Rosaria Silipo

Input features' impact on fuzzy decision processes

Many real-world applications have very high dimensionality and require very complex decision borders. In this case, the number of fuzzy rules can proliferate, and the easy interpretability of fuzzy models can progressively disappear. An important part of the model interpretation lies on the evaluation of the effectiveness of the input features on the decision process. In this paper, we present a method that quantifies the discriminative power of the input features in a fuzzy model. The separability among all the rules of the fuzzy model produces a measure of the information available in the system. Such measure of information is calculated to characterize the system before and after each input feature is used for classification. The resulting information gain quantifies the discriminative power of that input feature. The comparison among the information gains of the different input features can yield better insights into the selected fuzzy classification strategy, even for very high dimensional cases, and can lead to a possible reduction of the input space dimension. Several artificial and real-world data analysis scenarios are reported as examples in order to illustrate the characteristics and potentialities of the proposed method.

A characterization of HRV's nonlinear hidden dynamics by means of Markov models

A study of the 24-h heart rate variabilitys (HRV) hidden dynamic is performed hour by hour, in order to investigate the evolution of the nonlinear structure of the underlying nervous system. A hierarchy of null hypotheses of nonlinear Markov models with increasing order n is tested against the hidden dynamic of the HRV time series. The minimum accepted Markov order supplies information about the nonlinearity of the HRVs hidden dynamic and consequently of the underlying nervous system. The Markov model with minimum order is detected for each hour of the RR time series extracted from seven 24-h electrocardiogram records of patients in different patho-physiological conditions, some including ventricular tachycardia episodes. Heart rate, pNN30, and LF/HF index plots are reported to serve as a reference for the description of the patients cardiovascular frame during each examined hour. The minimum Markov order shows to be a promising index for quantifying the average nonlinearity of the autonomic nervous systems activity.

Brain tumor classification based on EEG hidden dynamics

The hard problem of brain tumor detection based on rest ElectroEncephaloGraphic EEG analysis is investigated, relying on the hypothesis that the EEG signal contains more hidden useful information than what is clinically employed. A nonlinear analysis is applied to the pair F3, F4 of EEG leads, that describe the electrical activity of the left and right brain hemisphere, respectively. The hidden dynamic of the pair F3, F4 is tested against a hierarchy of null hypotheses, corresponding to one-and two-dimensional nonlinear Markov models of increasing order. An approximative measure of information flow, based on higher order cumulants, quantifies the hidden dynamic of each time series and is used as a discriminating statistic for testing the null hypotheses. The minimum order of the accepted Markov models represents a measure of the intrinsic nonlinearity of the underlying system. Rest EEG records of 6 patients with evidence of meningeoma or malignant glioma in lead F4, or without any pathology, are investigated. A high order hidden dynamic is detected in normal EEG records, confirming the very complex structure of the underlying system. Different inter-dependence degrees between the hidden dynamics of leads F3, F4 discriminate meningeoma, malignant glioma, and no pathological status, while loss of structure in the hidden dynamic can represent a good hint for glioma/meningeoma localization.

Discriminative Power of Input Features in a Fuzzy Model

In many modern data analysis scenarios the first and most urgent task consists of reducing the redundancy in high dimensional input spaces. A method is presented that quantifies the discriminative power of the input features in a fuzzy model. A possibilistic information measure of the model is defined on the basis of the available fuzzy rules and the resulting possibilistic information gain, associated with the use of a given input dimension, characterizes the input features discriminative power. Due to the low computational expenses derived from the use of a fuzzy model, the proposed possibilistic information gain generates a simple and efficient algorithm for the reduction of the input dimensionality, even for high dimensional cases. As real-world example, the most informative electrocardiographic measures are detected for an arrhythmia classification problem.

Prosodic stress and topic detection in spoken sentences

The relationship between acoustic stress and the information content of words is investigated. On the one hand, the average acoustic stress is measured for each word throughout each utterance. On the other hand, an information retrieval (IR) index is calculated, based on the word frequency throughout the particular spoken sentence and throughout the collection of analysed spoken sentences. The scatter plots of the two measures (average acoustic stress on the y-axis and IR index on the x-axis) show higher values of average acoustic stress with increasing IR index of the word in the majority of the analysed utterances. A statistically more valid proof of such a relationship is derived from a histogram of the words with high average acoustic stress vs. the IR index. This confirms that a word with high average acoustic stress also has a high value of the IR index and, if we trust IR indexes, also a high information content.

Interpretability in Multidimensional Classification

Generating rule-based models from data is an efficient way of inferring information from large datasets. In high-dimensional spaces, the complexity of the model itself can undermine the interpretability of this information. This chapter introduces metrics quantifying the information flow between inputs, feature dimensions and output classes. These metrics are used to estimate the contribution of individual input features to a fuzzy classification task without making explicit use of the data underlying the model. Application of these techniques to a speech classification problem shows that significant reduction in the model dimensionality can be achieved with minimal accuracy loss.

Syllable‐based speech recognition using auditorylike features

Classical models of speech recognition (both human and machine) assume that a detailed, short‐term analysis of the signal is essential for accurate decoding of spoken language via a linear sequence of phonetic segments. This classical framework is incommensurate with quantitative acoustic/phonetic analyses of spontaneous discourse (e.g., the Switchboard corpus for American English). Such analyses indicate that the syllable, rather than the phone, is likely to serve as the representational interface between sound and meaning, providing a relatively stable representation of lexically relevant information across a wide range of speaking and acoustic conditions. The auditory basis of this syllabic representaion appears to be derived from the low‐frequency (2–16 Hz) modulation spectrum, whose temporal properties correspond closely to the distribution of syllabic durations observed in spontaneous speech. Perceptual experiments confirm the importance of the modulation spectrum for understanding spoken language a...

Markov models and heart rate variability hidden dynamic

The hidden dynamic of the 24-hour HRV time series extracted from the ECG records of 7 patients with different cardiac pathologies is investigated. The underlying structure of each 1-hour HRV subsequence is approximated by using Markov models with minimum order n. Such minimum order supplies a measure of the HRVs nonlinearity degree and of the underlying nervous system during each examined hour. The minimum Markov orders evolution is then investigated over the 24 hours. During the night a relatively stable minimum Markov order can be observed. The different pathologies seem to exhibit different minimum Markov order time evolutions. Finally VT episodes can be located inside periods of low nonlinear activity of the autonomic nervous system. The minimum Markov order shows to be a reliable index for quantifying the risk factor associated with the HRV parameter.

Investigating the underlying Markovian dynamics of ECG rhythms by information flow

Abstract Several approaches have been recently introduced to characterize and classify signals based on the underlying hidden dynamic. Markov models represent a natural choice for describing the dynamic evolution of a signal. However, the right selection of the memory of the process is essential for the correctness of the Markov model and a mathematically well-founded criterion is necessary to establish when the Markov model is a good approximation of the process. We review an information-theoretic based method that introduces the concept of information flow as such a criterion. The information flow describes the progressive loss of statistical dependence between the entire past and a point ahead in the future, which is indirectly related with the hidden dynamic of the signal. An approximated measure of information flow can be used as the discriminating statistic for selecting the optimal Markov model in terms of the shortest memory required. This technique is applied to investigate the underlying Markovian dynamics of the heart rate variability (HRV) for subjects in different patho-physiological conditions. Markov models with different memories seem to be associated with the circadian cycle and with different pathologies. Furthermore, the precursor character of the information flow for predicting ventricular tachycardia (VT) is discussed.

Extracting information from fuzzy models

The goal of this study is to quantify the importance of the input features in a fuzzy solution of two real-world problems. The first analysis definer the most effective ElectroCardioGraphic (ECG) measures for an automatic fuzzy recognition of cardiac arrhythmic beats. The second problem aims to assess the role played by duration, amplitude and pitch features of vocalic nuclei for the automatic recognition of prosodic stress in spoken American English. A similar analysis is performed for both problems by means of statistical decision trees under the form of the C4.5 algorithm. In general, decision trees and fuzzy systems seem to exploit the same or related input features for the analysis, especially if the input space dimension is low.