Factor Analysis — notes

Factor Analysis:

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:
            * used to estimate factor loadings and unique variances


    * [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:
    * Factor Loadings:
    * Interpreting Factor loadings:
    * Communality:
    * Spurious Solutions:
    * Uniqueness of Variable:
    * EigenValues/Characteristic Roots:
    * Extraction Sums of squared loadings:
    * 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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