Modeling the Ecological Footprint of Nations via Evolutionary Computation and Machine Learning Models

The per capita Ecological Footprint (EF) is one of the most-widely recognized measures of environmental sustainability. It seeks to quantify the Earth’s biological capacity required to support human activity. This study uses gene expression programming and Self-organizing Maps (SOM) to predict, classify and cluster the EF of 140 nations. A Bayesian approach was used to formally test the research hypotheses. By formulating the linear regression in a probabilistic framework, a Bayesian linear regression model is derived, and a specific simulation method, i.e., Markov Chain Monte Carlo (MCMC), is utilized to estimate the model parameters. Bayesian MCMC methods allow a richer and more complete representation of complex EF data. It also provides a computationally attractive and straightforward method to develop a full and complete description of the inherent uncertainty in parameters, quantiles and performance metrics.

Convergence property of topographic mapping formation from cell layer to cell layer through correlation learning rule

To elucidate the mechanism of topographic organization, we propose a simple topographic mapping formation model from one-dimensional cell layer to one-dimensional cell layer. In our model, each cell takes a binary state value and we consider several learning principles which are extensions of Hebb's rule. We pay special attention to a correlation learning rule where a synaptic weight value is increased if pre- and post-synaptic cells' state values are the same. First, we show that under a certain network size condition, a mapping is stable with respect to the correlation learning if and only if it is topographic. Second, we introduce a special class of weight matrices called band type and show that the set of band type weight matrices is strongly closed and such a weight matrix cannot yield a topographic mapping. Third, we show that any mapping, if it is defined by a non band type weight matrix, converges to a topographic mapping. The proof method is intrinsically of combinatorial nature in a framework of Markov process.

Laryngeal pathology detection by means of class-specific neural maps

Most of the existing systems and methods for laryngeal pathology detection are characterized by a classification error. One of the basic problems is the approximation and estimation of the probability density functions of the given classes. In order to increase the accuracy of laryngeal pathology detection and to eliminate the most dangerous error--classification of a patient with laryngeal disease as a normal speaker--here an approach based on modeling of the probability density functions (pdf's) of the input vectors of the normal and pathological speakers by means of two prototype distribution maps (PDM), respectively, is proposed. The pdf of the input vectors of an unknown normal or pathological speaker is also modeled by such a prototype distribution neural map--PDM(X)--and the pathology detection is done by means of a ratio of specific similarities rather than by a direct comparison of some type of distance/similarity with a threshold. The experiments show an increased classification accuracy and that the proposed method can be used for screening the laryngeal diseases. The method is applied in a consulting system for clinical practice.

Convergence properties of a class of learning vector quantization algorithms

A mathematical analysis of a class of learning vector quantization (LVQ) algorithms is presented. Using an appropriate time-coordinate transformation, we show that the LVQ algorithms under consideration can be transformed into linear time-varying stochastic difference equations. Using this fact, we apply stochastic Lyapunov stability arguments, and we prove that the LVQ algorithms under consideration do indeed converge, provided that some appropriate conditions hold.