Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page

Analysis of Dynamic Brain Imaging Data

Modern imaging techniques for probing brain function, including functional Magnetic Resonance Imaging, intrinsic and extrinsic contrast optical imaging, and magnetoencephalography, generate large data sets with complex content. In this paper we develop appropriate techniques of analysis and visualization of such imaging data, in order to separate the signal from the noise, as well as to characterize the signal. The techniques developed fall into the general category of multivariate time series analysis, and in particular we extensively use the multitaper framework of spectral analysis. We develop specific protocols for the analysis of fMRI, optical imaging and MEG data, and illustrate the techniques by applications to real data sets generated by these imaging modalities. In general, the analysis protocols involve two distinct stages: `noise' characterization and suppression, and `signal' characterization and visualization. An important general conclusion of our study is the utility of a frequency-based representation, with short, moving analysis windows to account for non-stationarity in the data. Of particular note are (a) the development of a decomposition technique (`space-frequency singular value decomposition') that is shown to be a useful means of characterizing the image data, and (b) the development of an algorithm, based on multitaper methods, for the removal of approximately periodic physiological artifacts arising from cardiac and respiratory sources.Comment: 40 pages; 26 figures with subparts including 3 figures as .gif files. Originally submitted to the neuro-sys archive which was never publicly announced (was 9804003

Partial Least Squares: A Versatile Tool for the Analysis of High-Dimensional Genomic Data

Partial Least Squares (PLS) is a highly efficient statistical regression technique that is well suited for the analysis of high-dimensional genomic data. In this paper we review the theory and applications of PLS both under methodological and biological points of view. Focusing on microarray expression data we provide a systematic comparison of the PLS approaches currently employed, and discuss problems as different as tumor classification, identification of relevant genes, survival analysis and modeling of gene networks

Multi-view Learning as a Nonparametric Nonlinear Inter-Battery Factor Analysis

Factor analysis aims to determine latent factors, or traits, which summarize a given data set. Inter-battery factor analysis extends this notion to multiple views of the data. In this paper we show how a nonlinear, nonparametric version of these models can be recovered through the Gaussian process latent variable model. This gives us a flexible formalism for multi-view learning where the latent variables can be used both for exploratory purposes and for learning representations that enable efficient inference for ambiguous estimation tasks. Learning is performed in a Bayesian manner through the formulation of a variational compression scheme which gives a rigorous lower bound on the log likelihood. Our Bayesian framework provides strong regularization during training, allowing the structure of the latent space to be determined efficiently and automatically. We demonstrate this by producing the first (to our knowledge) published results of learning from dozens of views, even when data is scarce. We further show experimental results on several different types of multi-view data sets and for different kinds of tasks, including exploratory data analysis, generation, ambiguity modelling through latent priors and classification.Comment: 49 pages including appendi

Subset selection in dimension reduction methods

Dimension reduction methods play an important role in multivariate statistical analysis, in particular with high-dimensional data. Linear methods can be seen as a linear mapping from the original feature space to a dimension reduction subspace. The aim is to transform the data so that the essential structure is more easily understood. However, highly correlated variables provide redundant information, whereas some other feature may be irrelevant, and we would like to identify and then discard both of them while pursuing dimension reduction. Here we propose a greedy search algorithm, which avoids the search over all possible subsets, for ranking subsets of variables based on their ability to explain variation in the dimension reduction variates.Dimension reduction methods, Linear mapping, Subset selection, Greedy search

Machine Learning and Integrative Analysis of Biomedical Big Data.

Recent developments in high-throughput technologies have accelerated the accumulation of massive amounts of omics data from multiple sources: genome, epigenome, transcriptome, proteome, metabolome, etc. Traditionally, data from each source (e.g., genome) is analyzed in isolation using statistical and machine learning (ML) methods. Integrative analysis of multi-omics and clinical data is key to new biomedical discoveries and advancements in precision medicine. However, data integration poses new computational challenges as well as exacerbates the ones associated with single-omics studies. Specialized computational approaches are required to effectively and efficiently perform integrative analysis of biomedical data acquired from diverse modalities. In this review, we discuss state-of-the-art ML-based approaches for tackling five specific computational challenges associated with integrative analysis: curse of dimensionality, data heterogeneity, missing data, class imbalance and scalability issues

Independent Process Analysis without A Priori Dimensional Information

Recently, several algorithms have been proposed for independent subspace analysis where hidden variables are i.i.d. processes. We show that these methods can be extended to certain AR, MA, ARMA and ARIMA tasks. Central to our paper is that we introduce a cascade of algorithms, which aims to solve these tasks without previous knowledge about the number and the dimensions of the hidden processes. Our claim is supported by numerical simulations. As a particular application, we search for subspaces of facial components.Comment: 9 pages, 2 figure

Damage identification in structural health monitoring: a brief review from its implementation to the Use of data-driven applications

The damage identification process provides relevant information about the current state of a structure under inspection, and it can be approached from two different points of view. The first approach uses data-driven algorithms, which are usually associated with the collection of data using sensors. Data are subsequently processed and analyzed. The second approach uses models to analyze information about the structure. In the latter case, the overall performance of the approach is associated with the accuracy of the model and the information that is used to define it. Although both approaches are widely used, data-driven algorithms are preferred in most cases because they afford the ability to analyze data acquired from sensors and to provide a real-time solution for decision making; however, these approaches involve high-performance processors due to the high computational cost. As a contribution to the researchers working with data-driven algorithms and applications, this work presents a brief review of data-driven algorithms for damage identification in structural health-monitoring applications. This review covers damage detection, localization, classification, extension, and prognosis, as well as the development of smart structures. The literature is systematically reviewed according to the natural steps of a structural health-monitoring system. This review also includes information on the types of sensors used as well as on the development of data-driven algorithms for damage identification.Peer ReviewedPostprint (published version