# Matrix-Based Introduction to Multivariate Data Analysis

@inproceedings{Adachi2016MatrixBasedIT, title={Matrix-Based Introduction to Multivariate Data Analysis}, author={Kohei Adachi}, year={2016} }

This book enables readers who may not be familiar with matrices to understand a variety of multivariate analysis procedures in matrix forms. Another feature of the book is that it emphasizes what model underlies a procedure and what objective function is optimized for fitting the model to data. The author believes that the matrix-based learning of such models and objective functions is the fastest way to comprehend multivariate data analysis. The text is arranged so that readers can intuitively…

## 44 Citations

### Selected Payback Statistical Contributions to Matrix/Linear Algebra: Some Counterflowing Conceptualizations

- MathematicsStats
- 2022

Matrix/linear algebra continues bestowing benefits on theoretical and applied statistics, a practice it began decades ago (re Fisher used the word matrix in a 1941 publication), through a myriad of…

### A unified representation of simultaneous analysis methods of reduction and clustering

- Computer ScienceJapanese Journal of Statistics and Data Science
- 2018

A simultaneous analysis framework that is composed of several possible reduction methods integrated with clustering methods is proposed that can display objects and variables in a low-dimensional subspace that reflects the cluster structure.

### Permutimin: Factor Rotation to Simple Structure with Permutation of Variables

- EngineeringMultivariate behavioral research
- 2019

A new rotation technique is proposed, which can give a p-variables -factors target matrix of zero and nonzero elements, which stands for the properties to be possessed by the rotated loading matrix, called Permutimin.

### Factor analysis: Latent variable, matrix decomposition, and constrained uniqueness formulations

- EngineeringWIREs Computational Statistics
- 2019

Factor analysis (FA) is a time‐honored multivariate analysis procedure for exploring the factors that underlie observed multiple variables to explain their variations. According to how the factors…

### Clustered Common Factor Exploration in Factor Analysis

- Computer SciencePsychometrika
- 2019

The paper proposes to select the undetermined part of the factor scores, such that the resulting common factor scores have the following feature: the rows (i.e., individuals) of the common factor score matrix are as well classified as possible into few clusters.

### Some inequalities contrasting principal component and factor analyses solutions

- MathematicsJapanese Journal of Statistics and Data Science
- 2019

Principal component analysis (PCA) and factor analysis (FA) are two time-honored dimension reduction methods. In this paper, some inequalities are presented to contrast the parameters’ estimates in…

### Kernel canonical correlation analysis for data combination of multiple-source datasets

- Computer Science
- 2020

A data combination method that combines extension of kernel canonical correlation analysis and statistical matching is proposed that can estimate canonical variables of a common low-dimensional space that can preserve the relationship between covariates and outcome variables.

### Factor Analysis Procedures Revisited from the Comprehensive Model with Unique Factors Decomposed into Specific Factors and Errors

- MathematicsPsychometrika
- 2022

Factor analysis (FA) procedures can be classified into three types (Adachi in WIREs Comput Stat https://onlinelibrary.wiley.com/doi/abs/10.1002/wics.1458, 2019): latent variable FA (LVFA), matrix…

### Tucker-3 decomposition with sparse core array using a penalty function based on Gini-index

- Computer ScienceJapanese Journal of Statistics and Data Science
- 2022

A novel estimation method for Tucker-3 decomposition with a penalty function based on the Gini index, which is a measure of sparsity and variance, is proposed and revealed that the performance is superior to that of the estimation method with existing penalties.

### An Introduction to Kristof’s Theorem for Solving Least-Square Optimization Problems Without Calculus

- MathematicsMultivariate behavioral research
- 2018

The underlying logic of Kristof's Theorem is described in simple terms by reviewing four key mathematical ideas that are used in the theorem's proof and it is shown how Kristof’s Theorem can be used to provide novel derivations to two cognate models from statistics and psychometrics.