A similar problem on a smaller scale. I can walk through minutes, I could have walked back to save them, but I let them die because it meant a monster would remain gone. What merit is a gamble, a sacrifice, if you stake things that matter nothing to you?
have been doing this for ten years. I admire you for retaining your…” he trailed off.
“Not a word I’m familiar with, Weaver. Faith?”
“I have none left, after ten years. No faith. We are a wretched, petty species, and we have been given power to destroy ourselves with
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: