# Factor Analysis — notes

## Multiple Classifications:

``````Aka [Dimensionality reduction](https://en.wikipedia.org/wiki/Dimensionality_reduction)
Aka
[Dimensionality Estimation] (http://disco.ethz.ch/lectures/fs11/seminar/paper/samuel-1.pdf)
###  Methods:
* [Intrinsic Dimension Estimation](https://www.stat.berkeley.edu/~bickel/mldim.pdf)
or (http://www.sciencedirect.com/science/article/pii/S0020025515006179)
* [PCA](http://www.music.mcgill.ca/~ich/classes/mumt611_07/classifiers/lda_theory.pdf)
* [Kernel-PCA](http://papers.nips.cc/paper/1491-kernel-pca-and-de-noising-in-feature-spaces.pdf)
* [Graph-based kernel PCA](http://ieeexplore.ieee.org/abstract/document/1261097/)
* [Linear Discriminant Analysis](http://www.music.mcgill.ca/~ich/classes/mumt611_07/classifiers/lda_theory.pdfhttp://www.music.mcgill.ca/~ich/classes/mumt611_07/classifiers/lda_theory.pdf)
* [Generalized Discriminant Analysis](http://www.jmlr.org/papers/v6/ye05a.html)
* [Manifold Learning] (http://scikit-learn.org/stable/modules/manifold.html)
### Factor Analysis(based on goal):

*  [Exploratory Factor
Analysis](https://en.wikipedia.org/wiki/Exploratory_factor_analysis):
#### Fitting Procedures:

* [Confirmatory Factor
Analysis](https://en.wikipedia.org/wiki/Confirmatory_factor_analysis):

### Types of factoring:
* [Principal Component
Analysis](https://en.wikipedia.org/wiki/Principal_component_analysis):

* Canonical Factor Analysis: aka Rao's canonical factoring, uses principal axis
method, unaffected by arbitrary rescaling, highest canonical correlation measure.

* Common Factor Analysis: aka principal factor analysis, least no. of variables
accounting for the common variance of a set of variables.

* Image Factoring: based on correlation matrix of predicted variables, where each
prediction is done via [multiple
regression](https://en.wikipedia.org/wiki/Multiple_regression)

* Alpha Factoring: based on maximizing reliability of factors, assumes random
sampling of variables from universe of vars, (other methods assume fixed
variables)

* Factor Regression Model: Combinatorial model of factor and regression models,
aka hybrid factor model with partially known factors

### Terminology:
* Communality:
* Spurious Solutions:
* Uniqueness of Variable:
* EigenValues/Characteristic Roots:
* Factor Scores:

### Criteria for number of Factors:
* Horn's Parallel Analysis:
* Velicer's MAP test:
older methods
* Kaiser Criterion:
* Scree plot:
* Variance explained criteria:

### Rotation Methods:
* Varimax Rotation:
* Quartimax Rotation:
* Equimax Rotation:
* Direct oblimin Rotation:
* Promax Rotation:
``````

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