F. de A.T. de Carvalho

Dynamic Clustering of Interval-Valued Data Based on Adaptive Quadratic Distances

This paper presents partitioning dynamic clustering methods for interval-valued data based on suitable adaptive quadratic distances. These methods furnish a partition and a prototype for each cluster by optimizing an adequacy criterion that measures the fitting between the clusters and their representatives. These adaptive quadratic distances change at each algorithm iteration and can either be the same for all clusters or different from one cluster to another. Moreover, various tools for the partition and cluster interpretation of interval-valued data are also presented. Experiments with real and synthetic interval-valued data sets show the usefulness of these adaptive clustering methods and the merit of the partition and cluster interpretation tools.

Hybrid model with dynamic architecture for forecasting time series

Nonlinear artificial neural network models are very attractive for modeling and forecasting time series. The use of such models in these types of applications is motivated by experimental results that show a high capacity of approximation for functions with high accuracy. However, many researchers have used feedforward and/or backpropagation models for time series predictions. In this paper, a model is applied for neural networks with the dynamic architecture proposed by Ghiassi and Saidane (2005), known as the DAN2 model. The results of DAN2 are compared with auto-regressive integrated mobile average (ARIMA) models. As the main result of the paper, we propose a hybrid model with dynamic architecture (HAD) based on combinations of individual forecasts from the DAN2 and ARIMA models with the aim of obtaining more precise forecasts for poorly behaved time series. The results suggest that for this kind of series, the HAD hybrid model outperforms the individual DAN2 and ARIMA models.

Constrained linear regression models for interval-valued data with dependence

This paper introduces some approaches to fitting a constrained linear regression model to interval-valued data. The use of inequality constraints guarantee mathematical coherence between the predicted values of the lower bound (y circLi) and the upper bound (y circUi). The authors also propose expressions to the goodness of fit measure called determination coefficient. The assessment of the proposed prediction methods is based on the average behaviour of the root mean square error and of the square of the correlation coefficient in the framework of a Monte Carlo experiment. The synthetic data sets takes into account the dependence or not between the midpoint and range of the intervals, among others aspects. Finally, the approaches are applied in a real data-set.

Clustering symbolic interval data based on a single adaptive hausdorff distance

The recording of symbolic interval data has become popular with the recent advances in database technologies. This paper introduces a dynamic clustering method to partitioning symbolic interval data. This method furnishes a partition and a prototype for each cluster by optimizing an adequacy criterion that measures the fitting between the clusters and their representatives. To compare symbolic interval data, the method uses a single adaptive Hausdorff distance that at each iteration changes but is the same for all the clusters. Experiments with real and synthetic symbolic interval data sets showed the usefulness of the proposed method.

Nonlinear regression model to symbolic interval-valued variables

This paper introduces a nonlinear regression method to fit a regression model to symbolic interval-valued data set. The nonlinear method will be inspired in the method proposed by and will consider two independent nonlinear regression models fitted over the midpoint and range of the intervals. The assessment of the proposed prediction methods is based on the average behavior of the root mean square error and of the square of the correlation coefficient in the framework of a Monte Carlo experiment. The synthetic data sets taking into account the different degree of nonlinearity between the dependent and the independent interval variables, among others aspects.

Fuzzy Clustering Algorithms for Symbolic Interval Data based on L/sub 2/ Norm

The recording of symbolic interval data has become a common practice with the recent advances in database technologies. This paper introduces fuzzy clustering algorithms to partitioning symbolic interval data. The proposed methods furnish a fuzzy partition and a prototype (a vector of intervals) for each cluster by optimizing an adequacy criterion that measures the fitting between the clusters and their representatives. To compare symbolic interval data, the methods use a suitable (adaptive and non-adaptive) L2 norm defined on vectors of intervals. Experiments with real and synthetic symbolic interval data sets showed the usefulness of the proposed method.

Exponential smoothing methods for forecasting bar diagram-valued time series

When a set of categories with related frequencies of the observed variable is available for each time point we have a bar diagram-valued time series. This paper introduces exponential smoothing methods to forecast bar diagram-valued time series data. The proposed method is inspired in the approach introduced by Maia and De Carvalho (2011) to deal with inteval-valued time series. The smoothing parameters are estimated by using techniques for non-linear optimization problems with bound constraints. The results are discussed based on two wellknown classical performance measurements, which have been adapted here for this particular type of data: the U of Theil statistics and average relative variance (ARV) in the framework of a Monte Carlo experiment. The synthetic data sets take into account differents aspects, e.g., sample size and forecast horizons among others. Applications using real bar diagram-valued time series also were considered to demonstrate the practicality of the methods. The results demonstrate that the proposed approaches are useful in forecasting bar diagram-valued times series.

Clustering of symbolic data through a dissimilarity volume based measure

The recording of symbolic data has become a common practice with the advances in database technologies. This paper shows hard and fuzzy relational clustering in order to partition symbolic data. These methods optimize objective functions based on a dissimilarity function. The distance used is a volume based measure and may be applied to data described by set-valued, list-valued or interval-valued symbolic variables. Experiments with real and synthetic symbolic data sets show the usefulness of the proposed approach.

An evolutionary approach for the clustering data problem

The clustering problem consists in the discovery of interesting groups in a dataset. Such task is very important and widely tackled in the literature. In this paper, we propose an evolutionary method in order to obtain well formed and spatially separated clusters. The proposed algorithm uses a complete solution representation, each partition is represented by a length-variable chromosome. The variation operators were chosen to facilitate the exchange of clustering information between individuals. We have put two complementary clustering criteria together in the fitness function, so that the method can find clusters with arbitrary shapes. The k-means algorithm was the basis of the local search operator, such operator might refine the clustering solutions. The population diversity was an important issue for the algorithm, so a diversity maintenance scheme was employed. Differently from other existing clustering algorithms, our algorithm does not need the setting of the number of clusters in advance. We evaluated the method in different contexts, using both real and simulated data.

Evolving both size and accuracy of RBF networks using Memetic Algorithm

One of the main obstacles to obtain an artificial neural network with reasonable performance is the parameter setting. This work proposes a methodology to the automatic definition of RBF (radial basis function) networks with an appropriate configuration for the selected classification problems. We propose the use of a memetic algorithm in order to perform the search for networks with minimum architecture and error rate. A set of experiments was made with four datasets and we were able to show the effectiveness of the method.