Abstract
Principal components analysis (PCA) is probably the most popular descriptive multivariate method for analyzing quantitative data with ratio and interval scale measures. When applying PCA to nominal and ordinal data, the data are processed by a method such as optimal scaling, which nonlinearly transforms nominal and ordinal data into quantitative data. Therefore, PCA with optimal scaling is called nonlinear PCA. Nonlinear PCA reveals nonlinear relationships among variables with different measurement levels and therefore presents a more flexible alternative to ordinary PCA. The alternating least squares algorithm is utilized for nonlinear PCA. The algorithm alternates between optimal scaling for quantifying nominal and ordinal data and ordinary PCA for analyzing optimally scaled data. This article discusses two nonlinear PCA algorithms, namely, PRINCIPALS and PRINCALS.
| Original language | English |
|---|---|
| Pages (from-to) | 456-464 |
| Number of pages | 9 |
| Journal | Wiley Interdisciplinary Reviews: Computational Statistics |
| Volume | 5 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - Nov 2013 |
Fingerprint
Keywords
- Alternating least squares algorithm
- Homogeneity
- Optimal scaling
- Quantification
ASJC Scopus subject areas
- Statistics and Probability
Cite this
Alternating least squares in nonlinear principal components. / Kuroda, Masahiro; Mori, Yuichi; Iizuka, Masaya; Sakakihara, Michio.
In: Wiley Interdisciplinary Reviews: Computational Statistics, Vol. 5, No. 6, 11.2013, p. 456-464.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Alternating least squares in nonlinear principal components
AU - Kuroda, Masahiro
AU - Mori, Yuichi
AU - Iizuka, Masaya
AU - Sakakihara, Michio
PY - 2013/11
Y1 - 2013/11
N2 - Principal components analysis (PCA) is probably the most popular descriptive multivariate method for analyzing quantitative data with ratio and interval scale measures. When applying PCA to nominal and ordinal data, the data are processed by a method such as optimal scaling, which nonlinearly transforms nominal and ordinal data into quantitative data. Therefore, PCA with optimal scaling is called nonlinear PCA. Nonlinear PCA reveals nonlinear relationships among variables with different measurement levels and therefore presents a more flexible alternative to ordinary PCA. The alternating least squares algorithm is utilized for nonlinear PCA. The algorithm alternates between optimal scaling for quantifying nominal and ordinal data and ordinary PCA for analyzing optimally scaled data. This article discusses two nonlinear PCA algorithms, namely, PRINCIPALS and PRINCALS.
AB - Principal components analysis (PCA) is probably the most popular descriptive multivariate method for analyzing quantitative data with ratio and interval scale measures. When applying PCA to nominal and ordinal data, the data are processed by a method such as optimal scaling, which nonlinearly transforms nominal and ordinal data into quantitative data. Therefore, PCA with optimal scaling is called nonlinear PCA. Nonlinear PCA reveals nonlinear relationships among variables with different measurement levels and therefore presents a more flexible alternative to ordinary PCA. The alternating least squares algorithm is utilized for nonlinear PCA. The algorithm alternates between optimal scaling for quantifying nominal and ordinal data and ordinary PCA for analyzing optimally scaled data. This article discusses two nonlinear PCA algorithms, namely, PRINCIPALS and PRINCALS.
KW - Alternating least squares algorithm
KW - Homogeneity
KW - Optimal scaling
KW - Quantification
UR - http://www.scopus.com/inward/record.url?scp=84886748803&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84886748803&partnerID=8YFLogxK
U2 - 10.1002/wics.1279
DO - 10.1002/wics.1279
M3 - Article
VL - 5
SP - 456
EP - 464
JO - Wiley Interdisciplinary Reviews: Computational Statistics
JF - Wiley Interdisciplinary Reviews: Computational Statistics
SN - 1939-5108
IS - 6
ER -