Intelligent Data Analysis: An International Journal

Other than identifying whether a company may fail or not, explaining why a company may fail is essential. The most common way of explaining is to use a template like the standards used in commercial society. Because of the existence of heteroscedasticity, it is impossible to expect that there is only one standard within an industry. For instance, it is unrealistic to use one standard to evaluate performance of both a new-born company and a fifty-year old company. This paper presents a method of searching for templates using probabilistic neural networks. Each template represents a number of companies, which have similar financial performance and therefore similar financial outcomes. A comparison between a company and a template can explain how badly a company performs and what the problem is if its financial situation is not sound. The method has so far been applied to a data set of 2408 UK construction companies.

An alternative approach methodology for Correspondence Analysis is presented. This approach, called Grade Correspondence Analysis (GCA), utilizes Spearman's rho to detect underlying associations and trends. Two examples are presented using: (1) a contingency table (Heuer's suicide data) with cause of death, gender, and age; and (2) a survey questionnaire (data matrix) concerning employment, personal economics, computer skills, and disability level of handicapped computer specialists in Poland. GCA uses a search strategy (multi-starts / random starts) to detect trends (not forced to be orthogonal) among rows and columns. (A similar strategy permits the determination of significance levels.) Results are discussed using measures of the “representativness” of the trends, as well as measures of their “regularity”. Visualization of trends (as well as outlier trend detection) is via the concept of “overrepresentation” maps. Survey data may be measured on any non-negative scale. Meaningful disjoint aggregation (or division) of sub-populations and variables are possible. This paper is written for the practitioner and includes a “grade” concepts example in an appendix. There is also, however, an appendix with GCA theory relating to: grade distributions; local maxima of Spearman's rho and their representativness, regularity and regions of attraction; total positivity of order 2 (TP2); similarity measures; suitable “random references” for the determination of significance levels; and the application of GCA to non-negative data matrices.

A procedure for designing a multilayer perceptron for predicting time series is proposed. It is based on the generation, according to a set of rules emerging from an ARIMA model previously fitted, of a set of nonlinear forecasting models. These rules are extracted from the set of non-zero coefficients in the ARIMA model, so they consider the autocorrelation structure of the time series. The proposed procedure is intended to help the user in the task of specifying as simple models as possible, providing an unambiguous methodology to construct neural networks for time series forecasting. The performance of this procedure is empirically studied by means of a comparative analysis involving time series from three domains. The first part of the experiment is very extensive and works over 33 time series from the Active Population Survey in Andalusia, Spain. The training of the multilayer perceptron is performed by three different learning rules, incorporating multiple repetitions, and the hidden layer size is determined by means of a grid search. The obtained results show a better performance of these neural network models, in comparison with pure classical statistical techniques, namely ARIMA models and exponential smoothing techniques. These results are confirmed over two more concise studies from the tourist and geodynamic domains, where we graphically illustrate the superiority of the constructed neural networks in long-term forecasting, in comparison with ARIMA models.

This paper proposes a modified version of support vector machines (SVMs), called dynamic support vector machines (DSVMs), to model non-stationary time series. The DSVMs are obtained by incorporating the problem domain knowledge -- non-stationarity of time series into SVMs. Unlike the standard SVMs which use fixed values of the regularization constant and the tube size in all the training data points, the DSVMs use an exponentially increasing regularization constant and an exponentially decreasing tube size to deal with structural changes in the data. The dynamic regularization constant and tube size are based on the prior knowledge that in the non-stationary time series recent data points could provide more important information than distant data points. In the experiment, the DSVMs are evaluated using both simulated and real data sets. The simulation shows that the DSVMs generalize better than the standard SVMs in forecasting non-stationary time series. Another advantage of this modification is that the DSVMs use fewer support vectors, resulting in a sparser representation of the solution.

We present a graphical method for evaluating the quality of a feature extraction mapping. Based on the Bilipschitz criterion, this Bilipschitz Criterion Plot (BCP) can be used to evaluate dimension reducing mappings for relative quality and to estimate the injectivity of the reduction map (as well as the associated reconstruction map). It can also be used to survey regions where the map is locally an expansion or contraction map. The plot is easy and fast to construct, and gives much more insight than any single value can, such as the distance preservation error. We demonstrate the value of such a mapping when examining the quality of the Sammon map, Neuroscale, the autoassociative map, and a recent technique that is designed to optimize the BCP in a linear fashion, the adaptive secant basis algorithm.