arXiv subjects

Mehdi Maadooliat

Publications and source records attributed to Mehdi Maadooliat.

8 recordsLinked to original sources

arXiv2023

Regularized Multivariate Functional Principal Component Analysis

Multivariate Functional Principal Component Analysis (MFPCA) is a valuable tool for exploring relationships and identifying shared patterns of variation in multivariate functional data. However, controlling the roughness of the extracted Principal Components (PCs) can be challenging. This paper introduces a novel approach called regularized MFPCA (ReMFPCA) to address this issue and enhance the smoothness and interpretability of the multivariate functional PCs. ReMFPCA incorporates a roughness penalty within a penalized framework, using a parameter vector to regulate the smoothness of each functional variable. The proposed method generates smoothed multivariate functional PCs, providing a concise and interpretable representation of the data. Extensive simulations and real data examples demonstrate the effectiveness of ReMFPCA and its superiority over alternative methods. The proposed approach opens new avenues for analyzing and uncovering relationships in complex multivariate functional datasets.

stat.ME↗

arXiv2021

Functional Time Series Forecasting: Functional Singular Spectrum Analysis Approaches

In this paper, we propose two nonparametric methods used in the forecasting of functional time-dependent data, namely functional singular spectrum analysis recurrent forecasting and vector forecasting. Both algorithms utilize the results of functional singular spectrum analysis and past observations in order to predict future data points where recurrent forecasting predicts one function at a time and the vector forecasting makes predictions using functional vectors. We compare our forecasting methods to a gold standard algorithm used in the prediction of functional, time-dependent data by way of simulation and real data and we find our techniques do better for periodic stochastic processes.

stat.ML↗

arXiv2020

Torus Probabilistic Principal Component Analysis

Analyzing data in non-Euclidean spaces, such as bioinformatics, biology, and geology, where variables represent directions or angles, poses unique challenges. This type of data is known as circular data in univariate cases and can be termed spherical or toroidal in multivariate contexts. In this paper, we introduce a novel extension of Probabilistic Principal Component Analysis (PPCA) designed for toroidal (or torus) data, termed Torus Probabilistic PCA (TPPCA). We provide detailed algorithms for implementing TPPCA and demonstrate its applicability to torus data. To assess the efficacy of TPPCA, we perform comparative analyses using a simulation study and three real datasets. Our findings highlight the advantages and limitations of TPPCA in handling torus data. Furthermore, we propose statistical tests based on likelihood ratio statistics to determine the optimal number of components, enhancing the practical utility of TPPCA for real-world applications.

stat.AP↗

arXiv2020

Collective Spectral Density Estimation and Clustering for Spatially-Correlated Data

In this paper, we develop a method for estimating and clustering two-dimensional spectral density functions (2D-SDFs) for spatial data from multiple subregions. We use a common set of adaptive basis functions to explain the similarities among the 2D-SDFs in a low-dimensional space and estimate the basis coefficients by maximizing the Whittle likelihood with two penalties. We apply these penalties to impose the smoothness of the estimated 2D-SDFs and the spatial dependence of the spatially-correlated subregions. The proposed technique provides a score matrix, that is comprised of the estimated coefficients associated with the common set of basis functions representing the 2D-SDFs. {Instead of clustering the estimated SDFs directly, we propose to employ the score matrix for clustering purposes, taking advantage of its low-dimensional property.} In a simulation study, we demonstrate that our proposed method outperforms other competing estimation procedures used for clustering. Finally, to validate the described clustering method, we apply the procedure to soil moisture data from the Mississippi basin to produce homogeneous spatial clusters. We produce animations to dynamically show the estimation procedure, including the estimated 2D-SDFs and the score matrix, which provide an intuitive illustration of the proposed method.

stat.ME↗

arXiv2020

Multivariate Functional Singular Spectrum Analysis Over Different Dimensional Domains

In this work, we develop multivariate functional singular spectrum analysis (MFSSA) over different dimensional domains which is the functional extension of multivariate singular spectrum analysis (MSSA). In the following, we provide all of the necessary theoretical details supporting the work as well as the implementation strategy that contains the recipes needed for the algorithm. We provide a simulation study showcasing the better performance in reconstruction accuracy of a multivariate functional time series (MFTS) signal found using MFSSA as compared to other approaches and we give a real data study showing how MFSSA enriches analysis using intraday temperature curves and remote sensing images of vegetation. MFSSA is available for use through the Rfssa R package.

stat.ME↗

arXiv2019

Functional Singular Spectrum Analysis

In this paper, we introduce a new extension of the Singular Spectrum Analysis (SSA) called functional SSA to analyze functional time series. The new methodology is developed by integrating ideas from functional data analysis and univariate SSA. We explore the advantages of the functional SSA in terms of simulation results and two real data applications. We compare the proposed approach with Multivariate SSA (MSSA) and dynamic Functional Principal Component Analysis (dFPCA). The results suggest that further improvement to MSSA is possible, and the new method provides an attractive alternative to the dFPCA approach that is used for analyzing correlated functions. We implement the proposed technique to an application of remote sensing data and a call center dataset. We have also developed an efficient and user-friendly R package and a shiny web application to allow interactive exploration of the results.

stat.ME↗

arXiv2018

Estimation of Multivariate Wrapped Models for Data in Torus

Multivariate circular observations, i.e. points on a torus are nowadays very common. Multivariate wrapped models are often appropriate to describe data points scattered on p-dimensional torus. However, statistical inference based on this model is quite complicated since each contribution in the log likelihood involve an infinite sum of indices in Z^p where p is the dimension of the problem. To overcome this, two estimates procedures based on Expectation Maximization and Classification Expectation Maximization algorithms are proposed that worked well in moderate dimension size. The performance of the introduced methods are studied by Monte Carlo simulation and illustrated on three real data sets.

stat.CO↗

arXiv2017

Nonparametric collective spectral density estimation with an application to clustering the brain signals

In this paper, we develop a method for the simultaneous estimation of spectral density functions (SDFs) for a collection of stationary time series that share some common features. Due to the similarities among the SDFs, the log-SDF can be represented using a common set of basis functions. The basis shared by the collection of the log-SDFs is estimated as a low-dimensional manifold of a large space spanned by a pre-specified rich basis. A collective estimation approach pools information and borrows strength across the SDFs to achieve better estimation efficiency. Also, each estimated spectral density has a concise representation using the coefficients of the basis expansion, and these coefficients can be used for visualization, clustering, and classification purposes. The Whittle pseudo-maximum likelihood approach is used to fit the model and an alternating blockwise Newton-type algorithm is developed for the computation. A web-based shiny App found at "https://ncsde.shinyapps.io/NCSDE" is developed for visualization, training and learning the SDFs collectively using the proposed technique. Finally, we apply our method to cluster similar brain signals recorded by the electroencephalogram for identifying synchronized brain regions according to their spectral densities.

stat.ME↗