/*******************************************************************************
* Copyright (c) 2010 Haifeng Li
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*******************************************************************************/
package smile.plot;
import java.awt.Color;
/**
* A dendrogram is a tree diagram frequently used to illustrate the arrangement
* of the clusters produced by hierarchical clustering.
*
* @author Haifeng Li
*/
public class Dendrogram extends Plot {
/**
* The one end points of lines.
*/
private double[][] p1;
/**
* The other end points of lines.
*/
private double[][] p2;
/**
* The height of tree.
*/
private double height;
/**
* Constructor.
* @param merge an n-1 by 2 matrix of which row i describes the merging of clusters at
* step i of the clustering. If an element j in the row is less than n, then
* observation j was merged at this stage. If j ≥ n then the merge
* was with the cluster formed at the (earlier) stage j-n of the algorithm.
* @param height a set of n-1 non-decreasing real values, which are the clustering height,
* i.e., the value of the criterion associated with the clustering method
* for the particular agglomeration.
*/
public Dendrogram(int[][] merge, double[] height) {
this(merge, height, Color.BLACK);
}
/**
* Constructor.
* @param merge an n-1 by 2 matrix of which row i describes the merging of clusters at
* step i of the clustering. If an element j in the row is less than n, then
* observation j was merged at this stage. If j ≥ n then the merge
* was with the cluster formed at the (earlier) stage j-n of the algorithm.
* @param height a set of n-1 non-decreasing real values, which are the clustering height,
* i.e., the value of the criterion associated with the clustering method
* for the particular agglomeration.
* @param color the color for rendering the plot.
*/
public Dendrogram(int[][] merge, double[] height, Color color) {
super(color);
int n = merge.length + 1;
int[] order = new int[n];
dfs(merge, n - 2, order, 0);
double[][] pos = new double[2 * n - 1][2];
for (int i = 0; i < n; i++) {
pos[order[i]][0] = i;
pos[order[i]][1] = 0;
}
for (int i = 0; i < merge.length; i++) {
pos[n + i][0] = (pos[merge[i][0]][0] + pos[merge[i][1]][0]) / 2;
pos[n + i][1] = Math.max(pos[merge[i][0]][1], pos[merge[i][1]][1]) + height[i];
}
p1 = new double[3 * n - 3][2];
p2 = new double[3 * n - 3][2];
for (int i = 0; i < merge.length; i++) {
p1[3 * i][0] = pos[merge[i][0]][0];
p1[3 * i][1] = pos[merge[i][0]][1];
p2[3 * i][0] = pos[merge[i][0]][0];
p2[3 * i][1] = pos[n + i][1];
p1[3 * i + 1][0] = pos[merge[i][1]][0];
p1[3 * i + 1][1] = pos[merge[i][1]][1];
p2[3 * i + 1][0] = pos[merge[i][1]][0];
p2[3 * i + 1][1] = pos[n + i][1];
p1[3 * i + 2][0] = pos[merge[i][0]][0];
p1[3 * i + 2][1] = pos[n + i][1];
p2[3 * i + 2][0] = pos[merge[i][1]][0];
p2[3 * i + 2][1] = pos[n + i][1];
}
this.height = pos[2 * n - 2][1];
}
/**
* Returns the height of tree.
*/
public double getHeight() {
return height;
}
/**
* DFS the tree to find the order of leafs to avoid the cross of lines in
* the plot.
*/
private int dfs(int[][] merge, int index, int[] order, int i) {
int n = merge.length + 1;
if (merge[index][0] > merge.length) {
i = dfs(merge, merge[index][0] - n, order, i);
} else {
order[i++] = merge[index][0];
}
if (merge[index][1] > merge.length) {
i = dfs(merge, merge[index][1] - n, order, i);
} else {
order[i++] = merge[index][1];
}
return i;
}
@Override
public void paint(Graphics g) {
Color c = g.getColor();
g.setColor(getColor());
for (int i = 0; i < p1.length; i++) {
g.drawLine(p1[i], p2[i]);
}
g.setColor(c);
}
/**
* Create a dendrogram plot.
* @param merge an n-1 by 2 matrix of which row i describes the merging of clusters at
* step i of the clustering. If an element j in the row is less than n, then
* observation j was merged at this stage. If j ≥ n then the merge
* was with the cluster formed at the (earlier) stage j-n of the algorithm.
* @param height a set of n-1 non-decreasing real values, which are the clustering height,
* i.e., the value of the criterion associated with the clustering method
* for the particular agglomeration.
*/
public static PlotCanvas plot(int[][] merge, double[] height) {
int n = merge.length + 1;
Dendrogram dendrogram = new Dendrogram(merge, height);
double[] lowerBound = {-n / 100, 0};
double[] upperBound = {n + n / 100, 1.01 * dendrogram.getHeight()};
PlotCanvas canvas = new PlotCanvas(lowerBound, upperBound, false);
canvas.getAxis(0).setGridVisible(false);
canvas.getAxis(0).setLabelVisible(false);
canvas.add(dendrogram);
return canvas;
}
/**
* Create a dendrogram plot.
* @param id the id of the plot.
* @param merge an n-1 by 2 matrix of which row i describes the merging of clusters at
* step i of the clustering. If an element j in the row is less than n, then
* observation j was merged at this stage. If j ≥ n then the merge
* was with the cluster formed at the (earlier) stage j-n of the algorithm.
* @param height a set of n-1 non-decreasing real values, which are the clustering height,
* i.e., the value of the criterion associated with the clustering method
* for the particular agglomeration.
*/
public static PlotCanvas plot(String id, int[][] merge, double[] height) {
int n = merge.length + 1;
Dendrogram dendrogram = new Dendrogram(merge, height);
double[] lowerBound = {-n / 100, 0};
double[] upperBound = {n + n / 100, 1.01 * dendrogram.getHeight()};
PlotCanvas canvas = new PlotCanvas(lowerBound, upperBound, false);
canvas.getAxis(0).setGridVisible(false);
canvas.getAxis(0).setLabelVisible(false);
dendrogram.setID(id);
canvas.add(dendrogram);
return canvas;
}
}
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