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package de.lmu.ifi.dbs.elki.math.statistics;
/*
This file is part of ELKI:
Environment for Developing KDD-Applications Supported by Index-Structures
Copyright (C) 2011
Ludwig-Maximilians-Universität München
Lehr- und Forschungseinheit für Datenbanksysteme
ELKI Development Team
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Affero 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 Affero General Public License for more details.
You should have received a copy of the GNU Affero General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
import de.lmu.ifi.dbs.elki.math.linearalgebra.Matrix;
import de.lmu.ifi.dbs.elki.math.linearalgebra.Vector;
/**
* A polynomial fit is a specific type of multiple regression. The simple
* regression model (a first-order polynomial) can be trivially extended to
* higher orders.
* <p/>
* The regression model y = b0 + b1*x + b2*x^2 + ... + bp*x^p + e is a system of
* polynomial equations of order p with polynomial coefficients { b0 ... bp}.
* The model can be expressed using data matrix x, target vector y and parameter
* vector ?. The ith row of X and Y will contain the x and y value for the ith
* data sample.
* <p/>
* The variables will be transformed in the following way: x => x1, ..., x^p =>
* xp Then the model can be written as a multiple linear equation model: y = b0
* + b1*x1 + b2*x2 + ... + bp*xp + e
*
* @author Elke Achtert
*/
public class PolynomialRegression extends MultipleLinearRegression {
/**
* The order of the polynom.
*/
public final int p;
/**
* Provides a new polynomial regression model with the specified parameters.
*
* @param y the (n x 1) - vector holding the response values (y1, ..., yn)^T.
* @param x the (n x 1)-vector holding the x-values (x1, ..., xn)^T.
* @param p the order of the polynom.
*/
public PolynomialRegression(Vector y, Vector x, int p) {
super(y, xMatrix(x, p));
this.p = p;
}
private static Matrix xMatrix(Vector x, int p) {
int n = x.getRowDimensionality();
Matrix result = new Matrix(n, p + 1);
for(int i = 0; i < n; i++) {
for(int j = 0; j < p + 1; j++) {
result.set(i, j, Math.pow(x.get(i), j));
}
}
return result;
}
/**
* Returns the adapted coefficient of determination
*
* @return the adapted coefficient of determination
*/
public double adaptedCoefficientOfDetermination() {
int n = getEstimatedResiduals().getRowDimensionality();
return 1.0 - ((n - 1.0) / (n * 1.0 - p)) * (1 - coefficientOfDetermination());
}
/**
* Performs an estimation of y on the specified x value.
*
* @param x the x-value for which y is estimated
* @return the estimation of y
*/
public double estimateY(double x) {
return super.estimateY(xMatrix(new Vector(new double[] { x }), p));
}
}
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