Diego Liberati

A clustering technique for the identification of piecewise affine systems

We propose a new technique for the identification of discrete-time hybrid systems in the piecewise affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multi-dimensional domain. In order to achieve our goal, we provide an algorithm that exploits the combined use of clustering, linear identification, and pattern recognition techniques. This allows to identify both the affine submodels and the polyhedral partition of the domain on which each submodel is valid avoiding gridding procedures. Moreover, the clustering step (used for classifying the datapoints) is performed in a suitably defined feature space which allows also to reconstruct different submodels that share the same coefficients but are defined on different regions. Measures of confidence on the samples are introduced and exploited in order to improve the performance of both the clustering and the final linear regression procedure.

Spectral and cross-spectral analysis of heart rate and arterial blood pressure variability signals

A parametric method for autoregressive (AR) auto- and cross-spectral analysis is presented for the contemporaneous processing of heart rate and arterial blood pressure variability signals. In particular, the introduced bivariate spectral analysis (phase and coherence spectra) provides quantitative and objective means which are useful to measure the role played by the neural controlling systems (sympathetic and parasympathetic systems) on the cardiovascular signals under different pathophysiological conditions. Algorithmic aspects, connected to the way of processing discrete numerical series synchronized to single cardiac beats, are particularly stressed. Important applications are foreseen both in physiological studies and in clinical practice as an aid to the detection of various relevant cardiovascular pathologies such as hypertension and diabetes.

Measuring regularity by means of a corrected conditional entropy in sympathetic outflow

Abstract. A new method for measuring the regularity of a process over short data sequences is reported. This method is based on the definition of a new function (the corrected conditional entropy) and on the extraction of its minimum. This value is taken as an index in the information domain quantifying the regularity of the process. The corrected conditional entropy is designed to decrease in relation to the regularity of the process (like other estimates of the entropy rate), but it is able to increase when no robust statistic can be performed as a result of a limited amount of available samples. As a consequence of the minimisation procedure, the proposed index is obtained without an a-priori definition of the pattern length (i.e. of the embedding dimension of the reconstructed phase space). The method is validated on simulations and applied to beat- to-beat sequences of the sympathetic discharge obtained from decerebrate artificially ventilated cats. At control, regular, both quasiperiodic and periodic (locked to ventilation) dynamics are observed. During the sympathetic activation induced by inferior vena cava occlusion, the presence of phase-locked patterns and the increase in regularity of the sympathetic discharge evidence an augmented coupling between the sympathetic discharge and ventilation. The reduction of complexity of the neural control obtained by spinalization decreases the regularity in the sympathetic outflow, thus pointing to a weaker coupling between the sympathetic discharge and ventilation.

A parametric method of identification of single-trial event-related potentials in the brain

A parametric method of identification of event-related (or evoked) potentials on a single-trial basis through an ARX (autoregressive with exogenous input) algorithm is discussed. The basic estimation of the information contained in the single trial is taken from an average carried out on a sufficient number of trials, while the noise sources, EEG and EOG, are characterized as exogenous inputs in the model. The simulations as well as the experimental results confirm the capability of the model of drastically improving the S/N (signal-to-noise) ratio in each single trial and satisfactorily identifying the contributions of signal and noise to the overall recording. A particularly efficient reduction of ocular artifacts is also achieved.<<ETX>>

A Clustering Technique for the Identification of Piecewise Affine Systems

We propose a new technique for the identification of discrete-time hybrid systems in the Piece-Wise Affine (PWA) form. The identification algorithm proposed in [10] is first considered and then improved under various aspects. Measures of confidence on the samples are introduced and exploited in order to improve the performance of both the clustering algorithm used for classifying the data and the final linear regression procedure. Moreover, clustering is performed in a suitably defined space that allows also to reconstruct different submodels that share the same coefficients but are defined on different regions.

Single sweep analysis of visual evoked potentials through a model of parametric identification

An original method is presented for the single sweep analysis of visual evoked potentials (VEPs). The introduced algorithm bases upon an AutoRegressive with eXogenous input (ARX) modelling. A Least Squares procedure estimates the coefficients of the model and allows to obtain a complete black-box description of the signal generation mechanism, besides providing a filtered version of the single sweep potential. The performance of the algorithm is verified on proper simulation tests and the experimental results put into evidence the noticeable improvement of signal-to-noise ratio with a consequent better recognition of the classical parameters of the peaks (latencies and amplitudes). The possibility of measuring these parameters on a single sweep basis enables to evaluate the dynamics of the Central Nervous System response during the entire course of the examination. A classification of the estimated evoked potentials in a small number of subsets, on the basis of their morphology, is also possible.

Binary rule generation via Hamming Clustering

The generation of a set of rules underlying a classification problem is performed by applying a new algorithm called Hamming Clustering (HC). It reconstructs the AND-OR expression associated with any Boolean function from a training set of samples. The basic kernel of the method is the generation of clusters of input patterns that belong to the same class and are close to each other according to the Hamming distance. Inputs which do not influence the final output are identified, thus automatically reducing the complexity of the final set of rules. The performance of HC has been evaluated through a variety of artificial and real-world benchmarks. In particular, its application in the diagnosis of breast cancer has led to the derivation of a reduced set of rules solving the associated classification problem.

Identification of piecewise affine and hybrid systems

We focus on the identification of discrete time hybrid systems in the piecewise affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multidimensional domain. In order to achieve our goal, we propose an algorithm that exploits the combined use of clustering, linear identification, and classification techniques. This allows one to identify both the affine sub-models and the polyhedral partition of the domain on which each submodel is valid.

Linear and nonlinear techniques for the deconvolution of hormone time-series

Pulsatile hormone secretion is usually investigated by measuring hormone concentration in samples of peripheral plasma. Here, the deconvolution of hormone time series to reconstruct the instantaneous secretion rate of glands is considered. Various techniques are discussed and compared in order to overcome the ill-conditioning of the problem and reduce the computational burden. In particular, linear techniques based on least squares, maximum a posteriori (MAP) estimation, and Wiener filtering are compared. A new nonlinear MAP estimator that keeps into account the non-Gaussian distribution of the unknown signal is worked out and shown to yield the best results. The performances of the algorithms are tested on simulated time series as well as on series of luteinizing hormone.<<ETX>>

Training digital circuits with Hamming clustering

A new algorithm, called Hamming clustering (HC), for the solution of classification problems with binary inputs is proposed. It builds a logical network containing only AND, OR, and NOT ports which, in addition to satisfying all the input-output pairs included in a given finite consistent training set, is able to reconstruct the underlying Boolean function. The basic kernel of the method is the generation of clusters of input patterns that belong to the same class and are close to each other according to the Hamming distance. A pruning phase precedes the construction of the digital circuit so as to reduce its complexity or to improve its robustness. A theoretical evaluation of the execution time required by HC shows that the behavior of the computational cost is polynomial. This result is confirmed by extensive simulations on artificial and real-world benchmarks, which point out also the generalization ability of the logical networks trained by HC.