factor analysis

https://doi.org/10.1351/goldbook.10093

Matrix decomposition of a data matrix (\(\boldsymbol{X}\)) into the product of a scores matrix (\(\boldsymbol{T}\)) and the transpose of the loadings matrix (\(\boldsymbol{P}^{\rm{T}}\)).

Notes:
  1. Hence \(\boldsymbol{X} = \boldsymbol{TP}^{\rm{T}} + \boldsymbol{E}\), where \(\boldsymbol{E}\) is a residual matrix.
  2. Factor analysis methods include common factor analysis (also called ‘factor analysis’), principal component analysis, and multivariate curve resolution.
  3. The number of factors selected in factor analysis is smaller than the rank of the data matrix.
  4. Factor analysis is equivalent to a rotation in data space where the factors form the new axes. This is not necessarily rotation that maintains orthogonality except in the case of PCA.
  5. The residual matrix contains data that are not described by the factor analysis model, and is usually assumed to contain noise.
Source:
PAC, 2016, 88, 407. (Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)) on page 420 [Terms] [Paper]