Comments on the NIPALS algorithm | RDL Research Database

Abstract

Abstract The Non‐linear Iterative Partial Least Squares (NIPALS) algorithm is used in principal component analysis to decompose a data matrix into score vectors and eigenvectors (loading vectors) plus a residual matrix. NIPALS starts with some guessed starting vector. The principal components obtained by NIPALS depends on the starting vector; the first principal component could not always be computed. Wold has suggested a starting vector for NIPALS, but we have found that even if this starting vector is used, the first principal component cannot be obtained in all cases. The reason why such a situation occurs is explained by the power method. A simple modification of the original NIPALS procedure to avoid getting smaller eigenvalues is presented.

Keywords

Principal component analysisEigenvalues and eigenvectorsMathematicsResidualMatrix (chemical analysis)Simple (philosophy)AlgorithmApplied mathematicsIterative methodPower iterationPrincipal (computer security)Computer scienceStatistics

Affiliated Institutions

Toyohashi University of Technology JP

Related Publications

Super-sparse principal component analyses for high-throughput genomic data

Donghwan Lee , Woojoo Lee , Youngjo Lee +1 more

Abstract Background Principal component analysis (PCA) has gained popularity as a method for the analysis of high-dimensional genomic data. However, it is often difficult to int...

2010 BMC Bioinformatics 49 citations

Cross-Validatory Choice of the Number of Components From a Principal Component Analysis

Henry T. Eastment , W. J. Krzanowski

A method is described for choosing the number of components to retain in a principal component analysis when the aim is dimensionality reduction. The correspondence between prin...

1982 Technometrics 359 citations

The biplot graphic display of matrices with application to principal component analysis

K. R. Gabriel

Any matrix of rank two can be displayed as a biplot which consists of a vector for each row and a vector for each column, chosen so that any element of the matrix is exactly the...

1971 Biometrika 2807 citations

Comments on the power method

Mary Beth Seasholtz , Randy J. Pell , K. E. Gates

Abstract In a recent short communication, Miyashita et al. have commented on the weakness of the NIPALS algorithm (equivalently the power method) for calculating the eigenvalues...

1990 Journal of Chemometrics 12 citations

ON RELATIONSHIPS BETWEEN UNCENTRED AND COLUMN-CENTRED PRINCIPAL COMPONENT ANALYSIS

Jorge Cadima , Ian T. Jolliffe

Principal component analysis (PCA) can be seen as a singular value decomposition (SVD) of a column-centred data matrix. In a number of applications, no pre-processing of the dat...

2009 55 citations

Publication Info

Year: 1990
Type: article
Volume: 4
Issue: 1
Pages: 97-100
Citations: 43
Access: Closed

External Links

View on DOI.org

Social Impact

Altmetric

Comments on the NIPALS algorithm

PlumX Metrics

Social media, news, blog, policy document mentions

Citation Metrics

OpenAlex

Cite This

APA Style

                            
                                
                                    Yoshikatsu Miyashita, 
                                
                                    Toshiaki Itozawa, 
                                
                                    Hiroyuki Katsumi
                                
                                et al.
                            
                            (1990). 
                            Comments on the NIPALS algorithm. 
                            Journal of Chemometrics
                            , 4
                            (1)
                            , 97-100.
                            https://doi.org/10.1002/cem.1180040111
                        

Identifiers

DOI: 10.1002/cem.1180040111