A hierarchical latent variable model for data visualization

Visualization has proven to be a powerful and widely-applicable tool the analysis and interpretation of data. Most visualization algorithms aim to find a projection from the data space down to a two-dimensional visualization space. However, for complex data sets living in a high-dimensional space it is unlikely that a single two-dimensional projection can reveal all of the interesting structure. We therefore introduce a hierarchical visualization algorithm which allows the complete data set to be visualized at the top level, with clusters and sub-clusters of data points visualized at deeper levels. The algorithm is based on a hierarchical mixture of latent variable models, whose parameters are estimated using the expectation-maximization algorithm. We demonstrate the principle of the approach first on a toy data set, and then apply the algorithm to the visualization of a synthetic data set in 12 dimensions obtained from a simulation of multi-phase flows in oil pipelines and to data in 36 dimensions derived from satellite images

Seven clusters of data visualization articles in Scopus using social network analysis

The aim of this study was to analyse the bibliographic characteristics and content of articles on Data Visualization published in journals indexed by Scopus written by researchers from throughout the world. We conducted a bibliometric and content analysis of publication in the Scopus database. We only retrieved articles written in English. We conducted content analysis using the VOSviewer software and visualized the co-occurrence of keywords and bibliographic coupling of sources and countries. Following the study protocol, we found 862 articles on Data Visualization over the past 30 years. The most productive journal that published these articles was Lecture Notes In Computer Science (n=32). The most productive country was the United States (n=305). Based on citations, the most influential authors, and journals were Thorvaldsdóttir et al., (2013) [Thorvaldsdóttir, H., Robinson, J. T., & Mesirov, J. P. (2013). Integrative Genomics Viewer (IGV): High-performance genomics data visualization and exploration. Briefings in Bioinformatics, 14(2), 178–192.] (n=4699), and IEE Transactions on Visualization and Computer Graphics (n=656). The keywords of research on Data Visualization formed 7 clusters (e.g. Data Visualization, Visualization, and Human). From a global perspective, Data Visualization research in the past 30 years has increased significantly. There were European published journals nominated publications. Thus, Asian countries need to conduct more active research on this topic

Latent tree models

Latent tree models are graphical models defined on trees, in which only a subset of variables is observed. They were first discussed by Judea Pearl as tree-decomposable distributions to generalise star-decomposable distributions such as the latent class model. Latent tree models, or their submodels, are widely used in: phylogenetic analysis, network tomography, computer vision, causal modeling, and data clustering. They also contain other well-known classes of models like hidden Markov models, Brownian motion tree model, the Ising model on a tree, and many popular models used in phylogenetics. This article offers a concise introduction to the theory of latent tree models. We emphasise the role of tree metrics in the structural description of this model class, in designing learning algorithms, and in understanding fundamental limits of what and when can be learned

Joint and individual analysis of breast cancer histologic images and genomic covariates

A key challenge in modern data analysis is understanding connections between complex and differing modalities of data. For example, two of the main approaches to the study of breast cancer are histopathology (analyzing visual characteristics of tumors) and genetics. While histopathology is the gold standard for diagnostics and there have been many recent breakthroughs in genetics, there is little overlap between these two fields. We aim to bridge this gap by developing methods based on Angle-based Joint and Individual Variation Explained (AJIVE) to directly explore similarities and differences between these two modalities. Our approach exploits Convolutional Neural Networks (CNNs) as a powerful, automatic method for image feature extraction to address some of the challenges presented by statistical analysis of histopathology image data. CNNs raise issues of interpretability that we address by developing novel methods to explore visual modes of variation captured by statistical algorithms (e.g. PCA or AJIVE) applied to CNN features. Our results provide many interpretable connections and contrasts between histopathology and genetics

Probabilistic principal component analysis for metabolomic data

Background: Data from metabolomic studies are typically complex and high-dimensional. Principal component analysis (PCA) is currently the most widely used statistical technique for analyzing metabolomic data. However, PCA is limited by the fact that it is not based on a statistical model. Results: Here, probabilistic principal component analysis (PPCA) which addresses some of the limitations of PCA, is reviewed and extended. A novel extension of PPCA, called probabilistic principal component and covariates analysis (PPCCA), is introduced which provides a flexible approach to jointly model metabolomic data and additional covariate information. The use of a mixture of PPCA models for discovering the number of inherent groups in metabolomic data is demonstrated. The jackknife technique is employed to construct confidence intervals for estimated model parameters throughout. The optimal number of principal components is determined through the use of the Bayesian Information Criterion model selection tool, which is modified to address the high dimensionality of the data. Conclusions: The methods presented are illustrated through an application to metabolomic data sets. Jointly modeling metabolomic data and covariates was successfully achieved and has the potential to provide deeper insight to the underlying data structure. Examination of confidence intervals for the model parameters, such as loadings, allows for principled and clear interpretation of the underlying data structure. A software package called MetabolAnalyze, freely available through the R statistical software, has been developed to facilitate implementation of the presented methods in the metabolomics field.Irish Research Council for Science, Engineering and TechnologyHealth Research Boar

Robust estimation for mixtures of Gaussian factor analyzers, based on trimming and constraints

Producción CientíficaMixtures of Gaussian factors are powerful tools for modeling an unobserved heterogeneous population, offering - at the same time - dimension reduction and model-based clustering. Unfortunately, the high prevalence of spurious solutions and the disturbing effects of outlying observations, along maximum likelihood estimation, open serious issues. In this paper we consider restrictions for the component covariances, to avoid spurious solutions, and trimming, to provide robustness against violations of normality assumptions of the underlying latent factors. A detailed AECM algorithm for this new approach is presented. Simulation results and an application to the AIS dataset show the aim and effectiveness of the proposed methodology

The joint role of trimming and constraints in robust estimation for mixtures of Gaussian factor analyzers.

Producción CientíficaMixtures of Gaussian factors are powerful tools for modeling an unobserved heterogeneous population, offering – at the same time – dimension reduction and model-based clustering. The high prevalence of spurious solutions and the disturbing effects of outlying observations in maximum likelihood estimation may cause biased or misleading inferences. Restrictions for the component covariances are considered in order to avoid spurious solutions, and trimming is also adopted, to provide robustness against violations of normality assumptions of the underlying latent factors. A detailed AECM algorithm for this new approach is presented. Simulation results and an application to the AIS dataset show the aim and effectiveness of the proposed methodology.Ministerio de Economía y Competitividad and FEDER, grant MTM2014-56235-C2-1-P, and by Consejería de Educación de la Junta de Castilla y León, grant VA212U13, by grant FAR 2015 from the University of Milano-Bicocca and by grant FIR 2014 from the University of Catania