in Chap. 3, is an unsupervised ANN while K-CM, discussed in Chap. 6, is a supervised version of Auto-CM. However, in this chapter, we show that, in fact, supervised and unsupervised neural networks can be viewed within one framework in the case of the linear perceptron. The chapter ends with a brief look at some theoretical considerations.

Theory of impossible worlds: Toward a physics of information

In this paper, we introduce an innovative approach to the fusion between datasets in terms of attributes and observations, even when they are not related at all. With our technique, starting from datasets representing independent worlds, it is possible to analyze a single global dataset, and transferring each dataset onto the others is always possible. This procedure allows a deeper perspective in the study of a problem, by offering the chance of looking into it from other, independent points of view. Even unrelated datasets create a metaphoric representation of the problem, useful in terms of speed of convergence and predictive results, preserving the fundamental relationships in the data. In order to extract such knowledge, we propose a new learning rule named double backpropagation, by which an auto-encoder concurrently codifies all the different worlds. We test our methodology on different datasets and different issues, to underline the power and flexibility of the Theory of Impossible Worlds.

The ANNS approach to DEM reconstruction: THE ANNS APPROACH TO DEM RECONSTRUCTION

This research has 6 fundamental aims: (i) to present a modified version of Taylors interpolation, one that is more effective and faster than the original; (ii) outline the capability of artificial neural networks (ANNs) to perform an optimal functional approximation of the digital elevation model reconstruction from a satellite map, using a small and independent sample of Global Positioning System observations; (iii) demonstrate experimentally how ANNs outperform the traditional and most used algorithm for the height interpolation (Taylors interpolation); (iv) introduce a new ANN, the Conic Net, able to outperform the results of the classic and more known multilayer perceptron; (v) determine that Conic Nets, even when using Taylors modified interpolation as input features, are able to optimally approximate the heights with one order of magnitude more than the original satellite map; and (vi) make evident the possibility to interpolate the DEM heights through an ANN, which learns a data set of known points.

Auto-CM as a Dynamic Associative Memory

We look at how to use Auto-CM in the context of datasets that are changing in time. We modify our approach while keeping the original philosophy of Auto-CM.

Dataset Transformations and Auto-CM

We have looked at how to visualize the relationships among the elements of a dataset in Chap. 4. This chapter is devoted to the use of Auto-CM in the transformation of datasets for the purpose of extracting further relationships among data elements. The first transformation we call the FS-Transform, which looks beyond an all or nothing, binary relationship that is typical of most ANNs. The extraction of these perhaps more subtle relationships can be thought of as gradual relationships, zero denoting no relationship is present and one denoting a full/complete relationship that is absolutely present. It is thus, akin to a fuzzy set. The second transformation is one, which “morph” the delineation between records and variables within records that we call Hyper-Composition.

Comparison of Auto-CM to Various Other Data Understanding Approaches

We compare Auto-CM with various other methods that extract patterns from data. The way that we measure the results of comparisons uses MST.