public static void NIPALS(TransposableMatrix X, int numFactors, out TransposableMatrix factors, out TransposableMatrix loads)
{
X.ColumnsToZeroMean();
double original_variance = Math.Sqrt(X.SumOfSquares());
TransposableMatrix l = null;
TransposableMatrix t_prev = null;
TransposableMatrix t = null;
loads = new TransposableMatrix(numFactors, X.Columns);
factors = new TransposableMatrix(X.Rows, numFactors);
for (int nFactor = 0; nFactor < numFactors; nFactor++)
{
// 1. Guess the transposed Vector lT, use first row of X matrix
l = X.Submatrix(1, X.Columns); // l is now a horizontal vector
for (int iter = 0; iter < 500; iter++)
{
// 2. Calculate the new vector t for the factor values
l.Transpose(); // l is now a vertical vector
t = X * l; // t is also a vertical vector
l.Transpose(); // l horizontal again
t.Transpose(); // t is now horizontal
// Compare this with the previous one
if (t_prev != null && t_prev.IsEqualTo(t, 1E-6))
{
break;
}
// 3. Calculate the new loads
l = t * X; // gives a horizontal vector of load (= eigenvalue spectrum)
// normalize the (one) row
l.NormalizeRows(); // normalize the eigenvector spectrum
// 4. Goto step 2 or break after a number of iterations
t_prev = t;
}
// 5. Calculate the residual matrix
t.Transpose(); // t is now vertical again
factors.SetColumn(nFactor, t);
loads.SetRow(nFactor, l);
X = X - t * l; // X is now the residual matrix
} // for all factors
}
