net.maizegenetics.stats.PCA.PrinComp Maven / Gradle / Ivy

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package net.maizegenetics.stats.PCA;

import net.maizegenetics.matrixalgebra.Matrix.DoubleMatrix;
import net.maizegenetics.matrixalgebra.Matrix.DoubleMatrixFactory;
import net.maizegenetics.matrixalgebra.decomposition.SingularValueDecomposition;

public class PrinComp {
	public enum PC_TYPE {corr, cov};
	SingularValueDecomposition svd;
	DoubleMatrix datamatrix;
	
	/**
	 * The class uses singular value decomposition to find the eigenvalues, eigenvectors and principal components of either the covariance or correlation matrix 
	 * of the data. If covariance, then the result is the equivalent of finding the eighvalue decomposition of XX'/(n-1) where X is the data matrix with the 
	 * column means subtracted from the columns. If correlation, the column values are also scaled. 
	 * That is, after the mean is subtracted, the values are divided by the standard deviation.
	 * @param data	a matrix of data
	 * @param type	should the analysis use the covariance (cov) or the correlation (corr) matrix of the data
	 */
	public PrinComp(DoubleMatrix data, PC_TYPE type) {
		
		datamatrix = data;
		datamatrix = centerCols(data);
		if (type == PC_TYPE.corr) scaleCenteredMatrix(datamatrix);
		
		double multiplier = 1.0 / Math.sqrt(datamatrix.numberOfRows() - 1);
		svd = datamatrix.scalarMult(multiplier).getSingularValueDecomposition();
	}
	
	/**
	 * @return	a double[] of eigenvalues from the decomposition of either the covariance or correlation matrix of the data
	 */
	public double[] getEigenValues() {
		double[] singularvals = svd.getSingularValues();
		int n = singularvals.length;
		double[] eigenvals = new double[n]; 
		for (int i = 0; i < n; i++) eigenvals[i] = singularvals[i] * singularvals[i];
		return eigenvals;
	}
	
	/**
	 * @return	a column vector of eigenvalues from the decomposition of either the covariance or correlation matrix of the data
	 */
	public DoubleMatrix getEigenValuesAsColumnVector() {
		double[] eigenvals = getEigenValues();
		int n = eigenvals.length;
		return DoubleMatrixFactory.DEFAULT.make(n, 1, eigenvals);
	}
	
	/**
	 * @return a square matrix with diagonal equal to the eigenvalues of the covariance or correlation matrix of the data
	 */
	public DoubleMatrix getEigenvalueMatrix() {
		return DoubleMatrixFactory.DEFAULT.diagonal(getEigenValues());
	}
	
	/**
	 * @return	the eigenvectors from the decomposition of either the covariance or correlation matrix of the data	
	 */
	public DoubleMatrix getEigenVectors() {
		return svd.getV(false);
	}
	
	/**
	 * calculated as data * eigenvectors
	 * @return	all of the principal components
	 */
	public DoubleMatrix getPrincipalComponents() {
		return datamatrix.mult(svd.getV(false));
	}
	
	private DoubleMatrix centerCols(DoubleMatrix data) {
		int nrows = data.numberOfRows();
		int ncols = data.numberOfColumns();
		DoubleMatrix dm = data.copy();
		for (int c = 0; c < ncols; c++) {
			double colmean = dm.columnSum(c) / nrows;
			for (int r = 0; r < nrows; r++) {
				dm.set(r, c, dm.get(r, c) - colmean);
			}
		}
		
		return dm;
	}
	
	private void scaleCenteredMatrix(DoubleMatrix data) {
		int nrows = data.numberOfRows();
		int ncols = data.numberOfColumns();
		for (int c = 0; c < ncols; c++) {
			double sumsq = 0;
			for (int r = 0; r < nrows; r++) {
				double val = data.get(r, c);
				sumsq += val * val;
			}
			double stdDev = Math.sqrt(sumsq/(nrows - 1));
			for (int r = 0; r < nrows; r++) {
				double val = data.get(r, c);
				data.set(r, c, val/stdDev);
			}
		}
	}
}