Hugo Alonso

A Weighted Principal Component Analysis and Its Application to Gene Expression Data

In this work, we introduce in the first part new developments in Principal Component Analysis (PCA) and in the second part a new method to select variables (genes in our application). Our focus is on problems where the values taken by each variable do not all have the same importance and where the data may be contaminated with noise and contain outliers, as is the case with microarray data. The usual PCA is not appropriate to deal with this kind of problems. In this context, we propose the use of a new correlation coefficient as an alternative to Pearsons. This leads to a so-called weighted PCA (WPCA). In order to illustrate the features of our WPCA and compare it with the usual PCA, we consider the problem of analyzing gene expression data sets. In the second part of this work, we propose a new PCA-based algorithm to iteratively select the most important genes in a microarray data set. We show that this algorithm produces better results when our WPCA is used instead of the usual PCA. Furthermore, by using Support Vector Machines, we show that it can compete with the Significance Analysis of Microarrays algorithm.

The unimodal model for the classification of ordinal data

Many real life problems require the classification of items into naturally ordered classes. These problems are traditionally handled by conventional methods intended for the classification of nominal classes where the order relation is ignored. This paper introduces a new machine learning paradigm intended for multi-class classification problems where the classes are ordered. The theoretical development of this paradigm is carried out under the key idea that the random variable class associated with a given query should follow a unimodal distribution. In this context, two approaches are considered: a parametric, where the random variable class is assumed to follow a specific discrete distribution; a nonparametric, where the random variable class is assumed to be distribution-free. In either case, the unimodal model can be implemented in practice by means of feedforward neural networks and support vector machines, for instance. Nevertheless, our main focus is on feedforward neural networks. We also introduce a new coefficient, r(int), to measure the performance of ordinal data classifiers. An experimental study with artificial and real datasets is presented in order to illustrate the performances of both parametric and nonparametric approaches and compare them with the performances of other methods. The superiority of the parametric approach is suggested, namely when flexible discrete distributions, a new concept introduced here, are considered.

Hopfield neural networks for on-line parameter estimation

This paper addresses the problem of using Hopfield Neural Networks (HNNs) for on-line parameter estimation. As presented here, a HNN is a nonautonomous nonlinear dynamical system able to produce a time-evolving estimate of the actual parameterization. The stability analysis of the HNN is carried out under more general assumptions than those previously considered in the literature, yielding a weaker sufficient condition under which the estimation error asymptotically converges to zero. Furthermore, a robustness analysis is made, showing that, under the presence of perturbations, the estimation error converges to a bounded neighbourhood of zero, whose size decreases with the size of the perturbations. The results obtained are illustrated by means of two case studies, where the HNN is compared with two other methods.

A hybrid method for parameter estimation and its application to biomedical systems

A general version of a hybrid method for parameter estimation is presented with a theoretical support and an illustrative example of application. This method consists of a curve fitting algorithm that takes the initial estimate of the parameterization from an artificial neural network. The idea is to improve the convergence of the algorithm to the sought parameterization using a close initial estimate. The motivation arises from biomedical problems where one is interested in obtaining a meaningful estimate so that it can be used for both description and prediction purposes. Two strategies are proposed for the application of the hybrid method: one is of general applicability, the other is intended for systems defined by the series connection of various blocks. The feasibility of the method is illustrated with a case study related to the neuromuscular blockade of patients undergoing general anaesthesia.

A General Stability Test for Switched Positive Systems Based on a Multidimensional System Analysis

The main goal of this technical note is to present a new sufficient condition for the stability of switched positive linear systems. This condition is general in two senses. First of all, because it applies to switching systems of order composed of subsystems, for any and . Secondly, because it applies to both discrete- and continuous-time systems. Furthermore, it is easy to verify, as it amounts to check for the stability of a certain matrix. The new condition is derived from a multidimensional system analysis, where the relation between the stability of multidimensional and switched systems is investigated. A comparison with other existing tests is also presented, showing that the one proposed here allows to infer about the stability of a system in cases where other tests fail or do not apply at all.

Comparing different identification approaches for the depth of anesthesia using BIS measurements

Depth of anesthesia is usually quantified by the Bispectral Index (BIS) and refers to both loss of consciousness, resulting from the administration of a hypnotic like propofol, and inhibition of pain, resulting from the administration of an analgesic like remifentanil. This paper addresses the mathematical modeling of the joint effect of propofol and remifentanil in the depth of anesthesia, using BIS measurements. Two models and identification strategies are considered. The first model is based on standard pharmacokinetic/pharmacodynamic models and the associated identification strategy corresponds to the application of a hybrid method. The second model has a minimal number of parameters and the associated identification strategy corresponds to the application of a prediction error method. These two approaches are tested and compared on real data.

A target control infusion method for neuromuscular blockade based on hybrid parameter estimation

The paper presents a new method for target control infusion (TCI) for neuromuscular blockade (NMB) level control of patients subject to general anaesthesia. The method combines an inversion of the pharmacokinetic/pharmacodynamic (PK/PD) model with a hybrid parameter estimation method that uses on-line data from the initial bolus response to estimate the model parameters. Although atracurium is considered as relaxant, the newly proposed method may be applied to other drugs for which the PK/PD model is available. Simulation results on a bank of 100 patient models are presented to demonstrate the achievable performance.

A simple model for the identification of drug effects

This paper presents a new model for the identification of drug effects. The main advantage of this model over standard models is its simplicity. In fact, the proposed model establishes an affine relation between the drug infusion rate and the corresponding effect on the patient where there are few parameters to estimate, while standard models usually assume a nonlinear relation with many parameters to estimate. Furthermore, it is shown that the new model has a good ability to describe real data. Here, the case study focuses on the muscle relaxant atracurium and its influence on the neuromuscular blockade, but other drugs such as the hypnotic propofol and the analgesic remifentanil and their influence on the depth of anaesthesia may also be considered.

An automatic system for on-line change detection with application to structural health monitoring

This paper presents a new automatic system for on-line change detection in structural health monitoring. The system is based on a combination of a Hopfield neural network with an adaptive kernel density estimation method and a test for unimodality. The changes in the process being monitored are detected from a model of that process. A Hopfield neural network is used on-line to adapt the model, tracking parameter variations from the process data. Given that these data are often corrupted by random noise, the parameter estimator implemented by the network can be regarded as a random vector. In this context, an adaptive kernel density estimation method is used to estimate the marginal probability density functions of the parameter estimator. When a parameter changes, the corresponding estimator marginal density becomes nonunimodal and this change is automatically detected by a test for unimodality. The robustness of the proposed system is guaranteed by the robustness of both the network and density estimation method. The system performance in structural health monitoring is illustrated by means of a simulation study, where a comparison is carried out with another approach to the problem of on-line change detection.

A hybrid method for parameter estimation

In this paper a method is presented for plant model parameter estimation. The method combines the artificial neural networks ability for function approximation with a nonlinear least-squares regression technique using the Levenberg-Marquardt optimization method. This combination intends to overcome problems that arise when artificial neural networks or nonlinear least-squares regression are separately applied to parameter estimation, which is accomplished by means of potentiating each of the methods advantages. The estimation of atracurium effect concentration model parameters is used as a case study to show the efficiency of the proposed method.