矩阵的协方差矩阵是对称阵，用公式Cov(X, Y) = E[X * Y] - E[X] E[Y] 计算，其中E[X]和E[Y]是列的平局值，E[X*Y]是样本方差，可以用变换成Gramian矩阵减去E[X] E[Y] 后除以n-1，这样Cov(X, Y) = E[X * Y] - E[X] E[Y] 变换为 G[X*Y] /(m-1) - (m/m-1)E[X] E[Y].Gramian矩阵就是协方差的和。
这个逻辑就是Spark RowMatrix求协方差的逻辑，只不过运算的是RDD
代码如下
public class CovarianceTest { public static void main( String[] args ) { double[][] test = new double[][]{ new double[]{ 1, 2, 3 }, new double[]{ 4, 5, 6 }, new double[]{ 7, 8, 9 } }; double[][] value = caleCovariance( test ); System.out.println( "done" ); } private static double[][] caleCovariance( double[][] dss ) { int count = dss.length; int len = dss[0].length; double[][] retValue = new double[count][len]; double[] means = caleMean( dss ); double[][] G = caleGramian( dss ); int m1 = count - 1; for ( int i = 0; i < len; i++ ) { double alpha = ( (Integer) count ).doubleValue( ) / m1 * means[i]; for ( int j = i; j < len; j++ ) { double Gij = G[i][j] / m1 - alpha * means[j]; retValue[i][j] = Gij; retValue[j][i] = Gij; } } return retValue; } /** * 计算每列的平均值 * * @param dss * @return */ private static double[] caleMean( double[][] dss ) { int count = dss.length; int len = dss[0].length; double[] retValue = new double[len]; for ( int i = 0; i < len; i++ ) { for ( int j = 0; j < count; j++ ) { retValue[i] = retValue[i] + dss[j][i]; } } for ( int i = 0; i < len; i++ ) { retValue[i] = retValue[i] / count; } return retValue; } /** * 计算格拉姆矩阵矩阵 * * @param dss * @return */ private static double[][] caleGramian( double[][] dss ) { int count = dss.length; int len = dss[0].length; double[][] retValue = new double[count][len]; for ( int i = 0; i < count; i++ ) { for ( int j = i; j < len; j++ ) { for ( int k = 0; k < count; k++ ) { retValue[i][j] = retValue[i][j] + dss[k][i] * dss[k][j]; } } } for ( int i = 0; i < count; i++ ) { for ( int j = 0; j < len; j++ ) { if ( retValue[i][j] == 0 ) { retValue[i][j] = retValue[j][i]; } } } return retValue; } }
