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Java library of 2-dimensional matrix algorithms.
/*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see
* See here:
* Statmaster Module 7
*
* @author FracPete (fracpete at waikato dot ac dot nz)
*/
public class PLS1
extends AbstractSingleReponsePLS {
private static final long serialVersionUID = 4899661745515419256L;
/** the regression vector "r-hat" */
protected Matrix m_r_hat;
/** the P matrix */
protected Matrix m_P;
/** the W matrix */
protected Matrix m_W;
/** the b-hat vector */
protected Matrix m_b_hat;
/**
* Resets the member variables.
*/
@Override
protected void reset() {
super.reset();
m_r_hat = null;
m_P = null;
m_W = null;
m_b_hat = null;
}
/**
* Returns the all the available matrices.
*
* @return the names of the matrices
*/
@Override
public String[] getMatrixNames() {
return new String[]{
"r_hat",
"P",
"W",
"b_hat"
};
}
/**
* Returns the matrix with the specified name.
*
* @param name the name of the matrix
* @return the matrix, null if not available
*/
@Override
public Matrix getMatrix(String name) {
switch (name) {
case "RegVector":
return m_r_hat;
case "P":
return m_P;
case "W":
return m_W;
case "b_hat":
return m_b_hat;
default:
return null;
}
}
/**
* Whether the algorithm supports return of loadings.
*
* @return true if supported
* @see #getLoadings()
*/
public boolean hasLoadings() {
return true;
}
/**
* Returns the loadings, if available.
*
* @return the loadings, null if not available
*/
public Matrix getLoadings() {
return getMatrix("P");
}
/**
* Initializes using the provided data.
*
* @param predictors the input data
* @param response the dependent variable(s)
* @throws Exception if analysis fails
* @return null if successful, otherwise error message
*/
protected String doPerformInitialization(Matrix predictors, Matrix response) throws Exception {
Matrix X_trans;
Matrix W, w;
Matrix T, t, t_trans;
Matrix P, p, p_trans;
double b;
Matrix b_hat;
int j;
Matrix tmp;
X_trans = predictors.transpose();
// init
W = new Matrix(predictors.getColumnDimension(), getNumComponents());
P = new Matrix(predictors.getColumnDimension(), getNumComponents());
T = new Matrix(predictors.getRowDimension(), getNumComponents());
b_hat = new Matrix(getNumComponents(), 1);
for (j = 0; j < getNumComponents(); j++) {
// 1. step: wj
w = X_trans.times(response);
MatrixHelper.normalizeVector(w);
MatrixHelper.setColumnVector(w, W, j);
// 2. step: tj
t = predictors.times(w);
t_trans = t.transpose();
MatrixHelper.setColumnVector(t, T, j);
// 3. step: ^bj
b = t_trans.times(response).get(0, 0) / t_trans.times(t).get(0, 0);
b_hat.set(j, 0, b);
// 4. step: pj
p = X_trans.times(t).times(1 / t_trans.times(t).get(0, 0));
p_trans = p.transpose();
MatrixHelper.setColumnVector(p, P, j);
// 5. step: Xj+1
predictors = predictors.minus(t.times(p_trans));
response = response.minus(t.times(b));
}
// W*(P^T*W)^-1
tmp = W.times(((P.transpose()).times(W)).inverse());
// factor = W*(P^T*W)^-1 * b_hat
m_r_hat = tmp.times(b_hat);
// save matrices
m_P = P;
m_W = W;
m_b_hat = b_hat;
return null;
}
/**
* Transforms the data.
*
* @param predictors the input data
* @throws Exception if analysis fails
* @return the transformed data and the predictions
*/
@Override
protected Matrix doTransform(Matrix predictors) throws Exception {
Matrix result;
Matrix T, t;
Matrix x, X;
int i, j;
result = new Matrix(predictors.getRowDimension(), getNumComponents());
for (i = 0; i < predictors.getRowDimension(); i++) {
// work on each row
x = MatrixHelper.rowAsVector(predictors, i);
X = new Matrix(1, getNumComponents());
T = new Matrix(1, getNumComponents());
for (j = 0; j < getNumComponents(); j++) {
MatrixHelper.setColumnVector(x, X, j);
// 1. step: tj = xj * wj
t = x.times(MatrixHelper.getVector(m_W, j));
MatrixHelper.setColumnVector(t, T, j);
// 2. step: xj+1 = xj - tj*pj^T (tj is 1x1 matrix!)
x = x.minus(MatrixHelper.getVector(m_P, j).transpose().times(t.get(0, 0)));
}
MatrixHelper.setRowVector(T, result, i);
}
return result;
}
/**
* Returns whether the algorithm can make predictions.
*
* @return true if can make predictions
*/
public boolean canPredict() {
return true;
}
/**
* Performs predictions on the data.
*
* @param predictors the input data
* @throws Exception if analysis fails
* @return the transformed data and the predictions
*/
@Override
protected Matrix doPerformPredictions(Matrix predictors) throws Exception {
Matrix result;
Matrix T, t;
Matrix x, X;
int i, j;
result = new Matrix(predictors.getRowDimension(), 1);
for (i = 0; i < predictors.getRowDimension(); i++) {
// work on each row
x = MatrixHelper.rowAsVector(predictors, i);
X = new Matrix(1, getNumComponents());
T = new Matrix(1, getNumComponents());
for (j = 0; j < getNumComponents(); j++) {
MatrixHelper.setColumnVector(x, X, j);
// 1. step: tj = xj * wj
t = x.times(MatrixHelper.getVector(m_W, j));
MatrixHelper.setColumnVector(t, T, j);
// 2. step: xj+1 = xj - tj*pj^T (tj is 1x1 matrix!)
x = x.minus(MatrixHelper.getVector(m_P, j).transpose().times(t.get(0, 0)));
}
result.set(i, 0, T.times(m_b_hat).get(0, 0));
}
return result;
}
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