Principal Components Matrix Decomposition

Context:
- It can be produced by a PCA System (that solves a PCA task).
Example(s):
- …
Counter-Example(s):
- an LU Decomposition.
- an Orthogonal Decomposition.
- a Singular Value Decomposition.
- a QR Decomposition.
- an SVD Decomposition.
See: Principal Components Analysis.

References

Hyndman, Rob J., and Md Shahid Ullah. “Robust forecasting of mortality and fertility rates: a functional data approach." Computational Statistics & Data Analysis 51, no. 10 (2007).
- QUOTE: … data. Our approach for making the principal components decomposition robust is much more computationally efficient than their method (see Croux's contribution to the discussion of Locantore et al., 1999). Valderrama et al. …

(Landauer & Dumais, 1997) ⇒ Thomas K. Landauer, and Susan T. Dumais. (1997). “A Solution to Plato's Problem: The Latent Semantic Analysis Theory of Acquisition, Induction, and Representation of Knowledge..” In: Psychological review, 104(2). doi:10.1037/0033-295X.104.2.211
- QUOTE: A brief overview the mathematics of SVD is given in the appendix. For those who wish to skip it, we note that SVD is the general method for linear decomposition of a matrix into independent principal components of which factor analysis is the special case for square matrices with the same entities as columns and rows. Factor analysis finds a parsimonious representation of all the intercorrelations between a set of variables in terms of a new set of variables each of which is unrelated to any other but which can be combined to regenerate the original data. SVD does the same thing for an arbitrarily shaped rectangular matrix in which the columns and rows stand for different things, as in the present case one stands for words, the other for contexts in which the words appear. (For those with yet other vocabularies, SVD is a form of Eigenvalue-Eigenvector analysis or principal components decomposition and, in a more general sense, of multi-dimensional scaling. See Carroll & Arabie, in press.).