# Principal Component Analysis
Computes the top k principal component coefficients for the m-by-n data matrix X. Rows of X correspond to observations and columns correspond to variables. The coefficient matrix is n-by-k. Each column of the coefficients return matrix contains coefficients for one principal component, and the columns are in descending order of component variance. This function centers the data and uses the singular value decomposition (SVD) algorithm.
## Testing
Tests included:
* All principal components
* Only top k principal components
* Dense SVD tests
* Dense/sparse matrix tests
The results are tested against MATLAB's pca: http://www.mathworks.com/help/stats/pca.html
## Documentation
Added to mllib-guide.md
## Example Usage
Added to examples directory under SparkPCA.scala
Author: Reza Zadeh <rizlar@gmail.com>
Closes#88 from rezazadeh/sparkpca and squashes the following commits:
e298700 [Reza Zadeh] reformat using IDE
3f23271 [Reza Zadeh] documentation and cleanup
b025ab2 [Reza Zadeh] documentation
e2667d4 [Reza Zadeh] assertMatrixApproximatelyEquals
3787bb4 [Reza Zadeh] stylin
c6ecc1f [Reza Zadeh] docs
aa2bbcb [Reza Zadeh] rename sparseToTallSkinnyDense
56975b0 [Reza Zadeh] docs
2df9bde [Reza Zadeh] docs update
8fb0015 [Reza Zadeh] rcond documentation
dbf7797 [Reza Zadeh] correct argument number
a9f1f62 [Reza Zadeh] documentation
4ce6caa [Reza Zadeh] style changes
9a56a02 [Reza Zadeh] use rcond relative to larget svalue
120f796 [Reza Zadeh] housekeeping
156ff78 [Reza Zadeh] string comprehension
2e1cf43 [Reza Zadeh] rename rcond
ea223a6 [Reza Zadeh] many style changes
f4002d7 [Reza Zadeh] more docs
bd53c7a [Reza Zadeh] proper accumulator
a8b5ecf [Reza Zadeh] Don't use for loops
0dc7980 [Reza Zadeh] filter zeros in sparse
6115610 [Reza Zadeh] More documentation
36d51e8 [Reza Zadeh] use JBLAS for UVS^-1 computation
bc4599f [Reza Zadeh] configurable rcond
86f7515 [Reza Zadeh] compute per parition, use while
09726b3 [Reza Zadeh] more style changes
4195e69 [Reza Zadeh] private, accumulator
17002be [Reza Zadeh] style changes
4ba7471 [Reza Zadeh] style change
f4982e6 [Reza Zadeh] Use dense matrix in example
2828d28 [Reza Zadeh] optimizations: normalize once, use inplace ops
72c9fa1 [Reza Zadeh] rename DenseMatrix to TallSkinnyDenseMatrix, lean
f807be9 [Reza Zadeh] fix typo
2d7ccde [Reza Zadeh] Array interface for dense svd and pca
cd290fa [Reza Zadeh] provide RDD[Array[Double]] support
398d123 [Reza Zadeh] style change
55abbfa [Reza Zadeh] docs fix
ef29644 [Reza Zadeh] bad chnage undo
472566e [Reza Zadeh] all files from old pr
555168f [Reza Zadeh] initial files
tex formulas in the documentation
using mathjax.
and spliting the MLlib documentation by techniques
see jira
https://spark-project.atlassian.net/browse/MLLIB-19
and
https://github.com/shivaram/spark/compare/mathjax
Author: Martin Jaggi <m.jaggi@gmail.com>
== Merge branch commits ==
commit 0364bfabbfc347f917216057a20c39b631842481
Author: Martin Jaggi <m.jaggi@gmail.com>
Date: Fri Feb 7 03:19:38 2014 +0100
minor polishing, as suggested by @pwendell
commit dcd2142c164b2f602bf472bb152ad55bae82d31a
Author: Martin Jaggi <m.jaggi@gmail.com>
Date: Thu Feb 6 18:04:26 2014 +0100
enabling inline latex formulas with $.$
same mathjax configuration as used in math.stackexchange.com
sample usage in the linear algebra (SVD) documentation
commit bbafafd2b497a5acaa03a140bb9de1fbb7d67ffa
Author: Martin Jaggi <m.jaggi@gmail.com>
Date: Thu Feb 6 17:31:29 2014 +0100
split MLlib documentation by techniques
and linked from the main mllib-guide.md site
commit d1c5212b93c67436543c2d8ddbbf610fdf0a26eb
Author: Martin Jaggi <m.jaggi@gmail.com>
Date: Thu Feb 6 16:59:43 2014 +0100
enable mathjax formula in the .md documentation files
code by @shivaram
commit d73948db0d9bc36296054e79fec5b1a657b4eab4
Author: Martin Jaggi <m.jaggi@gmail.com>
Date: Thu Feb 6 16:57:23 2014 +0100
minor update on how to compile the documentation
