Related papers: Multiple factor analysis of distributional data
Canonical Correlation Analysis (CCA) and its regularised versions have been widely used in the neuroimaging community to uncover multivariate associations between two data modalities (e.g., brain imaging and behaviour). However, these…
The Bayesian approach to feature extraction, known as factor analysis (FA), has been widely studied in machine learning to obtain a latent representation of the data. An adequate selection of the probabilities and priors of these bayesian…
Detrended fluctuation analysis (DFA) is a scaling analysis method used to quantify long-range power-law correlations in signals. Many physical and biological signals are ``noisy'', heterogeneous and exhibit different types of…
By means of the multifractal analysis (MFA), the expressions of the probability density functions (PDFs) are unified in a compact analytical formula which is valid for various quantities in turbulence. It is shown that the formula can…
Latent variable models can be used to probabilistically "fill-in" missing data entries. The variational autoencoder architecture (Kingma and Welling, 2014; Rezende et al., 2014) includes a "recognition" or "encoder" network that infers the…
Meta-analyses are regarded as the highest level in the hierarchy of evidence, yet standard models traditionally concentrated on estimating the mean effect size, often under restrictive assumptions about the underlying distribution, such as…
The Morse-Smale complex of a function $f$ decomposes the sample space into cells where $f$ is increasing or decreasing. When applied to nonparametric density estimation and regression, it provides a way to represent, visualize, and compare…
We introduce a mathematical formulation of feature-informed data assimilation (FIDA). In FIDA, the information about feature events, such as shock waves, level curves, wavefronts and peak value, in dynamical systems are used for the…
A multifractal analysis (MFA) is performed on three-dimensional grayscale images associated with natural porous structures (soil samples). First, computed tomography (CT) scans are carried out on the samples to generate 3D grayscale images.…
Multimodal Sentiment Analysis (MSA) is an important research area that aims to understand and recognize human sentiment through multiple modalities. The complementary information provided by multimodal fusion promotes better sentiment…
A set of curves or images of similar shape is an increasingly common functional data set collected in the sciences. Principal Component Analysis (PCA) is the most widely used technique to decompose variation in functional data. However, the…
Various methods have been developed independently to study the multifractality of measures in many different contexts. Although they all convey the same intuitive idea of giving a "dimension" to sets where a quantity scales similarly within…
In this paper, we propose a distributed framework for reducing the dimensionality of high-dimensional, large-scale, heterogeneous matrix-variate time series data using a factor model. The data are first partitioned column-wise (or row-wise)…
Compositional data are commonly known as multivariate observations carrying relative information. Even though the case of vector or even two-factorial compositional data (compositional tables) is already well described in the literature,…
Principal component analysis (PCA) is a tool to capture factors that explain variation in data. Across domains, data are now collected across multiple contexts (for example, individuals with different diseases, cells of different types, or…
In Data Science, entities are typically represented by single valued measurements. Symbolic Data Analysis extends this framework to more complex structures, such as intervals and histograms, that express internal variability. We propose an…
We propose a new modeling paradigm for large dimensional aggregates of stochastic systems by Generalized Factor Analysis (GFA) models. These models describe the data as the sum of a flocking plus an uncorrelated idiosyncratic component. The…
Multifractal analysis is a forecasting technique used to study the scaling regularity properties of financial returns, to analyze the long-term memory and predictability of financial markets. In this paper, we propose a novel structural…
Data Warehouses are structures with large amount of data collected from heterogeneous sources to be used in a decision support system. Data Warehouses analysis identifies hidden patterns initially unexpected which analysis requires great…
How to extract useful insights from data is always a challenge, especially if the data is multidimensional. Often, the data can be organized according to certain hierarchical structure that are stemmed either from data collection process or…