Marco Picone

Model-based clustering of multivariate skew data with circular components and missing values

Motivated by classification issues that arise in marine studies, we propose a latent-class mixture model for the unsupervised classification of incomplete quadrivariate data with two linear and two circular components. The model integrates bivariate circular densities and bivariate skew normal densities to capture the association between toroidal clusters of bivariate circular observations and planar clusters of bivariate linear observations. Maximum-likelihood estimation of the model is facilitated by an expectation maximization (EM) algorithm that treats unknown class membership and missing values as different sources of incomplete information. The model is exploited on hourly observations of wind speed and direction and wave height and direction to identify a number of sea regimes, which represent specific distributional shapes that the data take under environmental latent conditions.

Maximum likelihood estimation of bivariate circular Hidden Markov models from incomplete data

In this paper, we propose a hidden Markov model for the analysis of the time series of bivariate circular observations, by assuming that the data are sampled from bivariate circular densities, whose parameters are driven by the evolution of a latent Markov chain. The model segments the data by accounting for redundancies due to correlations along time and across variables. A computationally feasible expectation maximization (EM) algorithm is provided for the maximum likelihood estimation of the model from incomplete data, by treating the missing values and the states of the latent chain as two different sources of incomplete information. Importance-sampling methods facilitate the computation of bootstrap standard errors of the estimates. The methodology is illustrated on a bivariate time series of wind and wave directions and compared with popular segmentation models for bivariate circular data, which ignore correlations across variables and/or along time.

A hidden Markov approach to the analysis of space–time environmental data with linear and circular components

The analysis of bivariate space–time series with linear and circular components is complicated by (1) multiple correlations, across time, space and between variables, (2) different supports on which the variables are observed, the real line and the circle, and (3) the periodic nature of circular data. We describe a multivariate hidden Markov model that includes these features of the data within a single framework. The model integrates a circular von Mises Markov field and a Gaussian Markov field, with parameters that evolve in time according to a latent (hidden) Markov chain. It allows to describe the data by means of a finite number of time-varying latent regimes, associated with easily interpretable components of large-scale and small-scale spatial variation. It can be estimated by a computationally feasible expectation–maximization algorithm. In a case study of sea currents in the Northern Adriatic Sea, it provides a parsimonious representation of the sea surface in terms of alternating environmental states.

Dynamic mixtures of factor analyzers to characterize multivariate air pollutant exposures

The assessment of pollution exposure is based on the analysis of a multivariate time series that include the concentrations of several pollutants as well as the measurements of multiple atmospheric variables. It typically requires methods of dimensionality reduction that are capable of identifying potentially dangerous combinations of pollutants and simultaneously segmenting exposure periods according to air quality conditions. When the data are high-dimensional, however, efficient methods of dimensionality reduction are challenging because of the formidable structure of cross-correlations that arise from the dynamic interaction between weather conditions and natural/anthropogenic pollution sources. In order to assess pollution exposure in an urban area while taking the above mentioned difficulties into account, we have developed a class of parsimonious hidden Markov models. In a multivariate time series setting, this approach simultaneously allows for the performance of temporal segmentation and dimensionality reduction. We specifically approximate the distribution of multiple pollutant concentrations by mixtures of factor analysis models, whose parameters evolve according to a latent Markov chain. Covariates are included as predictors of the chain transition probabilities. Parameter constraints on the factorial component of the model are exploited to tune the flexibility of dimensionality reduction. In order to estimate the model parameters efficiently, we have proposed a novel three-step Alternating Expected Conditional Maximization (AECM) algorithm, which is also assessed in a simulation study. In the case study, the proposed methods could (1) describe the exposure to pollution in terms of a few latent regimes, (2) associate these regimes with specific combinations of pollutant concentration levels as well as distinct correlation structures between concentrations, and (3) capture the influence of weather conditions on transitions between regimes. Paper scaricabile da: https://projecteuclid.org/euclid.aoas/1507168842 Mercoledì 31 Gennaio 2018, ore 11:30 Aula 1 Palazzo delle Scienze, Corso Italia 55, Catania

Model-based segmentation of spatial cylindrical data

ABSTRACT A new hidden Markov random field model is proposed for the analysis of cylindrical spatial series, i.e. bivariate spatial series of intensities and angles. It allows us to segment cylindrical spatial series according to a finite number of latent classes that represent the conditional distributions of the data under specific environmental conditions. The model parsimoniously accommodates circular–linear correlation, multimodality, skewness and spatial autocorrelation. A numerically tractable expectation–maximization algorithm is provided to compute parameter estimates by exploiting a mean-field approximation of the complete-data log-likelihood function. These methods are illustrated on a case study of marine currents in the Adriatic sea.

Unsupervised Classification of Multivariate Time Series Data for the Identification of Sea Regimes

Unsupervised classification of marine data is helpful to identify relevant sea regimes, i.e. specific shapes that the distribution of wind and wave data takes under latent environmental conditions. We cluster multivariate marine data by estimating a multivariate hidden Markov model that integrates multivariate von Mises and normal densities. Taking this approach, we obtain a classification that accounts for the mixed (linear and circular) support of the observations, the temporal autocorrelation of the data, and the occurrence of missing values.

A Gaussian–Von Mises Hidden Markov Model for Clustering Multivariate Linear-Circular Data

A multivariate hidden Markov model is proposed for clustering mixed linear and circular time-series data with missing values. The model integrates von Mises and normal densities to describe the distribution that the data take under different latent regimes, with parameters that depend on the evolution of an unobserved Markov chain. Estimation is facilitated by an EM algorithm that treats the states of the latent chain and missing values as different sources of incomplete information. The model is exploited to identify sea regimes from multivariate marine data.

Classification of Multivariate Linear-Circular Data with Nonignorable Missing Values

A latent-class mixture model is proposed for the unsupervised classification of incomplete multivariate data with mixed linear and circular components. The model allows for nonignorable missing values and integrates circular and normal densities to capture the association between toroidal clusters of circular observations and elliptical clusters of linear observations. Maximum likelihood estimation of the model is facilitated by an EM algorithm that treats unknown class membership and missing values as different sources of incomplete information. The model is exploited on incomplete time series of wind speed and direction and wave height and direction to identify a number of sea regimes.