Kronecker Graphs: An Approach to Modeling Networks

How can we model networks with a mathematically tractable model that allows for rigorous analysis of network properties? Networks exhibit a long list of surprising properties: heavy tails for the degree distribution; small diameters; and densification and shrinking diameters over time. Most present network models either fail to match several of the above properties, are complicated to analyze mathematically, or both. In this paper we propose a generative model for networks that is both mathematically tractable and can generate networks that have the above mentioned properties. Our main idea is to use the Kronecker product to generate graphs that we refer to as "Kronecker graphs". First, we prove that Kronecker graphs naturally obey common network properties. We also provide empirical evidence showing that Kronecker graphs can effectively model the structure of real networks. We then present KronFit, a fast and scalable algorithm for fitting the Kronecker graph generation model to large real networks. A naive approach to fitting would take super- exponential time. In contrast, KronFit takes linear time, by exploiting the structure of Kronecker matrix multiplication and by using statistical simulation techniques. Experiments on large real and synthetic networks show that KronFit finds accurate parameters that indeed very well mimic the properties of target networks. Once fitted, the model parameters can be used to gain insights about the network structure, and the resulting synthetic graphs can be used for null- models, anonymization, extrapolations, and graph summarization

Data-Driven Shape Analysis and Processing

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and visualization of geometric data. In contrast to traditional approaches, a key feature of data-driven approaches is that they aggregate information from a collection of shapes to improve the analysis and processing of individual shapes. In addition, they are able to learn models that reason about properties and relationships of shapes without relying on hard-coded rules or explicitly programmed instructions. We provide an overview of the main concepts and components of these techniques, and discuss their application to shape classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis, through reviewing the literature and relating the existing works with both qualitative and numerical comparisons. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing.Comment: 10 pages, 19 figure

Local matching learning of large scale biomedical ontologies

Les larges ontologies biomédicales décrivent généralement le même domaine d'intérêt, mais en utilisant des modèles de modélisation et des vocabulaires différents. Aligner ces ontologies qui sont complexes et hétérogènes est une tâche fastidieuse. Les systèmes de matching doivent fournir des résultats de haute qualité en tenant compte de la grande taille de ces ressources. Les systèmes de matching d'ontologies doivent résoudre deux problèmes: (i) intégrer la grande taille d'ontologies, (ii) automatiser le processus d'alignement. Le matching d'ontologies est une tâche difficile en raison de la large taille des ontologies. Les systèmes de matching d'ontologies combinent différents types de matcher pour résoudre ces problèmes. Les principaux problèmes de l'alignement de larges ontologies biomédicales sont: l'hétérogénéité conceptuelle, l'espace de recherche élevé et la qualité réduite des alignements résultants. Les systèmes d'alignement d'ontologies combinent différents matchers afin de réduire l'hétérogénéité. Cette combinaison devrait définir le choix des matchers à combiner et le poids. Différents matchers traitent différents types d'hétérogénéité. Par conséquent, le paramétrage d'un matcher devrait être automatisé par les systèmes d'alignement d'ontologies afin d'obtenir une bonne qualité de correspondance. Nous avons proposé une approche appele "local matching learning" pour faire face à la fois à la grande taille des ontologies et au problème de l'automatisation. Nous divisons un gros problème d'alignement en un ensemble de problèmes d'alignement locaux plus petits. Chaque problème d'alignement local est indépendamment aligné par une approche d'apprentissage automatique. Nous réduisons l'énorme espace de recherche en un ensemble de taches de recherche de corresondances locales plus petites. Nous pouvons aligner efficacement chaque tache de recherche de corresondances locale pour obtenir une meilleure qualité de correspondance. Notre approche de partitionnement se base sur une nouvelle stratégie à découpes multiples générant des partitions non volumineuses et non isolées. Par conséquence, nous pouvons surmonter le problème de l'hétérogénéité conceptuelle. Le nouvel algorithme de partitionnement est basé sur le clustering hiérarchique par agglomération (CHA). Cette approche génère un ensemble de tâches de correspondance locale avec un taux de couverture suffisant avec aucune partition isolée. Chaque tâche d'alignement local est automatiquement alignée en se basant sur les techniques d'apprentissage automatique. Un classificateur local aligne une seule tâche d'alignement local. Les classificateurs locaux sont basés sur des features élémentaires et structurelles. L'attribut class de chaque set de donne d'apprentissage " training set" est automatiquement étiqueté à l'aide d'une base de connaissances externe. Nous avons appliqué une technique de sélection de features pour chaque classificateur local afin de sélectionner les matchers appropriés pour chaque tâche d'alignement local. Cette approche réduit la complexité d'alignement et augmente la précision globale par rapport aux méthodes d'apprentissage traditionnelles. Nous avons prouvé que l'approche de partitionnement est meilleure que les approches actuelles en terme de précision, de taux de couverture et d'absence de partitions isolées. Nous avons évalué l'approche d'apprentissage d'alignement local à l'aide de diverses expériences basées sur des jeux de données d'OAEI 2018. Nous avons déduit qu'il est avantageux de diviser une grande tâche d'alignement d'ontologies en un ensemble de tâches d'alignement locaux. L'espace de recherche est réduit, ce qui réduit le nombre de faux négatifs et de faux positifs. L'application de techniques de sélection de caractéristiques à chaque classificateur local augmente la valeur de rappel pour chaque tâche d'alignement local.Although a considerable body of research work has addressed the problem of ontology matching, few studies have tackled the large ontologies used in the biomedical domain. We introduce a fully automated local matching learning approach that breaks down a large ontology matching task into a set of independent local sub-matching tasks. This approach integrates a novel partitioning algorithm as well as a set of matching learning techniques. The partitioning method is based on hierarchical clustering and does not generate isolated partitions. The matching learning approach employs different techniques: (i) local matching tasks are independently and automatically aligned using their local classifiers, which are based on local training sets built from element level and structure level features, (ii) resampling techniques are used to balance each local training set, and (iii) feature selection techniques are used to automatically select the appropriate tuning parameters for each local matching context. Our local matching learning approach generates a set of combined alignments from each local matching task, and experiments show that a multiple local classifier approach outperforms conventional, state-of-the-art approaches: these use a single classifier for the whole ontology matching task. In addition, focusing on context-aware local training sets based on local feature selection and resampling techniques significantly enhances the obtained results

A formal concept analysis approach to consensus clustering of multi-experiment expression data

Background: Presently, with the increasing number and complexity of available gene expression datasets, the combination of data from multiple microarray studies addressing a similar biological question is gaining importance. The analysis and integration of multiple datasets are expected to yield more reliable and robust results since they are based on a larger number of samples and the effects of the individual study-specific biases are diminished. This is supported by recent studies suggesting that important biological signals are often preserved or enhanced by multiple experiments. An approach to combining data from different experiments is the aggregation of their clusterings into a consensus or representative clustering solution which increases the confidence in the common features of all the datasets and reveals the important differences among them. Results: We propose a novel generic consensus clustering technique that applies Formal Concept Analysis (FCA) approach for the consolidation and analysis of clustering solutions derived from several microarray datasets. These datasets are initially divided into groups of related experiments with respect to a predefined criterion. Subsequently, a consensus clustering algorithm is applied to each group resulting in a clustering solution per group. These solutions are pooled together and further analysed by employing FCA which allows extracting valuable insights from the data and generating a gene partition over all the experiments. In order to validate the FCA-enhanced approach two consensus clustering algorithms are adapted to incorporate the FCA analysis. Their performance is evaluated on gene expression data from multi-experiment study examining the global cell-cycle control of fission yeast. The FCA results derived from both methods demonstrate that, although both algorithms optimize different clustering characteristics, FCA is able to overcome and diminish these differences and preserve some relevant biological signals. Conclusions: The proposed FCA-enhanced consensus clustering technique is a general approach to the combination of clustering algorithms with FCA for deriving clustering solutions from multiple gene expression matrices. The experimental results presented herein demonstrate that it is a robust data integration technique able to produce good quality clustering solution that is representative for the whole set of expression matrices

A Primer on the Data Cleaning Pipeline

The availability of both structured and unstructured databases, such as electronic health data, social media data, patent data, and surveys that are often updated in real time, among others, has grown rapidly over the past decade. With this expansion, the statistical and methodological questions around data integration, or rather merging multiple data sources, has also grown. Specifically, the science of the ``data cleaning pipeline'' contains four stages that allow an analyst to perform downstream tasks, predictive analyses, or statistical analyses on ``cleaned data.'' This article provides a review of this emerging field, introducing technical terminology and commonly used methods

Robust Temporally Coherent Laplacian Protrusion Segmentation of 3D Articulated Bodies

In motion analysis and understanding it is important to be able to fit a suitable model or structure to the temporal series of observed data, in order to describe motion patterns in a compact way, and to discriminate between them. In an unsupervised context, i.e., no prior model of the moving object(s) is available, such a structure has to be learned from the data in a bottom-up fashion. In recent times, volumetric approaches in which the motion is captured from a number of cameras and a voxel-set representation of the body is built from the camera views, have gained ground due to attractive features such as inherent view-invariance and robustness to occlusions. Automatic, unsupervised segmentation of moving bodies along entire sequences, in a temporally-coherent and robust way, has the potential to provide a means of constructing a bottom-up model of the moving body, and track motion cues that may be later exploited for motion classification. Spectral methods such as locally linear embedding (LLE) can be useful in this context, as they preserve "protrusions", i.e., high-curvature regions of the 3D volume, of articulated shapes, while improving their separation in a lower dimensional space, making them in this way easier to cluster. In this paper we therefore propose a spectral approach to unsupervised and temporally-coherent body-protrusion segmentation along time sequences. Volumetric shapes are clustered in an embedding space, clusters are propagated in time to ensure coherence, and merged or split to accommodate changes in the body's topology. Experiments on both synthetic and real sequences of dense voxel-set data are shown. This supports the ability of the proposed method to cluster body-parts consistently over time in a totally unsupervised fashion, its robustness to sampling density and shape quality, and its potential for bottom-up model constructionComment: 31 pages, 26 figure

Topology-based Clusterwise Regression for User Segmentation and Demand Forecasting

Topological Data Analysis (TDA) is a recent approach to analyze data sets from the perspective of their topological structure. Its use for time series data has been limited. In this work, a system developed for a leading provider of cloud computing combining both user segmentation and demand forecasting is presented. It consists of a TDA-based clustering method for time series inspired by a popular managerial framework for customer segmentation and extended to the case of clusterwise regression using matrix factorization methods to forecast demand. Increasing customer loyalty and producing accurate forecasts remain active topics of discussion both for researchers and managers. Using a public and a novel proprietary data set of commercial data, this research shows that the proposed system enables analysts to both cluster their user base and plan demand at a granular level with significantly higher accuracy than a state of the art baseline. This work thus seeks to introduce TDA-based clustering of time series and clusterwise regression with matrix factorization methods as viable tools for the practitioner