算法概述
算法：基于密度的局部离群点检测（lof算法）
输入：样本集合D，正整数K（用于计算第K距离）
输出：各样本点的局部离群点因子
过程：
- 计算每个对象与其他对象的欧几里得距离
- 对欧几里得距离进行排序，计算第k距离以及第K领域
- 计算每个对象的可达密度
- 计算每个对象的局部离群点因子
- 对每个点的局部离群点因子进行排序，输出。
算法Java源码
本算法包括两个类文件，一个是：DataNode，另一个是：OutlierNodeDetect
DataNode的源码
package com.bigdata.ml.outlier;
import java.util.ArrayList;
import java.util.List;
public class DataNode {
private String nodeName; // 样本点名
private double[] dimensioin; // 样本点的维度
private double kDistance; // k-距离
private List<DataNode> kNeighbor = new ArrayList<DataNode>();// k-领域
private double distance; // 到给定点的欧几里得距离
private double reachDensity;// 可达密度
private double reachDis;// 可达距离
private double lof;// 局部离群因子
public DataNode() {
}
public DataNode(String nodeName, double[] dimensioin) {
this.nodeName = nodeName;
this.dimensioin = dimensioin;
}
public String getNodeName() {
return nodeName;
}
public void setNodeName(String nodeName) {
this.nodeName = nodeName;
}
public double[] getDimensioin() {
return dimensioin;
}
public void setDimensioin(double[] dimensioin) {
this.dimensioin = dimensioin;
}
public double getkDistance() {
return kDistance;
}
public void setkDistance(double kDistance) {
this.kDistance = kDistance;
}
public List<DataNode> getkNeighbor() {
return kNeighbor;
}
public void setkNeighbor(List<DataNode> kNeighbor) {
this.kNeighbor = kNeighbor;
}
public double getDistance() {
return distance;
}
public void setDistance(double distance) {
this.distance = distance;
}
public double getReachDensity() {
return reachDensity;
}
public void setReachDensity(double reachDensity) {
this.reachDensity = reachDensity;
}
public double getReachDis() {
return reachDis;
}
public void setReachDis(double reachDis) {
this.reachDis = reachDis;
}
public double getLof() {
return lof;
}
public void setLof(double lof) {
this.lof = lof;
}
}OutlierNodeDetect.java的源码如下：
package com.bigdata.ml.outlier;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;
public class OutlierNodeDetect {
private static int INT_K = 5;//正整数K
// 1.找到给定点与其他点的欧几里得距离
// 2.对欧几里得距离进行排序，找到前5位的点，并同时记下k距离
// 3.计算每个点的可达密度
// 4.计算每个点的局部离群点因子
// 5.对每个点的局部离群点因子进行排序，输出。
public List<DataNode> getOutlierNode(List<DataNode> allNodes) {
List<DataNode> kdAndKnList = getKDAndKN(allNodes);
calReachDis(kdAndKnList);
calReachDensity(kdAndKnList);
calLof(kdAndKnList);
//降序排序
Collections.sort(kdAndKnList, new LofComparator());
return kdAndKnList;
}
private void calLof(List<DataNode> kdAndKnList) {
for (DataNode node : kdAndKnList) {
List<DataNode> tempNodes = node.getkNeighbor();
double sum = 0.0;
for (DataNode tempNode : tempNodes) {
double rd = getRD(tempNode.getNodeName(), kdAndKnList);
sum = rd / node.getReachDensity() + sum;
}
sum = sum / (double) INT_K;
node.setLof(sum);
}
}
private void calReachDensity(List<DataNode> kdAndKnList) {
for (DataNode node : kdAndKnList) {
List<DataNode> tempNodes = node.getkNeighbor();
double sum = 0.0;
double rd = 0.0;
for (DataNode tempNode : tempNodes) {
sum = tempNode.getReachDis() + sum;
}
rd = (double) INT_K / sum;
node.setReachDensity(rd);
}
}
private void calReachDis(List<DataNode> kdAndKnList) {
for (DataNode node : kdAndKnList) {
List<DataNode> tempNodes = node.getkNeighbor();
for (DataNode tempNode : tempNodes) {
//获取tempNode点的k-距离
double kDis = getKDis(tempNode.getNodeName(), kdAndKnList);
//reachdis(p,o)=max{ k-distance(o),d(p,o)}
if (kDis < tempNode.getDistance()) {
tempNode.setReachDis(tempNode.getDistance());
} else {
tempNode.setReachDis(kDis);
}
}
}
}
private double getKDis(String nodeName, List<DataNode> nodeList) {
double kDis = 0;
for (DataNode node : nodeList) {
if (nodeName.trim().equals(node.getNodeName().trim())) {
kDis = node.getkDistance();
break;
}
}
return kDis;
}
private double getRD(String nodeName, List<DataNode> nodeList) {
double kDis = 0;
for (DataNode node : nodeList) {
if (nodeName.trim().equals(node.getNodeName().trim())) {
kDis = node.getReachDensity();
break;
}
}
return kDis;
}
private List<DataNode> getKDAndKN(List<DataNode> allNodes) {
List<DataNode> kdAndKnList = new ArrayList<DataNode>();
for (int i = 0; i < allNodes.size(); i++) {
List<DataNode> tempNodeList = new ArrayList<DataNode>();
DataNode nodeA = new DataNode(allNodes.get(i).getNodeName(), allNodes
.get(i).getDimensioin());
//1,找到给定点NodeA与其他点NodeB的欧几里得距离，并记录在NodeB点的distance变量中。
for (int j = 0; j < allNodes.size(); j++) {
DataNode nodeB = new DataNode(allNodes.get(j).getNodeName(), allNodes
.get(j).getDimensioin());
//计算NodeA与NodeB的欧几里得距离(distance)
double tempDis = getDis(nodeA, nodeB);
nodeB.setDistance(tempDis);
tempNodeList.add(nodeB);
}
//2,对所有NodeB点中的欧几里得距离（distance）进行升序排序。
Collections.sort(tempNodeList, new DistComparator());
for (int k = 1; k < INT_K; k++) {
//3,找到NodeB点的前5位的欧几里得距离点，并记录到到NodeA的kNeighbor变量中。
nodeA.getkNeighbor().add(tempNodeList.get(k));
if (k == INT_K - 1) {
//4,找到NodeB点的第5位距离，并记录到NodeA点的kDistance变量中。
nodeA.setkDistance(tempNodeList.get(k).getDistance());
}
}
kdAndKnList.add(nodeA);
}
return kdAndKnList;
}
private double getDis(DataNode A, DataNode B) {
double dis = 0.0;
double[] dimA = A.getDimensioin();
double[] dimB = B.getDimensioin();
if (dimA.length == dimB.length) {
for (int i = 0; i < dimA.length; i++) {
double temp = Math.pow(dimA[i] - dimB[i], 2);
dis = dis + temp;
}
dis = Math.pow(dis, 0.5);
}
return dis;
}
class DistComparator implements Comparator<DataNode> {
public int compare(DataNode A, DataNode B) {
//return A.getDistance() - B.getDistance() < 0 ? -1 : 1;
if((A.getDistance()-B.getDistance())<0)
return -1;
else if((A.getDistance()-B.getDistance())>0)
return 1;
else return 0;
}
}
class LofComparator implements Comparator<DataNode> {
public int compare(DataNode A, DataNode B) {
//return A.getLof() - B.getLof() < 0 ? 1 : -1;
if((A.getLof()-B.getLof())<0)
return 1;
else if((A.getLof()-B.getLof())>0)
return -1;
else return 0;
}
}
public static void main(String[] args) {
java.text.DecimalFormat df =new java.text.DecimalFormat("#.####");
ArrayList<DataNode> dpoints = new ArrayList<DataNode>();
double[] a = { 2, 3 };
double[] b = { 2, 4 };
double[] c = { 1, 4 };
double[] d = { 1, 3 };
double[] e = { 2, 2 };
double[] f = { 3, 2 };
double[] g = { 8, 7 };
double[] h = { 8, 6 };
double[] i = { 7, 7 };
double[] j = { 7, 6 };
double[] k = { 8, 5 };
double[] l = { 100, 2 };// 孤立点
double[] m = { 8, 20 };
double[] n = { 8, 19 };
double[] o = { 7, 18 };
double[] p = { 7, 17 };
double[] q = { 8, 21 };
dpoints.add(new DataNode("a", a));
dpoints.add(new DataNode("b", b));
dpoints.add(new DataNode("c", c));
dpoints.add(new DataNode("d", d));
dpoints.add(new DataNode("e", e));
dpoints.add(new DataNode("f", f));
dpoints.add(new DataNode("g", g));
dpoints.add(new DataNode("h", h));
dpoints.add(new DataNode("i", i));
dpoints.add(new DataNode("j", j));
dpoints.add(new DataNode("k", k));
dpoints.add(new DataNode("l", l));
dpoints.add(new DataNode("m", m));
dpoints.add(new DataNode("n", n));
dpoints.add(new DataNode("o", o));
dpoints.add(new DataNode("p", p));
dpoints.add(new DataNode("q", q));
OutlierNodeDetect lof = new OutlierNodeDetect();
List<DataNode> nodeList = lof.getOutlierNode(dpoints);
for (DataNode node : nodeList) {
System.out.println(node.getNodeName() + " " + df.format(node.getLof()));
}
}
}测试
测试结果如下：
l 39.3094
n 0.8867
h 0.8626
j 0.8626
f 0.8589
a 0.8498
d 0.8498
m 0.8176
o 0.8176
g 0.7837
b 0.7694
c 0.7694
i 0.7518
k 0.7518
e 0.7485
p 0.7459
q 0.7459
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