pcacorr.java

PCA in (learning machine) java.

import java.io.*;
import java.util.*;
import java.text.*;
import Jama.*;

/**
 * PCAcorr - Principal Components Analysis on correlations <p>
 * Jama Matrix class package, "JAMA: A Java Matrix Package" is used.<br>
 * See: http://math.nist.gov/javanumerics/jama <p>
 * Example of use: <p>
 * <tt> javac PCAcorr.java </tt> <br>
 * <tt> java PCAcorr <a href="../iris.dat">iris.dat</a> > 
 * <a href="pcaoutput.txt">pcaoutput.txt</a></tt> <p>
 * Format of input data set: 
 * <ul>
 * <li> integer row and column dimensions, 
 * <li> followed by floating values 
 * <li> which are read row-wise.
 * </ul>
 * Outputs produced:
 * <ul>
 * <li> Echo of input file name, input dimensions, sample of data
 * <li> Variable means and standard deviations
 * <li> Correlation matrix to be diagonalized
 * <li> Eigenvectors
 * <li> Eigenvalues and as cumulative percentages
 * <li> Row projections in new principal component space
 * <li> Column projections in new principal component space
 * </ul>
 * Version: 2002 Aug. 15 <br>
 * Author: F. Murtagh, [e-mail]
 * @version 2002 Aug 15
 * @author F. Murtagh, [e-mail]
 */
public class PCAcorr{

public static void main (String argv[])
{
  PrintStream out = System.out;

  try{

     //-------------------------------------------------------------------
     if (argv.length == 0) {
        System.out.println(" Syntax: java PCAcorr infile.dat ");
        System.out.println(" Input file format: ");
        System.out.println(" Line 1: integer no. rows, no. cols.");
        System.out.println(" Successive lines: matrix values, floating");
        System.out.println(" Read in row-wise");
        System.exit (1);
     }
     String filname = argv[0]; 
     System.out.println (" Input file name: " + filname);

     // Open the matrix file
     FileInputStream is  = new FileInputStream(filname);
     BufferedReader  bis = new BufferedReader(new InputStreamReader(is));
     StreamTokenizer st  = new StreamTokenizer(bis);

     // Row and column sizes, read in first
     st.nextToken();  int n = (int)st.nval;
     st.nextToken();  int m = (int)st.nval;

     System.out.println(" No. of rows, n = " + n);
     System.out.println(" No. of cols, m = " + m);
     
     // Input array, values to be read in successively, float
     double[][] indat = new double[n][m]; 
     double inval;

     // New read in input array values, successively
     System.out.println
        (" Input data sample follows as a check, first 4 values.");
     for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
             st.nextToken();
             inval = (double)st.nval;
             indat[i][j] = inval;
             if (i < 2 && j < 2) {
                System.out.println(" value = " + inval);
             }
        }
     }  
     System.out.println();

     //-------------------------------------------------------------------
     // Data preprocessing - standardization and determining correlations 
     double[][] indatstd = Standardize(n, m, indat);
     // use Jama matrix class  
     Matrix X = new Matrix(indatstd);

     // Sums of squares and cross-products matrix
     Matrix Xprime = X.transpose();
     Matrix SSCP   = Xprime.times(X);
     // Note the following:
     // - with no preprocessing of the input data, we have an SSCP matrix
     // - with centering of columns (i.e. each col. has col. mean 
     //   [vector in row-space] subtracted) we have variances/covariances
     // - with centering and reduction to unit variance [i.e. centered
     //   cols. are divided by std. dev.] we have correlations
     // Note: the current version supports correlations only

     // Print out SSCP matrix 
     // Parameters: floating value width, and no. of decimal places
     // Comment out this line for large data sets, and/or diff. precision
     System.out.println();
     System.out.println 
            (" SSCP or sums-of-squares and cross-products matrix:");
     System.out.println (" (Note: correlations in this implementation)");
     SSCP.print(6,2);

     //-------------------------------------------------------------------
     // Eigen decomposition
     EigenvalueDecomposition evaldec = SSCP.eig();
     Matrix evecs = evaldec.getV();
     double[] evals = evaldec.getRealEigenvalues();

     // print out eigenvectors
     System.out.println (" Eigenvectors (leftmost col <--> largest eval):");
     // evecs contains the cols. ordered right to left
     // Evecs is the more natural order with cols. ordered left to right
     // So to repeat: leftmost col. of Evecs is assoc with largest Evals
     // Evals and Evecs ordered from left to right

     double tot = 0.0; 
     for (int j = 0; j < evals.length; j++)  {
         tot += evals[j]; 
     }

     // reverse order of evals into Evals
     double[] Evals = new double[m];
     for (int j = 0; j < m; j++) {
         Evals[j] = evals[m - j - 1];
     }
     // reverse order of Matrix evecs into Matrix Evecs
     double[][] tempold = evecs.getArray();
     double[][] tempnew = new double[m][m]; 
     for (int j1 = 0; j1 < m; j1++) {
         for (int j2 = 0; j2 < m; j2++) {
             tempnew[j1][j2] = tempold[j1][m - j2 - 1];
	 }
     }
     Matrix Evecs = new Matrix(tempnew);
     Evecs.print(10,4);

     System.out.println();
     System.out.println (" Eigenvalues and as cumulative percentages:"); 
     double runningtotal = 0.0;
     double[] percentevals = new double[m];
     for (int j = 0; j < Evals.length; j++) {
         percentevals[j] = runningtotal + 100.0*Evals[j]/tot;
         runningtotal    = percentevals[j];
     }
     printVect(Evals, 4, 10);
     printVect(percentevals, 4, 10);

     //-------------------------------------------------------------------
     // Projections - row, and col
     // Row projections in new space, X U  Dims: (n x m) x (m x m)
     System.out.println();
     System.out.println(" Row projections in new principal component space:");
     Matrix rowproj = X.times(Evecs);
     rowproj.print(10,4);

     // Col projections (X'X) U    (4x4) x4  And col-wise div. by sqrt(evals)
     Matrix colproj = SSCP.times(Evecs);
   
     // We need to leave colproj Matrix class and instead use double array
     double[][] ynew = colproj.getArray();
     for (int j1 = 0; j1 < m; j1++) {
         for (int j2 = 0; j2 < m; j2++) {
             if (Evals[j2] > 0.00005) {
                 ynew[j1][j2] = ynew[j1][j2]/Math.sqrt(Evals[j2]); }
             if (Evals[j2] <= 0.00005) {
                 ynew[j1][j2] = 0.0; }
         }
     }
     System.out.println ();
     System.out.println (" Column projections in new princ. comp. space.");
     printMatrix(m, m, ynew, 4, 8);

     //-------------------------------------------------------------------
     // That's it.

  }

  catch (IOException e) {
     out.println("error: " + e);
     System.exit(1);
  }

} // end of main

    //-------------------------------------------------------------------  
    // Little method for helping in output formating  
    public static String getSpaces(int n) {

    StringBuffer sb = new StringBuffer(n);
    for (int i = 0; i < n; i++) sb.append(' ');
    return sb.toString();
    } // getSpaces
   
    //-------------------------------------------------------------------
    /**
     * Method for printing a matrix  <br>
     * Based on ER Harold, "Java I/O", O'Reilly, around p. 473.
     * @param n1 row dimension of matrix
     * @param n2 column dimension of matrix
     * @param m input matrix values 
     * @param d display precision, number of decimal places
     * @param w display precision, total width of floating value
     */
    public static void printMatrix(int n1, int n2, double[][] m, int d, int w)
    {
	// Some definitions for handling output formating
      NumberFormat myFormat = NumberFormat.getNumberInstance();
      FieldPosition fp = new FieldPosition(NumberFormat.INTEGER_FIELD);
      myFormat.setMaximumIntegerDigits(d);
      myFormat.setMaximumFractionDigits(d);
      myFormat.setMinimumFractionDigits(d);
      for (int i=0; i<n1; i++)
	  {
	      // Print each row, elements separated by spaces
              for (int j=0; j<n2; j++)
		  // Following unfortunately doesn't format at all
		  //                  System.out.print(m[i][j] + "  ");
                  {
                  String valString = myFormat.format(
                       m[i][j], new StringBuffer(), fp).toString();
                  valString = getSpaces(w - fp.getEndIndex()) + valString;
                  System.out.print(valString);
                  }
              // Start a new line at the end of a row
              System.out.println();
          }
      // Leave a gap after the entire matrix
      System.out.println();
    } // printMatrix

    //-------------------------------------------------------------------
    /**
     * Method printVect for printing a vector <br>
     * Based on ER Harold, "Java I/O", O'Reilly, around p. 473.
     * @param m input vector of length m.length
     * @param d display precision, number of decimal places
     * @param w display precision, total width of floating value
     */
    public static void printVect(double[] m, int d, int w)
    {
	// Some definitions for handling output formating
      NumberFormat myFormat = NumberFormat.getNumberInstance();
      FieldPosition fp = new FieldPosition(NumberFormat.INTEGER_FIELD);
      myFormat.setMaximumIntegerDigits(d);
      myFormat.setMaximumFractionDigits(d);
      myFormat.setMinimumFractionDigits(d);
      int len = m.length;
      for (int i=0; i<len; i++)
	  {
	      // Following would be nice, but doesn't format adequately
	      //                  System.out.print(m[i] + "  ");
             String valString = myFormat.format(
                   m[i], new StringBuffer(), fp).toString();
             valString = getSpaces(w - fp.getEndIndex()) + valString;
                   System.out.print(valString);
          }
          // Start a new line at the row end
          System.out.println();
      // Leave a gap after the entire vector
      System.out.println();
    } // printVect

    //-------------------------------------------------------------------
    /**
     * Method for standardizing the input data <p>
     * Note the formalas used (since these vary between implementations):<br>
     * reduction: (vect - meanvect)/sqrt(nrow)*colstdev <br>
     * colstdev:  sum_cols ((vect - meanvect)^2/nrow) <br>
     * if colstdev is close to 0, then set it to 1.
     * @param nrow number of rows in input matrix
     * @param ncol number of columns in input matrix
     * @param A input matrix values
     */
    public static double[][] Standardize(int nrow, int ncol, double[][] A)
    {
    double[] colmeans = new double[ncol];
    double[] colstdevs = new double[ncol];
    // Adat will contain the standardized data and will be returned
    double[][] Adat = new double[nrow][ncol];
    double[] tempcol = new double[nrow];
    double tot; 

    // Determine means and standard deviations of variables/columns
    for (int j=0; j<ncol; j++)
        {
         tot = 0.0;
         for (int i=0; i<nrow; i++)
             {
                tempcol[i] = A[i][j];
                tot += tempcol[i];
             }

	 // For this col, det mean
         colmeans[j] = tot/(double)nrow;
         for (int i=0; i<nrow; i++) {
                colstdevs[j] += Math.pow(tempcol[i]-colmeans[j], 2.0);
             }
             colstdevs[j] = Math.sqrt(colstdevs[j]/((double)nrow));
             if (colstdevs[j] < 0.0001) { colstdevs[j] = 1.0; }
	}

        System.out.println(" Variable means:");
        printVect(colmeans, 4, 8);
        System.out.println(" Variable standard deviations:");
        printVect(colstdevs, 4, 8);

	// Now ceter to zero mean, and reduce to unit standard deviation
    for (int j=0; j<ncol; j++)
        {
         for (int i=0; i<nrow; i++)
             {
               Adat[i][j] = (A[i][j] - colmeans[j])/
                 (Math.sqrt((double)nrow)*colstdevs[j]);
             }
        }
    return Adat;
    } // Standardize
    //-------------------------------------------------------------------




}  // PCAcorr