数据挖掘算法总结-kmeans算法

  数据挖掘算法总结-kmeans算法

 

 

作者：刘伟民

毕业于：中科院计算所

职业：搜索工程师

 

1.  什么是kmeans算法？

k-means 算法接受参数 k ；然后将事先输入的n个数据对象划分为 k个聚类以便使得所获得的聚类满足：同一聚类中的对象相似度较高；而不同聚类中的对象相似度较小。聚类相似度是利用各聚类中对象的均值所获得一个“中心对象”（引力中心）来进行计算的。

2.  算法流程

首先从n个数据对象任意选择 k 个对象作为初始聚类中心；而对于所剩下其它对象，则根据它们与这些聚类中心的相似度（距离），分别将它们分配给与其最相似的（聚类中心所代表的）聚类；然后再计算每个所获新聚类的聚类中心（该聚类中所有对象的均值）；不断重复这一过程直到标准测度函数开始收敛为止。一般都采用均方差作为标准测度函数. k个聚类具有以下特点：各聚类本身尽可能的紧凑，而各聚类之间尽可能的分开。

3.  具体流程

输入：k, data[n];

a)    选择k个初始中心点，例如c[0]=data[0],…c[k-1]=data[k-1];

b)    对于data[0]….data[n], 分别与c[0]…c[k-1]比较，假定与c[i]差值最少，就标记为i;

c)    对于所有标记为i点，重新计算c[i]={ 所有标记为i的data[j]之和}/标记为i的个数；

d)    重复(2)(3),直到所有c[i]值的变化小于给定阈值。

4.  Matlab中有现成的kmeans函数。并且很多开源的软件中都有这个函数。

5.后附kmeans   java代码（代码是网上收集）

---------------JCA.java------------- package org.c4s.algorithm.cluster; import java.util.Vector; /** This class is the entry point for constructing Cluster Analysis objects. Each instance of JCA object is associated with one or more clusters, and a Vector of DataPoint objects. The JCA and DataPoint classes are the only classes available from other packages. @see DataPoint **/ public class JCA { private Cluster[] clusters; private int miter; private Vector mDataPoints = new Vector(); private double mSWCSS; public JCA(int k, int iter, Vector dataPoints) { clusters = new Cluster[k]; for (int i = 0; i < k; i++) { clusters[i] = new Cluster("Cluster" + i); } this.miter = iter; this.mDataPoints = dataPoints; } private void calcSWCSS() { double temp = 0; for (int i = 0; i < clusters.length; i++) { temp = temp + clusters[i].getSumSqr(); } mSWCSS = temp; } public void startAnalysis() { //set Starting centroid positions - Start of Step 1 setInitialCentroids(); int n = 0; //assign DataPoint to clusters loop1: while (true) { for (int l = 0; l < clusters.length; l++) { clusters[l].addDataPoint((DataPoint)mDataPoints.elementAt(n)); n++; if (n >= mDataPoints.size()) break loop1; } } //calculate E for all the clusters calcSWCSS(); //recalculate Cluster centroids - Start of Step 2 for (int i = 0; i < clusters.length; i++) { clusters[i].getCentroid().calcCentroid(); } //recalculate E for all the clusters calcSWCSS(); for (int i = 0; i < miter; i++) { //enter the loop for cluster 1 for (int j = 0; j < clusters.length; j++) { for (int k = 0; k < clusters[j].getNumDataPoints(); k++) { //pick the first element of the first cluster //get the current Euclidean distance double tempEuDt = clusters[j].getDataPoint(k).getCurrentEuDt(); Cluster tempCluster = null; boolean matchFoundFlag = false; //call testEuclidean distance for all clusters for (int l = 0; l < clusters.length; l++) { //if testEuclidean < currentEuclidean then if (tempEuDt > clusters[j].getDataPoint(k).testEuclideanDistance(clusters[l].getCentroid())) { tempEuDt = clusters[j].getDataPoint(k).testEuclideanDistance(clusters[l].getCentroid()); tempCluster = clusters[l]; matchFoundFlag = true; } //if statement - Check whether the Last EuDt is > Present EuDt } //for variable 'l' - Looping between different Clusters for matching a Data Point. //add DataPoint to the cluster and calcSWCSS if (matchFoundFlag) { tempCluster.addDataPoint(clusters[j].getDataPoint(k)); clusters[j].removeDataPoint(clusters[j].getDataPoint(k)); for (int m = 0; m < clusters.length; m++) { clusters[m].getCentroid().calcCentroid(); } //for variable 'm' - Recalculating centroids for all Clusters calcSWCSS(); } //if statement - A Data Point is eligible for transfer between Clusters. } //for variable 'k' - Looping through all Data Points of the current Cluster. }//for variable 'j' - Looping through all the Clusters. }//for variable 'i' - Number of iterations. } public Vector[] getClusterOutput() { Vector v[] = new Vector[clusters.length]; for (int i = 0; i < clusters.length; i++) { v[i] = clusters[i].getDataPoints(); } return v; } private void setInitialCentroids() { //kn = (round((max-min)/k)*n)+min where n is from 0 to (k-1). double cx = 0, cy = 0; for (int n = 1; n <= clusters.length; n++) { cx = (((getMaxXValue() - getMinXValue()) / (clusters.length + 1)) * n) + getMinXValue(); cy = (((getMaxYValue() - getMinYValue()) / (clusters.length + 1)) * n) + getMinYValue(); Centroid c1 = new Centroid(cx, cy); clusters[n - 1].setCentroid(c1); c1.setCluster(clusters[n - 1]); } } private double getMaxXValue() { double temp; temp = ((DataPoint) mDataPoints.elementAt(0)).getX(); for (int i = 0; i < mDataPoints.size(); i++) { DataPoint dp = (DataPoint) mDataPoints.elementAt(i); temp = (dp.getX() > temp) ? dp.getX() : temp; } return temp; } private double getMinXValue() { double temp = 0; temp = ((DataPoint) mDataPoints.elementAt(0)).getX(); for (int i = 0; i < mDataPoints.size(); i++) { DataPoint dp = (DataPoint) mDataPoints.elementAt(i); temp = (dp.getX() < temp) ? dp.getX() : temp; } return temp; } private double getMaxYValue() { double temp = 0; temp = ((DataPoint) mDataPoints.elementAt(0)).getY(); for (int i = 0; i < mDataPoints.size(); i++) { DataPoint dp = (DataPoint) mDataPoints.elementAt(i); temp = (dp.getY() > temp) ? dp.getY() : temp; } return temp; } private double getMinYValue() { double temp = 0; temp = ((DataPoint) mDataPoints.elementAt(0)).getY(); for (int i = 0; i < mDataPoints.size(); i++) { DataPoint dp = (DataPoint) mDataPoints.elementAt(i); temp = (dp.getY() < temp) ? dp.getY() : temp; } return temp; } public int getKValue() { return clusters.length; } public int getIterations() { return miter; } public int getTotalDataPoints() { return mDataPoints.size(); } public double getSWCSS() { return mSWCSS; } public Cluster getCluster(int pos) { return clusters[pos]; } } /*-----------------Cluster.java----------------*/ package org.c4s.algorithm.cluster; import java.util.Vector; /** * This class represents a Cluster in a Cluster Analysis Instance. A Cluster is associated * with one and only one JCA Instance. A Cluster is related to more than one DataPoints and * one centroid. * @author Shyam Sivaraman * @version 1.1 * @see DataPoint * @see Centroid */ class Cluster { private String mName; private Centroid mCentroid; private double mSumSqr; private Vector mDataPoints; public Cluster(String name) { this.mName = name; this.mCentroid = null; //will be set by calling setCentroid() mDataPoints = new Vector(); } public void setCentroid(Centroid c) { mCentroid = c; } public Centroid getCentroid() { return mCentroid; } public void addDataPoint(DataPoint dp) { //called from CAInstance dp.setCluster(this); //initiates a inner call to calcEuclideanDistance() in DP. this.mDataPoints.addElement(dp); calcSumOfSquares(); } public void removeDataPoint(DataPoint dp) { this.mDataPoints.removeElement(dp); calcSumOfSquares(); } public int getNumDataPoints() { return this.mDataPoints.size(); } public DataPoint getDataPoint(int pos) { return (DataPoint) this.mDataPoints.elementAt(pos); } public void calcSumOfSquares() { //called from Centroid int size = this.mDataPoints.size(); double temp = 0; for (int i = 0; i < size; i++) { temp = temp + ((DataPoint) this.mDataPoints.elementAt(i)).getCurrentEuDt(); } this.mSumSqr = temp; } public double getSumSqr() { return this.mSumSqr; } public String getName() { return this.mName; } public Vector getDataPoints() { return this.mDataPoints; } } /*---------------Centroid.java-----------------*/ package org.c4s.algorithm.cluster; /** * This class represents the Centroid for a Cluster. The initial centroid is calculated * using a equation which divides the sample space for each dimension into equal parts * depending upon the value of k. * @author Shyam Sivaraman * @version 1.0 * @see Cluster */ class Centroid { private double mCx, mCy; private Cluster mCluster; public Centroid(double cx, double cy) { this.mCx = cx; this.mCy = cy; } public void calcCentroid() { //only called by CAInstance int numDP = mCluster.getNumDataPoints(); double tempX = 0, tempY = 0; int i; //caluclating the new Centroid for (i = 0; i < numDP; i++) { tempX = tempX + mCluster.getDataPoint(i).getX(); //total for x tempY = tempY + mCluster.getDataPoint(i).getY(); //total for y } this.mCx = tempX / numDP; this.mCy = tempY / numDP; //calculating the new Euclidean Distance for each Data Point tempX = 0; tempY = 0; for (i = 0; i < numDP; i++) { mCluster.getDataPoint(i).calcEuclideanDistance(); } //calculate the new Sum of Squares for the Cluster mCluster.calcSumOfSquares(); } public void setCluster(Cluster c) { this.mCluster = c; } public double getCx() { return mCx; } public double getCy() { return mCy; } public Cluster getCluster() { return mCluster; } } /*----------------DataPoint.java----------------*/ package org.c4s.algorithm.cluster; /** This class represents a candidate for Cluster analysis. A candidate must have a name and two independent variables on the basis of which it is to be clustered. A Data Point must have two variables and a name. A Vector of Data Point object is fed into the constructor of the JCA class. JCA and DataPoint are the only classes which may be available from other packages. @author Shyam Sivaraman @version 1.0 @see JCA @see Cluster */ public class DataPoint { private double mX,mY; private String mObjName; private Cluster mCluster; private double mEuDt; public DataPoint(double x, double y, String name) { this.mX = x; this.mY = y; this.mObjName = name; this.mCluster = null; } public void setCluster(Cluster cluster) { this.mCluster = cluster; calcEuclideanDistance(); } public void calcEuclideanDistance() { //called when DP is added to a cluster or when a Centroid is recalculated. mEuDt = Math.sqrt(Math.pow((mX - mCluster.getCentroid().getCx()), 2) + Math.pow((mY - mCluster.getCentroid().getCy()), 2)); } public double testEuclideanDistance(Centroid c) { return Math.sqrt(Math.pow((mX - c.getCx()), 2) + Math.pow((mY - c.getCy()), 2)); } public double getX() { return mX; } public double getY() { return mY; } public Cluster getCluster() { return mCluster; } public double getCurrentEuDt() { return mEuDt; } public String getObjName() { return mObjName; } } /*-----------------PrgMain.java---------------*/ import org.c4s.algorithm.cluster.DataPoint; import org.c4s.algorithm.cluster.JCA; import java.util.Vector; import java.util.Iterator; /** * Created by IntelliJ IDEA. * User: shyam.s * Date: Apr 18, 2004 * Time: 4:26:06 PM */ public class PrgMain { public static void main (String args[]){ Vector dataPoints = new Vector(); dataPoints.add(new DataPoint(22,21,"p53")); dataPoints.add(new DataPoint(19,20,"bcl2")); dataPoints.add(new DataPoint(18,22,"fas")); dataPoints.add(new DataPoint(1,3,"amylase")); dataPoints.add(new DataPoint(3,2,"maltase")); JCA jca = new JCA(2,1000,dataPoints); jca.startAnalysis(); Vector[] v = jca.getClusterOutput(); for (int i=0; i<v.length; i++){ Vector tempV = v[i]; System.out.println("-----------Cluster"+i+"---------"); Iterator iter = tempV.iterator(); while(iter.hasNext()){ DataPoint dpTemp = (DataPoint)iter.next(); System.out.println(dpTemp.getObjName()+" ["+dpTemp.getX()+","+dpTemp.getY()+"]"); } } } }