Carlos Maté

iMLP: Applying Multi-Layer Perceptrons to Interval-Valued Data

Interval-valued data offer a valuable way of representing the available information in complex problems where uncertainty, inaccuracy or variability must be taken into account. In addition, the combination of Interval Analysis with soft-computing methods, such as neural networks, have shown their potential to satisfy the requirements of the decision support systems when tackling complex situations. This paper proposes and analyzes a new model of Multilayer Perceptron based on interval arithmetic that facilitates handling input and output interval data, but where weights and biases are single-valued and not interval-valued. Two applications are considered. The first one shows an interval-valued function approximation model and the second one evaluates the prediction intervals of crisp models fed with interval-valued input data. The approximation capabilities of the proposed model are illustrated by means of its application to the forecasting of daily electricity price intervals. Finally, further research issues are discussed.

Smoothing methods for histogram-valued time series: an application to value-at-risk

We adapt smoothing methods to histogram-valued time series (HTS) by introducing a barycentric histogram that emulates the “average” operation, which is the key to any smoothing filter. We show that, due to its linear properties, only the Mallows-barycenter is acceptable if we wish to preserve the essence of any smoothing mechanism. We implement a barycentric exponential smoothing to forecast the HTS of daily histograms of intradaily returns to both the SP500 and the IBEX 35 indexes. We construct a one-step-ahead histogram forecast, from which we retrieve a desired γ-value-at-risk (VaR) forecast. In the case of the SP500 index, a barycentric exponential smoothing delivers a better forecast, in the MSE sense, than those derived from vector autoregression models, especially for the 5% VaR. In the case of IBEX35, the forecasts from both methods are equally good.

Hierarchical Clustering for Boxplot Variables

Boxplots are well-known exploratory charts used to extract meaningful information from batches of data at a glance. Their strength lies in their ability to summarize data retaining the key information, which also is a desirable property of symbolic variables. In this paper, boxplots are presented as a new kind of symbolic variable. In addition, two different approaches to measure distances between boxplot variables are proposed. The usefulness of these distances is illustrated by means of a hierarchical clustering of boxplot data.

Exploring the characteristics of rotating electric machines with factor analysis

Applications of multivariate statistics in engineering are hard to find, apart from those in quality control. However, we think that further insight into some technological cases may be gained by using adequate multivariate analysis tools. In this paper, we propose a review of the key parameters of rotating electric machines with factor analysis. This statistical technique allows not only the reduction of the dimension of the case we are analysing, but also reveals subtle relationships between the variables under study. We show an application of this methodology by studying the interrelations between the key variables in an electric machine, in this case the squirrel-cage induction motor. Through a step-by-step presentation of the case study, we deal with some of the topics an applied researcher may face, such as the rotation of the original factors, the extraction of higher-order factors and the development of the exploratory model. As a result, we present a worthwhile framework to both confirm our previous knowledge and capture unexplored facts. Moreover, it may provide a new approach to describing and understanding the design, performance and operating characteristics of these machines.