# University of Hertfordshire

## Estimating Invariant Principal Components Using Diagonal Regression

Research output: Working paper

### Standard

University of Hertfordshire, 2005. (Business School Working Papers; Vol. UHBS 2005-4).

Research output: Working paper

### Harvard

Leznik, M & Tofallis, C 2005 'Estimating Invariant Principal Components Using Diagonal Regression' Business School Working Papers, vol. UHBS 2005-4, University of Hertfordshire.

### APA

Leznik, M., & Tofallis, C. (2005). Estimating Invariant Principal Components Using Diagonal Regression. (Business School Working Papers; Vol. UHBS 2005-4). University of Hertfordshire.

### Vancouver

Leznik M, Tofallis C. Estimating Invariant Principal Components Using Diagonal Regression. University of Hertfordshire. 2005. (Business School Working Papers).

### Author

Leznik, M. ; Tofallis, C. / Estimating Invariant Principal Components Using Diagonal Regression. University of Hertfordshire, 2005. (Business School Working Papers).

### Bibtex

@techreport{d3379080bda24d76ab8db557c7fabea1,
title = "Estimating Invariant Principal Components Using Diagonal Regression",
abstract = "In this work we apply the method of diagonal regression to derive an alternative version of Principal Component Analysis (PCA). Diagonal regression was introduced by Ragnar Frisch (the first economics Nobel laureate) in his paper Correlation and Scatter in Statistical Variables (1928). The benefits of using diagonal regression in PCA are that it provides components that are scale-invariant (i.e. changing the units of measurement leads to an equivalent result), and which reflect both the correlation structure of the data set, and the variance structure as well. By contrast PCA based on the correlation matrix will only reflect the correlation structure of the data. The problem is formulated as a generalized eigen-analysis and is demonstrated using a numerical example which highlights some desirable properties of what we call Invariant Principal Components Analysis (IPCA).",
author = "M. Leznik and C. Tofallis",
year = "2005",
language = "English",
series = "Business School Working Papers",
publisher = "University of Hertfordshire",
type = "WorkingPaper",
institution = "University of Hertfordshire",

}

### RIS

TY - UNPB

T1 - Estimating Invariant Principal Components Using Diagonal Regression

AU - Leznik, M.

AU - Tofallis, C.

PY - 2005

Y1 - 2005

N2 - In this work we apply the method of diagonal regression to derive an alternative version of Principal Component Analysis (PCA). Diagonal regression was introduced by Ragnar Frisch (the first economics Nobel laureate) in his paper Correlation and Scatter in Statistical Variables (1928). The benefits of using diagonal regression in PCA are that it provides components that are scale-invariant (i.e. changing the units of measurement leads to an equivalent result), and which reflect both the correlation structure of the data set, and the variance structure as well. By contrast PCA based on the correlation matrix will only reflect the correlation structure of the data. The problem is formulated as a generalized eigen-analysis and is demonstrated using a numerical example which highlights some desirable properties of what we call Invariant Principal Components Analysis (IPCA).

AB - In this work we apply the method of diagonal regression to derive an alternative version of Principal Component Analysis (PCA). Diagonal regression was introduced by Ragnar Frisch (the first economics Nobel laureate) in his paper Correlation and Scatter in Statistical Variables (1928). The benefits of using diagonal regression in PCA are that it provides components that are scale-invariant (i.e. changing the units of measurement leads to an equivalent result), and which reflect both the correlation structure of the data set, and the variance structure as well. By contrast PCA based on the correlation matrix will only reflect the correlation structure of the data. The problem is formulated as a generalized eigen-analysis and is demonstrated using a numerical example which highlights some desirable properties of what we call Invariant Principal Components Analysis (IPCA).

M3 - Working paper

T3 - Business School Working Papers

BT - Estimating Invariant Principal Components Using Diagonal Regression

PB - University of Hertfordshire

ER -