Rui Jorge Almeida

Comparison of fuzzy clustering algorithms for classification

The identification of fuzzy models for classification is a very complex task. Often, real world databases have a large number of features and the most relevant ones must be chosen. Recently, a new automatic feature selection for classification problems was proposed to construct compact fuzzy classification models. This technique used the classical fuzzy c-means algorithm. However, other fuzzy clustering algorithms, such as possibilistic c-means, fuzzy possibilistic c-means or possibilistic fuzzy c-means can be used to cluster the data. An open topic of research is what clustering algorithms can be used to derive fuzzy models for classification. This paper addresses this topic, by comparing fuzzy clustering algorithms in terms of computational efficiency and accuracy in classification problems. The algorithms were tested in well-known data sets: iris plant, wine, hepatitis, breast cancer and in a difficult real-world problem: the prediction of bankruptcy

Conditional Density Estimation Using Probabilistic Fuzzy Systems

We consider conditional density approximation by fuzzy systems. Fuzzy systems are typically used to approximate deterministic functions in which the stochastic uncertainty is ignored. We propose probabilistic fuzzy systems (PFSs), in which the probabilistic nature of uncertainty is taken into account. These systems take also fuzzy uncertainty into account by their fuzzy partitioning of input and output spaces. We discuss an additive reasoning scheme for PFSs that leads to the estimation of conditional probability densities and prove how such fuzzy systems compute the expected value of this conditional density function. We show that some of the most commonly used fuzzy systems can compute the same expected output value, and we derive how their parameters should be selected in order to achieve this goal. The additional information and process understanding provided by the different interpretations of the PFS models are illustrated using a real-world example.

Mortality prediction of septic shock patients using probabilistic fuzzy systems

Graphical abstractDisplay Omitted HighlightsProbabilistic fuzzy systems (PFS) are used to predict mortality of septic shock patients.PFS models are compared with Takagi-Sugeno fuzzy models and logistic regression models.The methods are tested using ICU patients with abdominal septic shock.PFS models increase the transparency of the learned system using fuzzy rules.By providing estimates for the mortality risk, PFS help clinical decision making. Mortality scores based on multiple regressions are common in critical care medicine for prognostic stratification of patients. However, to be used at the point of care, they need to be both accurate and easily interpretable. In this work, we propose the application of one existent type of rule base system using statistical information - probabilistic fuzzy systems (PFS) - to predict mortality of septic shock patients. To assess its accuracy and interpretability, these models are compared to methodologies previously proposed in this domain: Takagi-Sugeno fuzzy models and logistic regression models. The methods are tested using a retrospective cohort study including ICU patients with abdominal septic shock. Regarding accuracy, PFS models are comparable to fuzzy modeling and logistic regression. In terms of interpretability, results indicate that PFS models increase the transparency of the learned system (using fuzzy rules), but at the same time, provide additional means for validating the fuzzy classifier using expert knowledge (from physicians in this paper). By providing accurate and interpretable estimates for the mortality risk, results suggest the usefulness of PFS to develop scores for critical care medicine.

A multi-covariate semi-parametric conditional volatility model using probabilistic fuzzy systems

Value at Risk (VaR) has been successfully estimated using single covariate probabilistic fuzzy systems (PFS), a method which combines a linguistic description of the system behaviour with statistical properties of data. In this paper, we consider VaR estimation based on a PFS model for density forecast of a continuous response variable conditional on a high-dimensional set of covariates. The PFS model parameters are estimated by a novel two-step process. The performance of the proposed model is compared to the performance of a GARCH model for VaR estimation of the S&P 500 index. Furthermore, the additional information and process understanding provided by the different interpretations of the PFS models are illustrated. Our findings show that the validity of GARCH models are sometimes rejected, while those of PFS models of VaR are never rejected. Additionally, the PFS model captures both instant and periods of high volatility, and leads to less conservative models.

Prediction of the MSCI EURO index based on fuzzy grammar fragments extracted from European Central Bank statements

We focus on predicting the movement of the MSCI EURO index based on European Central Bank (ECB) statements. For this purpose we learn and extract fuzzy grammars from the text of the ECB statements. Based on a set of selected General Inquirer (GI) categories, the extracted fuzzy grammars are grouped around individual content categories. The frequency at which these fuzzy grammars are encountered in the text constitute input to a Fuzzy Inference System (FIS). The FIS maps these frequencies to the levels of the MSCI EURO index. Ultimately, the goal is to predict whether the MSCI EURO index will exhibit upward or downward movement based on the content of ECB statements, as quantified through the use of fuzzy grammars and GI content categories.

Linguistic summaries of categorical time series for septic shock patient data

Linguistic summarization is a data mining and knowledge discovery approach to extract patterns and sum up large volume of data into simple sentences. There is a large research in generating linguistic summaries which can be used to better understand and communicate about patterns, evolution and long trends in numerical, time series or labelled data. The objective of this work is to develop a computational system capable of automatically generating linguistic descriptions of time series data of septic shock patients containing labelled data, not only of the whole series, but also on the differences between subsets of the data. This is of particular interest in septic shock, as the differences between patients are not well understood. For this purpose we propose a new type of differential summaries, based on a numerical criterion assessing the characteristics of the summary on each subset of interest. Furthermore, this paper proposes an extension of linguistic summaries to provide temporal and categorical contextualization. This is of particular interest in healthcare to detect differences related to a condition or illness as well as the effectiveness of the administered treatment.

A new approach to dealing with missing values in data-driven fuzzy modeling

Real word data sets often contain many missing elements. Most algorithms that automatically develop a rule-based model are not well suited to deal with incomplete data. The usual technique is to disregard the missing values or substitute them by a best guess estimate, which can bias the results. In this paper we propose a new method for estimating the parameters of a Takagi-Sugeno fuzzy model in the presence of incomplete data. We also propose an inference mechanism that can deal with the incomplete data. The presented method has the added advantage that it does not require imputation or iterative guess-estimate of the missing values. This methodology is applied to fuzzy modeling of a classification and regression problem. The performance of the obtained models are comparable with the results obtained when using a complete data set.

A fuzzy model of the MSCI EURO index based on content analysis of European Central Bank statements

In this paper we investigate whether the MSCI EURO index can be predicted based on the content of European Central Bank (ECB) statements. We propose a new model to retrieve information from free text and transform it into a quantitative output. For this purpose, we first identify all adjectives in an ECB statement by using the Stanford Part-of-Speech Tagger and feed these to the General Inquirer (GI) content analysis tool. From GI we obtain a matrix that provides for each document and for each content category the percentage of words in the document that fall under each category. After normalizing the data, we develop a Takagi-Sugeno (TS) fuzzy model using fuzzy c-means clustering. The TS fuzzy system is used to model the levels of the MSCI EURO index. To determine the performance of the model, we focus on the accuracy of predicting upward or downward movement in the index, and obtain, on average, an accuracy of 66%, that corresponds to an improvement of 16% over a random classifier.

Probabilistic Fuzzy Systems as Additive Fuzzy Systems

Probabilistic fuzzy systems combine a linguistic description of the system behaviour with statistical properties of data. It was originally derived based on Zadeh’s concept of probability of a fuzzy event. Two possible and equivalent additive reasoning schemes were proposed, that lead to the estimation of the output’s conditional probability density. In this work we take a complementary approach and derive a probabilistic fuzzy system from an additive fuzzy system. We show that some fuzzy systems with universal approximation capabilities can compute the same expected output value as probabilistic fuzzy systems and discuss some similarities and differences between them. A practical relevance of this functional equivalence result is that learning algorithms, optimization techniques and design issues can, under certain circumstances, be transferred across different paradigms.

Probabilistic fuzzy systems for seasonality analysis and multiple horizon forecasts

Probabilistic fuzzy systems (PFS), a model which combines a linguistic description of the system behaviour with statistical properties of data, have been successfully applied to one day ahead Value at Risk (VaR) estimation for the stock market returns data. In this work, we propose a multi-covariate multi-output PFS model which provides the conditional density forecasts of returns for one day ahead and one month ahead periods. Such a multi-output PFS model was not considered in the literature. Furthermore, this model allows to analyze seasonal patterns in returns. The proposed model is applied to daily S&P500 stock returns. It is found that the proposed model indicates seasonal patterns in short and longer horizons as well as conservative VaR in long term forecasts. The model is shown to perform well in VaR estimation according to the unconditional coverage and independence tests.