Rita Morisi

Sparse solutions to the average consensus problem via l 1 -norm regularization of the fastest mixing Markov-chain problem

In the consensus problem on multi-agent systems, in which the states of the agents represent opinions, the agents aim at reaching a common opinion (or consensus state) through local exchange of information. An important design problem is to choose the degree of interconnection of the subsystems to achieve a good trade-off between a small number of interconnections and a fast convergence to the consensus state, which is the average of the initial opinions under mild conditions. This paper addresses this problem through l1-norm and l0-“pseudo-norm” regularized versions of the well-known Fastest Mixing Markov-Chain (FMMC) problem. We show that such versions can be interpreted as robust forms of the FMMC problem and provide results to guide the choice of the regularization parameter.

Synthetic Generation of Myocardial Blood–Oxygen-Level-Dependent MRI Time Series Via Structural Sparse Decomposition Modeling

This paper aims to identify approaches that generate appropriate synthetic data (computer generated) for cardiac phase-resolved blood-oxygen-level-dependent (CP-BOLD) MRI. CP-BOLD MRI is a new contrast agent- and stress-free approach for examining changes in myocardial oxygenation in response to coronary artery disease. However, since signal intensity changes are subtle, rapid visualization is not possible with the naked eye. Quantifying and visualizing the extent of disease relies on myocardial segmentation and registration to isolate the myocardium and establish temporal correspondences and ischemia detection algorithms to identify temporal differences in BOLD signal intensity patterns. If transmurality of the defect is of interest pixel-level analysis is necessary and thus a higher precision in registration is required. Such precision is currently not available affecting the design and performance of the ischemia detection algorithms. In this work, to enable algorithmic developments of ischemia detection irrespective to registration accuracy, we propose an approach that generates synthetic pixel-level myocardial time series. We do this by 1) modeling the temporal changes in BOLD signal intensity based on sparse multi-component dictionary learning, whereby segmentally derived myocardial time series are extracted from canine experimental data to learn the model; and 2) demonstrating the resemblance between real and synthetic time series for validation purposes. We envision that the proposed approach has the capacity to accelerate development of tools for ischemia detection while markedly reducing experimental costs so that cardiac BOLD MRI can be rapidly translated into the clinical arena for the noninvasive assessment of ischemic heart disease.

Supervised and semi-supervised classifiers for the detection of flood-prone areas

Supervised and semi-supervised machine-learning techniques are applied and compared for the recognition of the flood hazard. The learning goal consists in distinguishing between flood-exposed and marginal-risk areas. Kernel-based binary classifiers using six quantitative morphological features, derived from data stored in digital elevation models, are trained to model the relationship between morphology and the flood hazard. According to the experimental outcomes, such classifiers are appropriate tools when one is interested in performing an initial low-cost detection of flood-exposed areas, to be possibly refined in successive steps by more time-consuming and costly investigations by experts. The use of these automatic classification techniques is valuable, e.g., in insurance applications, where one is interested in estimating the flood hazard of areas for which limited labeled information is available. The proposed machine-learning techniques are applied to the basin of the Italian Tanaro River. The experimental results show that for this case study, semi-supervised methods outperform supervised ones when—the number of labeled examples being the same for the two cases—only a few labeled examples are used, together with a much larger number of unsupervised ones.

Sparse Solutions to the Average Consensus Problem via Various Regularizations of the Fastest Mixing Markov-Chain Problem

In the “consensus problem” on multi-agent systems, in which the states of the agents are “opinions”, the agents aim at reaching a common opinion (or “consensus state”) through local exchange of information. An important design problem is to choose the degree of interconnection of the subsystems so as to achieve a good trade-off between a small number of interconnections and a fast convergence to the consensus state, which is the average of the initial opinions under mild conditions. This paper addresses this problem through l1-norm regularized versions of the well-known fastest mixing Markov-chain problem, which are investigated theoretically. In particular, it is shown that such versions can be interpreted as “robust” forms of the fastest mixing Markov-chain problem. Theoretical results useful to guide the choice of the regularization parameters are also provided, together with a numerical example.

Online learning as an LQG optimal control problem with random matrices

In this paper, we combine optimal control theory and machine learning techniques to propose and solve an optimal control formulation of online learning from supervised examples, which are used to learn an unknown vector parameter modeling the relationship between the input examples and their outputs. We show some connections of the problem investigated with the classical LQG optimal control problem, of which the proposed problem is a non-trivial variation, as it involves random matrices. We also compare the optimal solution to the proposed problem with the Kalman-filter estimate of the parameter vector to be learned, demonstrating its larger smoothness and robustness to outliers. Extension of the proposed online-learning framework are mentioned at the end of the paper.

Multi-class parkinsonian disorders classification with quantitative MR markers and graph-based features using support vector machines

BACKGROUND AND PURPOSE In this study we attempt to automatically classify individual patients with different parkinsonian disorders, making use of pattern recognition techniques to distinguish among several forms of parkinsonisms (multi-class classification), based on a set of binary classifiers that discriminate each disorder from all others. METHODS We combine diffusion tensor imaging, proton spectroscopy and morphometric-volumetric data to obtain MR quantitative markers, which are provided to support vector machines with the aim of recognizing the different parkinsonian disorders. Feature selection is used to find the most important features for classification. We also exploit a graph-based technique on the set of quantitative markers to extract additional features from the dataset, and increase classification accuracy. RESULTS When graph-based features are not used, the MR markers that are most frequently automatically extracted by the feature selection procedure reflect alterations in brain regions that are also usually considered to discriminate parkinsonisms in routine clinical practice. Graph-derived features typically increase the diagnostic accuracy, and reduce the number of features required. CONCLUSIONS The results obtained in the work demonstrate that support vector machines applied to multimodal brain MR imaging and using graph-based features represent a novel and highly accurate approach to discriminate parkinsonisms, and a useful tool to assist the diagnosis.

A hierarchical consensus method for the approximation of the consensus state, based on clustering and spectral graph theory

A hierarchical method for the approximate computation of the consensus state of a network of agents is investigated. The method is motivated theoretically by spectral graph theory arguments. In a first phase, the graph is divided into a number of subgraphs with good spectral properties, i.e., a fast convergence toward the local consensus state of each subgraph. To find the subgraphs, suitable clustering methods are used. Then, an auxiliary graph is considered, to determine the final approximation of the consensus state in the original network. A theoretical investigation is performed of cases for which the hierarchical consensus method has a better performance guarantee than the non-hierarchical one (i.e., it requires a smaller number of iterations to guarantee a desired accuracy in the approximation of the consensus state of the original network). Moreover, numerical results demonstrate the effectiveness of the hierarchical consensus method for several case studies modeling real-world networks.

Binary and Multi-class Parkinsonian Disorders Classification Using Support Vector Machines

This paper presents a method for an automated Parkinsonian disorders classification using Support Vector Machines (SVMs). Magnetic Resonance quantitative markers are used as features to train SVMs with the aim of automatically diagnosing patients with different Parkinsonian disorders. Binary and multi–class classification problems are investigated and applied with the aim of automatically distinguishing the subjects with different forms of disorders. A ranking feature selection method is also used as a preprocessing step in order to asses the significance of the different features in diagnosing Parkinsonian disorders. In particular, it turns out that the features selected as the most meaningful ones reflect the opinions of the clinicians as the most important markers in the diagnosis of these disorders. Concerning the results achieved in the classification phase, they are promising; in the two multi–class classification problems investigated, an average accuracy of \(81\,\%\) and \(90\,\%\) is obtained, while in the binary scenarios taken in consideration, the accuracy is never less than \(88\,\%\).

Semi-automated scar detection in delayed enhanced cardiac magnetic resonance images

Late enhancement cardiac magnetic resonance images (MRI) has the ability to precisely delineate myocardial scars. We present a semi-automated method for detecting scars in cardiac MRI. This model has the potential to improve routine clinical practice since quantification is not currently offered due to time constraints. A first segmentation step was developed for extracting the target regions for potential scar and determining pre-candidate objects. Pattern recognition methods are then applied to the segmented images in order to detect the position of the myocardial scar. The database of late gadolinium enhancement (LE) cardiac MR images consists of 111 blocks of images acquired from 63 patients at the University Hospital Southampton NHS Foundation Trust (UK). At least one scar was present for each patient, and all the scars were manually annotated by an expert. A group of images (around one third of the entire set) was used for training the system which was subsequently tested on all the remaining images. Four different classifiers were trained (Support Vector Machine (SVM), k-nearest neighbor (KNN), Bayesian and feed-forward neural network) and their performance was evaluated by using Free response Receiver Operating Characteristic (FROC) analysis. Feature selection was implemented for analyzing the importance of the various features. The segmentation method proposed allowed the region affected by the scar to be extracted correctly in 96% of the blocks of images. The SVM was shown to be the best classifier for our task, and our system reached an overall sensitivity of 80% with less than 7 false positives per patient. The method we present provides an effective tool for detection of scars on cardiac MRI. This may be of value in clinical practice by permitting routine reporting of scar quantification.

Supervised learning modelization and segmentation of cardiac scar in delayed enhanced MRI

Delayed Enhancement Magnetic Resonance Imaging can be used to non-invasively differentiate viable from non-viable myocardium within the Left Ventricle in patients suffering from myocardial diseases. Automated segmentation of scarified tissue can be used to accurately quantify the percentage of myocardium affected. This paper presents a method for cardiac scar detection and segmentation based on supervised learning and level set segmentation. First, a model of the appearance of scar tissue is trained using a Support Vector Machines classifier on image-derived descriptors. Based on the areas detected by the classifier, an accurate segmentation is performed using a segmentation method based on level sets.