This paper investigates excitation information propagation in artificial societies. We use a cellular automaton approach, in which it is assumed that social media is composed of tens of thousands of community agents, where useful (innovative) information can be transmitted to the closest neighbouring agents. The model's originality consists of the exploitation of artificial neuron-based agent schema with a nonlinear activation function to determine the reaction delay, the refractory (agent recovery) period and algorithms that define mutual cooperation among several excitable groups that comprise the agent population. In the grouped model, each agent group can send its excitation signal to the leaders of the groups. The novel media model allows a methodical analysis of the propagation of several competing innovation signals. The simulations are very fast and can be useful for understanding and controlling excitation propagation in social media, planning, and social and economic research.

Improved cellular-automaton-based models of excitable media were employed to mimic economic and financial units in rapidly changing environments. Depending on the model parameters we can obtain chaotic, spiral, vibrant, or regular agents' behaviors. Sums of the outputs of groups of integrated agents are fluctuating in time, similar to observed oscillations in the financial time series. The spectral representation of the output time series allows classification of the agent groups and determination of the model parameters. This inspired the creation of spectra-based clustering of financial time series and the development of a two-stage multi-agent system (MAS). With specific trading agents, the latest training data interval is less useful than previous agents for selecting the best well-timed detected data history segments. The adaptive MAS-based schema notably outperforms three benchmark methods in situations in which we have very complex portfolios with several thousand investment profiles.

In this paper, we consider using profit/loss histories of multiple automated trading systems (ATSs) as N input variables in portfolio management. By means of multivariate statistical analysis and simulation studies, we analyze the influences of sample size (L) and input dimensionality on the accuracy of determining the portfolio weights. We find that degradation in portfolio performance due to inexact estimation of N means and N(N - 1)/2 correlations is proportional to N/L; however, estimation of N variances does not worsen the result. To reduce unhelpful sample size/dimensionality effects, we perform a clustering of N time series and split them into a small number of blocks. Each block is composed of mutually correlated ATSs. It generates an expert trading agent based on a nontrainable 1/N portfolio rule. To increase the diversity of the expert agents, we use training sets of different lengths for clustering. In the output of the portfolio management system, the regularized mean-variance framework-based fusion agent is developed in each walk-forward step of an out-of-sample portfolio validation experiment. Experiments with the real financial data (2003-2012) confirm the effectiveness of the suggested approach.

To improve portfolio management process we suggest using profit histories of automated trading strategies instead of actual assets. Such history can be generated by simulating hundreds of automated trading strategies (robots). We developed three-level decision making system aimed to find the portfolio weights. At the first level, virtual robots trade the assets, at the second level we create virtual profit fusion agents that calculate weighted sums of the profit series created by the first level robots. At the third level, we rank the fusion agents, select a set of the best ones and construct the final portfolio. Experiments with real financial 2004–2011 years data confirm usefulness of the novel approach.

We analyze portfolio creation techniques in a high frequency trading domain and randomly changing environments. We aim to create the best risk/reward portfolio based on thousands of profit histories of automated trading robots. We show that the effectiveness of standard portfolio weight calculation rules depends on the dimensionality, N, and the sample size, L, ratio. To resolve dimensionality / sample size dilemma we suggest designing a multistage feed-forward multi-agent system (MAS). At first we make simple 1/N Portfolio based expert agents. Then we use them and the regularized mean-variance framework to form a large number of more complex fusion agents. Finally we use a trained cost sensitive set of perceptrons to recognize the most successful fusion agents for making a final 1/N Portfolio based weights calculation. Experiments with 7708-dimensional 2004-2012 data confirm the effectiveness of the new approach.

To use human factors together with financial ones in portfolio management task we analyze lengthy series of successes and losses of numerous automated high frequency trading systems that buy and sell assets. We found that in spite of sparse, bimodal non-Gaussian time series, modern Markowitz solutions can be applied to weigh up contributions of diverse trading strategies. Training history should be rather short in situations where technological, social, financial, economic and political situations are changing swiftly. The Markowitz portfolio coefficients finding algorithm can be improved by careful application of the regularization and matrix structurization methods.

A novel loss function to train a net of K single-layer perceptrons (KSLPs) is suggested, where pairwise misclassification cost matrix can be incorporated directly. The complexity of the network remains the same; a gradient's computation of the loss function does not necessitate additional calculations. Minimization of the loss requires a smaller number of training epochs. Efficacy of cost-sensitive methods depends on the cost matrix, the overlap of the pattern classes, and sample sizes. Experiments with real-world pattern recognition (PR) tasks show that employment of novel loss function usually outperforms three benchmark methods.

The standard cost function of multicategory single-layer perceptrons (SLPs) does not minimize the classification error rate. In order to reduce classification error, it is necessary to: 1) refuse the traditional cost function, 2) obtain near to optimal pairwise linear classifiers by specially organized SLP training and optimal stopping, and 3) fuse their decisions properly. To obtain better classification in unbalanced training set situations, we introduce the unbalance correcting term. It was found that fusion based on the Kulback-Leibler (K-L) distance and the Wu-Lin-Weng (WLW) method result in approximately the same performance in situations where sample sizes are relatively small. The explanation for this observation is by theoretically known verity that an excessive minimization of inexact criteria becomes harmful at times. Comprehensive comparative investigations of six real-world pattern recognition (PR) problems demonstrated that employment of SLP-based pairwise classifiers is comparable and as often as not outperforming the linear support vector (SV) classifiers in moderate dimensional situations. The colored noise injection used to design pseudovalidation sets proves to be a powerful tool for facilitating finite sample problems in moderate-dimensional PR tasks.

We consider the trainable fusion rule design problem when the expert classifiers provide crisp outputs and the behavior space knowledge method is used to fuse local experts' decisions. If the training set is utilized to design both the experts and the fusion rule, the experts' outputs become too self-assured. In small sample situations, "optimistically biased" experts' outputs bluffs the fusion rule designer. If the experts differ in complexity and in classification performance, then the experts' boasting effect and can severely degrade the performance of a multiple classification system. Theoretically-based and experimental procedures are suggested to reduce the experts' boasting effect.

Structuralization of the covariance matrix reduces the number of parameters to be estimated from the training data and does not affect an increase in the generalization error asymptotically as both the number of dimensions and training sample size grow. A method to benefit from approximately correct assumptions about the first order tree dependence between components of the feature vector is proposed. We use a structured estimate of the covariance matrix to decorrelate and scale the data and to train a single-layer perceptron in the transformed feature space. We show that training the perceptron can reduce negative effects of inexact a priori information. Experiments performed with 13 artificial and 10 real world data sets show that the first-order tree-type dependence model is the most preferable one out of two dozen of the covariance matrix structures investigated.

Nonrandom initial values of the weight vector can contain useful information. A weighted combination of the initial and final values of the weight vector can help to utilise this information. In adaptive training, at a start, we need to scale the initial weights and to stop training earlier before a minimum of the cost function is obtained. In order to weight, scale or to stop training optimally one needs to know the accuracy of determination of initial and final weights.

The relation between classifier complexity and learning set size is very important in discriminant analysis. One of the ways to overcome the complexity control problem is to add noise to the training objects, increasing in this way the size of the training set. Both the amount and the directions of noise injection are important factors which determine the effectiveness for classifier training. In this paper the effect is studied of the injection of Gaussian spherical noise and -nearest neighbors directed noise on the performance of multilayer perceptrons. As it is impossible to provide an analytical investigation for multilayer perceptrons, a theoretical analysis is made for statistical classifiers. The goal is to get a better understanding of the effect of noise injection on the accuracy of sample-based classifiers. By both empirical as well as theoretical studies, it is shown that the -nearest neighbors directed noise injection is preferable over the Gaussian spherical noise injection for data with low intrinsic dimensionality.

This paper compares two nonparametric linear classification algorithms $the zero empirical error classifier and the maximum margin classifier - with parametric linear classifiers designed to classify multivariate Gaussian populations. Formulae and a table for the mean expected probability of misclassification MEP/sub N/ are presented. They show that the classification error is mainly determined by N/p, a learning-set size/dimensionality ratio. However, the influences of learning-set size on the generalization error of parametric and nonparametric linear classifiers are quite different. Under certain conditions the nonparametric approach allows us to obtain reliable rules, even in cases where the number of features is larger than the number of training vectors.

It is shown adaptive training of the nonlinear single layer perceptron can lead to seven different statistical classifiers: (1) Euclidean distance classifier; (2) standard Fisher linear discriminant function; (3) Fisher linear discriminant function, with pseudoinverse of the covariance matrix; (4) regularised discriminant analysis; (5) generalised Fisher discriminant function; (6) minimum empirical error classifier; and (7) maximum margin classifier and to intermediate ones. Which particular type of the classifier will be obtained depends on: 1) initialisation interval and its relation to the training data; 2) an initial value of the learning step; and 3) its change during the iteration process, the stopping criteria.

This paper compares two linear nonparametric classification algorithms-zero empirical error classifier and maximum margin classifier with parametric linear classifiers designed by using assumptions that pattern classes are multivariate Gaussian. Analytical formulae and a table for the mean expected probability of misclassification EP/sub N/ are presented and show the classification error is mainly determined by N/p, a learning set size/dimensionality ratio. However an influence of the learning sample size on generalization error of parametric and nonparametric linear classifiers is totally different. It is shown that the nonparametric approach to design the linear classifier allows to obtain reliable rules even in cases when the number of features is significantly larger than the number of training vectors.

Feature selection and feature extraction are common information processing stages in statistical pattern recognition and ANN classifier design. The number of samples used to evaluate the quality of feature subset and the use of simplified measures to speed up the evaluation procedures can cause a significant increase in a generalization error. Factors that determine the increase mentioned are analyzed and a method to determine this increase in practical work is proposed.>

The effects of sample size on feature selection and error estimation for several types of classifiers are discussed. The focus is on the two-class problem. Classifier design in the context of small design sample size is explored. The estimation of error rates under small test sample size is given. Sample size effects in feature selection are discussed. Recommendations for the choice of learning and test sample sizes are given. In addition to surveying prior work in this area, an emphasis is placed on giving practical advice to designers and users of statistical pattern recognition systems.>

The authors discuss the effects of sample size on the feature selection and error estimation for several types of classifiers. In addition to surveying prior work in this area, they give practical advice to today's designers and users of statistical pattern recognition systems. It is pointed out that one needs a large number of training samples if a complex classification rule with many features is being utilized. In many pattern recognition problems, the number of potential features is very large and not much is known about the characteristics of the pattern classes under consideration: thus, it is difficult to determine a priori the complexity of the classification rule needed. Therefore, even when the designer believes that a large number of training samples has been selected, they may not be enough for designing and evaluating the classification problem at hand. It is further noted that a small sample size can cause many problems in the design of a pattern recognition system.>

Analytical and simulation studies show that a variance of the bootstrap estimator discussed is lower than that of the commonly used leave-one-out estimator only when sample size is extremely small or when the classification error is large. An essential feature of the bootstrap method is that observations of the training sample (TS) play the role of a general population and are used to determine the optimistic bias of the resubstitution estimate. A bootstrap training sample (BTS) is formed from the TS in a random way. A classification rule is designed using a BTS and is tested twice.>

This paper compares four classification algorithms-discriminant functions when classifying individuals into two multivariate populations. The discriminant functions (DF's) compared are derived according to the Bayes rule for normal populations and differ in assumptions on the covariance matrices' structure. Analytical formulas for the expected probability of misclassification EPN are derived and show that the classification error EPN depends on the structure of a classification algorithm, asymptotic probability of misclassification P¿, and the ratio of learning sample size N to dimensionality p:N/p for all linear DF's discussed and N2/p for quadratic DF's. The tables for learning quantity H = EPN/P¿ depending on parameters P¿, N, and p for four classifilcation algorithms analyzed are presented and may be used for estimating the necessary learning sample size, detennining the optimal number of features, and choosing the type of the classification algorithm in the case of a limited learning sample size.