PCA

Principal component analysis

Description

• Center, scale and transpose data matrices
• Calculate covariance and correlation matrices
• Calculate eigenvector decomposition for symmetric matrices (such as covariance and correlation matrices)
• Calculate principal component scores based on an eigenvector matrix and an original data matrix.
• Change orientation of PCA results: Calculate "transposed eigenvectors" under certain circumstances

This program uses MTJ (Matrix Toolkits Java) which tries to utilize Java Native Interface to run machine-optimized code. MTJ tells on runtime whether using natives succeeds or not. It's a LOT faster with natives.

MTJ

Benchmarks of Java matrix libraries

Requirements

Java 8

Input data format

All commands use one or more input matrices. These should be tab-delimited text files. They can be plain text or gzipped. The first row in a data file, as well as the first column on each row, should contain headers. The input matrices are assumed to be ok: No missing values, no unparseable values, all rows of the same length.

Output data format

Output matrices have the same format as input matrices. Output matrices are written in plain text.

Data centering

java -jar PCA.jar center-rows file

Writes:

• file.centered-rows.txt (a tab-delimited matrix with zero mean for every row)

java -jar PCA.jar center-columns file

Writes:

• file.centered-columns.txt (a tab-delimited matrix with zero mean for every column)

Data scaling

java -jar PCA.jar scale-rows file

Writes:

• file.scaled-rows.txt (a tab-delimited matrix with standard deviation one for every row)

java -jar PCA.jar scale-columns file

Writes:

• file.scaled-columns.txt (a tab-delimited matrix with standard deviation one for every column)

Transposition

java -jar PCA.jar transpose file

The first command line argument should be "transpose". The second command line argument should be a path to a tab-delimited text file containing a matrix.

Writes:

• file.transposed.txt (a tab-delimited matrix with the data transposed)

Covariance

java -jar PCA.jar covariance-rows file

Writes:

• file.covariance-rows.txt (a tab-delimited symmetric covariance matrix with covariance calculated for each pair of rows)

java -jar PCA.jar covariance-columns file

Writes:

• file.covariance-columns.txt (a tab-delimited symmetric covariance matrix with covariance calculated for each pair of columns)

Correlation

java -jar PCA.jar correlation-rows file

Writes:

• file.correlation-rows.txt (a tab-delimited symmetric correlation matrix with correlation calculated for each pair of rows)

java -jar PCA.jar correlation-columns file

Writes:

• file.correlation-columns.txt (a tab-delimited symmetric correlation matrix with correlation calculated for each pair of columns)

Eigenvector decomposition

java -jar PCA.jar evd symmetricmatrixfile

Writes:

• file.eigenvectors.txt (a tab-delimited matrix: all right eigenvectors on rows)
• file.eigenvalues.txt (real parts of eigenvalues, one per line)

Principal component scores

java -jar PCA.jar scores eigenvectorfile originalfile

eigenvectorfile should contain eigenvectors on rows. The orientation of originalfile is determined automatically.

Writes:

• originalfile.scores.txt (a tab-delimited matrix: all principal component scores on rows)
• originalfile.cronbachsAlpha.txt (Cronbach's alpha for each component, one per line)

Transformation of orientation: "Transposed eigenvectors" from principal component scores and eigenvalues

java -jar PCA.jar transform scorefile eigenvaluefile

scorefile should contain principal component scores on rows (i.e. each row corresponds to a component). eigenvalues in eigenvaluefile should correspond to the eigenvectors based on which the principal component scores have been calculated.

Note: This operation works in the following scenario:

• There is an original input matrix X
• Each column of X has been centered (zero mean for each column)
• A covariance matrix has been calculated over rows (for pairs of rows) of X
• Eigenvector decomposition has been done for this covariance matrix
• Principal component scores have been calculated based on the resulting eigenvectors

Then, this method calculates "transposed eigenvectors": eigenvectors as they would be if PCA had been done this way:

• Original input matrix Y = X' (X transposed)
• Each column of Y has been centered (zero mean for each column)
• A covariance matrix has been calculated over rows (for pairs of rows) of Y
• Eigenvector decomposition has been done for this covariance matrix

Writes:

• scorefile.transformed.txt (a tab-delimited matrix: all "transposed eigenvectors" on rows)