Related papers: Multiple Correspondence Analysis & the Multilogit …

Describing the dimension reduction (DR) techniques by means of probabilistic models has recently been given special attention. Probabilistic models, in addition to a better interpretability of the DR methods, provide a framework for further…

Canonical Correlation Analysis (CCA) is a statistical technique used to extract common information from multiple data sources or views. It has been used in various representation learning problems, such as dimensionality reduction, word…

In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…

Studies often estimate associations between an outcome and multiple variates. For example, studies of diagnostic test accuracy estimate sensitivity and specificity, and studies of predictive and prognostic factors typically estimate…

Classical Biplot Methods allow for the simultaneous representation of individuals (rows) and variables (columns) of a data matrix. For Binary data, Logistic biplots have been recently developed.When data are nominal, linear or even binary…

Robust classification becomes challenging when each class consists of multiple subclasses. Examples include multi-font optical character recognition and automated protein function prediction. In correlation-based nearest-neighbor…

This paper models categorical data with two or multiple responses, focusing on the interactions between responses. We propose an efficient iterative procedure based on sufficient dimension reduction. We study the theoretical guarantees of…

As electronically stored data grow in daily life, obtaining novel and relevant information becomes challenging in text mining. Thus people have sought statistical methods based on term frequency, matrix algebra, or topic modeling for text…

Modern methods for multi-criteria assessment (MCA), such as Data Envelopment Analysis (DEA), Stochastic Frontier Analysis (SFA), and Multiple Criteria Decision-Making (MCDM), are utilized to appraise a collection of Decision-Making Units…

We present a fast algorithm for approximate Canonical Correlation Analysis (CCA). Given a pair of tall-and-thin matrices, the proposed algorithm first employs a randomized dimensionality reduction transform to reduce the size of the input…

Understanding the relationships between different properties of data, such as whether a connectome or genome has information about disease status, is becoming increasingly important in modern biological datasets. While existing approaches…

In this paper, we consider multivariate response regression models with high dimensional predictor variables. One way to model the correlation among the response variables is through the low rank decomposition of the coefficient matrix,…

Since the beginning of the 21st century, the size, breadth, and granularity of data in biology and medicine has grown rapidly. In the example of neuroscience, studies with thousands of subjects are becoming more common, which provide…

Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…

This paper presents an extension of Correspondence Analysis (CA) to tensors through High Order Singular Value Decomposition (HOSVD) from a geometric viewpoint. Correspondence analysis is a well-known tool, developed from principal component…

Recently there has been many works on adaptive subspace filtering in the signal processing literature. Most of them are concerned with tracking the signal subspace spanned by the eigenvectors corresponding to the eigenvalues of the…

Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…

A mediation analysis approach is proposed for multiple exposures, multiple mediators, and a continuous scalar outcome under the linear structural equation modeling framework. It assumes that there exist orthogonal components that…

Numeric tabular datasets are the dominant data format in scientific practice, yet large language models lack native mechanisms for representing numeric datasets in a meaningful way across heterogeneous feature spaces. Existing approaches…

Principal Component Analysis (PCA) is known to be the most widely applied dimensionality reduction approach. A lot of improvements have been done on the traditional PCA, in order to obtain optimal results in the dimensionality reduction of…