Graphical Model approaches for Biclustering

In many scientific areas, it is crucial to group (cluster) a set of objects, based on a set of observed features. Such operation is widely known as Clustering and it has been exploited in the most different scenarios ranging from Economics to Biology passing through Psychology. Making a step forward, there exist contexts where it is crucial to group objects and simultaneously identify the features that allow to recognize such objects from the others. In gene expression analysis, for instance, the identification of subsets of genes showing a coherent pattern of expression in subsets of objects/samples can provide crucial information about active biological processes. Such information, which cannot be retrieved by classical clustering approaches, can be extracted with the so called Biclustering, a class of approaches which aim at simultaneously clustering both rows and columns of a given data matrix (where each row corresponds to a different object/sample and each column to a different feature). The problem of biclustering, also known as co-clustering, has been recently exploited in a wide range of scenarios such as Bioinformatics, market segmentation, data mining, text analysis and recommender systems. Many approaches have been proposed to address the biclustering problem, each one characterized by different properties such as interpretability, effectiveness or computational complexity. A recent trend involves the exploitation of sophisticated computational models (Graphical Models) to face the intrinsic complexity of biclustering, and to retrieve very accurate solutions. Graphical Models represent the decomposition of a global objective function to analyse in a set of smaller/local functions defined over a subset of variables. The advantages in using Graphical Models relies in the fact that the graphical representation can highlight useful hidden properties of the considered objective function, plus, the analysis of smaller local problems can be dealt with less computational effort. Due to the difficulties in obtaining a representative and solvable model, and since biclustering is a complex and challenging problem, there exist few promising approaches in literature based on Graphical models facing biclustering. 3 This thesis is inserted in the above mentioned scenario and it investigates the exploitation of Graphical Models to face the biclustering problem. We explored different type of Graphical Models, in particular: Factor Graphs and Bayesian Networks. We present three novel algorithms (with extensions) and evaluate such techniques using available benchmark datasets. All the models have been compared with the state-of-the-art competitors and the results show that Factor Graph approaches lead to solid and efficient solutions for dataset of contained dimensions, whereas Bayesian Networks can manage huge datasets, with the overcome that setting the parameters can be not trivial. As another contribution of the thesis, we widen the range of biclustering applications by studying the suitability of these approaches in some Computer Vision problems where biclustering has been never adopted before. Summarizing, with this thesis we provide evidence that Graphical Model techniques can have a significant impact in the biclustering scenario. Moreover, we demonstrate that biclustering techniques are ductile and can produce effective solutions in the most different fields of applications

Fouille de données complexes et biclustering avec l'analyse formelle de concepts

Knowledge discovery in database (KDD) is a process which is applied to possibly large volumes of data for discovering patterns which can be significant and useful. In this thesis, we are interested in data transformation and data mining in knowledge discovery applied to complex data, and we present several experiments related to different approaches and different data types.The first part of this thesis focuses on the task of biclustering using formal concept analysis (FCA) and pattern structures. FCA is naturally related to biclustering, where the objective is to simultaneously group rows and columns which verify some regularities. Related to FCA, pattern structures are its generalizations which work on more complex data. Partition pattern structures were proposed to discover constant-column biclustering, while interval pattern structures were studied in similar-column biclustering. Here we extend these approaches to enumerate other types of biclusters: additive, multiplicative, order-preserving, and coherent-sign-changes.The second part of this thesis focuses on two experiments in mining complex data. First, we present a contribution related to the CrossCult project, where we analyze a dataset of visitor trajectories in a museum. We apply sequence clustering and FCA-based sequential pattern mining to discover patterns in the dataset and to classify these trajectories. This analysis can be used within CrossCult project to build recommendation systems for future visitors. Second, we present our work related to the task of antibacterial drug discovery. The dataset for this task is generally a numerical matrix with molecules as rows and features/attributes as columns. The huge number of features makes it more complex for any classifier to perform molecule classification. Here we study a feature selection approach based on log-linear analysis which discovers associations among features.As a synthesis, this thesis presents a series of different experiments in the mining of complex real-world data.L'extraction de connaissances dans les bases de données (ECBD) est un processus qui s'applique à de (potentiellement larges) volumes de données pour découvrir des motifs qui peuvent être signifiants et utiles. Dans cette thèse, on s'intéresse à deux étapes du processus d'ECBD, la transformation et la fouille, que nous appliquons à des données complexes. Nous présentons de nombreuses expérimentations s'appuyant sur des approches et des types de données variés.La première partie de cette thèse s'intéresse à la tâche de biclustering en s'appuyant sur l'analyse formelle de concepts (FCA) et aux pattern structures. FCA est naturellement liées au biclustering, dont l'objectif consiste à grouper simultanément un ensemble de lignes et de colonnes qui vérifient certaines régularités. Les pattern structures sont une généralisation de la FCA qui permet de travailler avec des données plus complexes. Les "partition pattern structures'' ont été proposées pour du biclustering à colonnes constantes tandis que les "interval pattern structures'' ont été étudiées pour du biclustering à colonnes similaires. Nous proposons ici d'étendre ces approches afin d'énumérer d'autres types de biclusters : additif, multiplicatif, préservant l'ordre, et changement de signes cohérents.Dans la seconde partie, nous nous intéressons à deux expériences de fouille de données complexes. Premièrement, nous présentons une contribution dans la quelle nous analysons les trajectoires des visiteurs d'un musée dans le cadre du projet CrossCult. Nous utilisons du clustering de séquences et de la fouille de motifs séquentiels basée sur l'analyse formelle de concepts pour découvrir des motifs dans les données et classifier les trajectoires. Cette analyse peut ensuite être exploitée par un système de recommandation pour les futurs visiteurs. Deuxièmement, nous présentons un travail sur la découverte de médicaments antibactériens. Les jeux de données pour cette tâche, généralement des matrices numériques, décrivent des molécules par un certain nombre de variables/attributs. Le grand nombre de variables complexifie la classification des molécules par les classifieurs. Ici, nous étudions une approche de sélection de variables basée sur l'analyse log-linéaire qui découvre des associations entre variables.En somme, cette thèse présente différentes expériences de fouille de données réelles et complexes

Evolutionary framework for DNA Microarry Cluster Analysis

En esta investigación se propone un framework evolutivo donde se fusionan un método de clustering jerárquico basado en un modelo evolutivo, un conjunto de medidas de validación de agrupamientos (clusters) de datos y una herramienta de visualización de clusterings. El objetivo es crear un marco apropiado para la extracción de conocimiento a partir de datos provenientes de DNA-microarrays. Por una parte, el modelo evolutivo de clustering de nuestro framework es una alternativa novedosa que intenta resolver algunos de los problemas presentes en los métodos de clustering existentes. Por otra parte, nuestra alternativa de visualización de clusterings, materializada en una herramienta, incorpora nuevas propiedades y nuevos componentes de visualización, lo cual permite validar y analizar los resultados de la tarea de clustering. De este modo, la integración del modelo evolutivo de clustering con el modelo visual de clustering, convierta a nuestro framework evolutivo en una aplicación novedosa de minería de datos frente a los métodos convencionales

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters

CLADAG 2021 BOOK OF ABSTRACTS AND SHORT PAPERS

The book collects the short papers presented at the 13th Scientific Meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society (SIS). The meeting has been organized by the Department of Statistics, Computer Science and Applications of the University of Florence, under the auspices of the Italian Statistical Society and the International Federation of Classification Societies (IFCS). CLADAG is a member of the IFCS, a federation of national, regional, and linguistically-based classification societies. It is a non-profit, non-political scientific organization, whose aims are to further classification research

Bioinformatics

This book is divided into different research areas relevant in Bioinformatics such as biological networks, next generation sequencing, high performance computing, molecular modeling, structural bioinformatics, molecular modeling and intelligent data analysis. Each book section introduces the basic concepts and then explains its application to problems of great relevance, so both novice and expert readers can benefit from the information and research works presented here

A Statistical Approach to the Alignment of fMRI Data

Multi-subject functional Magnetic Resonance Image studies are critical. The anatomical and functional structure varies across subjects, so the image alignment is necessary. We define a probabilistic model to describe functional alignment. Imposing a prior distribution, as the matrix Fisher Von Mises distribution, of the orthogonal transformation parameter, the anatomical information is embedded in the estimation of the parameters, i.e., penalizing the combination of spatially distant voxels. Real applications show an improvement in the classification and interpretability of the results compared to various functional alignment methods

A comparison of the CAR and DAGAR spatial random effects models with an application to diabetics rate estimation in Belgium

When hierarchically modelling an epidemiological phenomenon on a finite collection of sites in space, one must always take a latent spatial effect into account in order to capture the correlation structure that links the phenomenon to the territory. In this work, we compare two autoregressive spatial models that can be used for this purpose: the classical CAR model and the more recent DAGAR model. Differently from the former, the latter has a desirable property: its ρ parameter can be naturally interpreted as the average neighbor pair correlation and, in addition, this parameter can be directly estimated when the effect is modelled using a DAGAR rather than a CAR structure. As an application, we model the diabetics rate in Belgium in 2014 and show the adequacy of these models in predicting the response variable when no covariates are available