前言：
众所周知，关联规则挖掘是数据挖掘中重要的一部分，如著名的啤酒和尿布的问题。今天要学习的是经典的关联规则挖掘算法——Apriori算法
一、算法的基本原理
由k项频繁集去导出k+1项频繁集。
二、算法流程
1.扫描事务数据库，找出1项集，并根据最小支持度计数，剪枝得出频繁1项集。k=1.
2.由频繁k项集进行连接步操作，形成候选的k+1项集，并扫描数据库，得出每一项的支持度计数，并根据最小支持度计数，剪枝得到频繁k+1项集。
迭代的进行第2步直到频繁k项集是空的。
3.由频繁项集构造关联规则。先列出所有可能的关联规则，然后计算相应的置信度，最终筛选出满足最小置信度的强关联规则。
三、算法实现
测试数据集：data.txt
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871, 5, 36, 41, 42 872, 5, 22, 31, 37, 47 873, 5, 7, 20 874, 4, 14, 16, 37, 44 875, 3, 18, 35 876, 8, 21, 29, 33, 42 877, 5, 14, 18 878, 27 879, 14, 20, 22, 24 880, 1, 3, 14, 31, 44, 45, 47 881, 29, 36, 41, 46 882, 16, 32, 45 883, 23, 24, 40, 41, 43 884, 7, 11, 19, 38, 42, 43, 47 885, 0, 27, 28, 32 886, 0, 2, 28, 41, 46 887, 23, 24, 40, 41, 43 888, 3, 18, 35 889, 14, 31 890, 8, 14, 44 891, 3, 14, 18, 22, 35 892, 1, 3, 30 893, 6, 12, 41, 44 894, 11, 30, 43 895, 7, 15, 49 896, 0, 2, 46 897, 1, 17, 38, 43 898, 25, 36 899, 7, 9, 27 900, 5, 13, 22 901, 12, 31, 36, 48 902, 26, 39, 43 903, 12, 26, 38 904, 1, 16, 20, 40 905, 23, 24, 40, 41, 43 906, 6, 28, 37, 38, 49 907, 14, 16, 17, 18, 26, 31 908, 37, 44 909, 11, 30 910, 22, 28, 41, 48 911, 12, 31, 36, 48 912, 4, 5, 7, 21 913, 3, 9, 18, 35, 41 914, 5, 27, 28, 42 915, 5, 22, 31 916, 33, 42 917, 4, 9, 15 918, 7, 11, 37, 45 919, 23, 24, 40, 41, 43 920, 40 921, 1, 8, 14, 19 922, 14, 31, 44 923, 6, 28, 33, 39 924, 0, 6, 16, 30, 39, 47 925, 12, 31, 36 926, 1, 36, 46 927, 27, 42, 44 928, 4, 9 929, 20 930, 5, 22 931, 10, 16, 26 932, 13, 36, 42 933, 12, 33, 42, 47 934, 4, 27, 28 935, 1, 19, 39 936, 1, 16, 32 937, 12, 31, 36 938, 16, 32, 41, 45 939, 16, 33, 42 940, 12, 13, 31, 35, 36, 41, 44 941, 6, 9, 19, 24, 44 942, 23, 24, 40, 41, 43 943, 5, 12, 31, 36, 48 944, 0, 2, 20, 44, 46 945, 3, 18, 35 946, 4, 12, 14, 19, 32, 48 947, 41 948, 0, 14, 44 949, 1, 10, 13, 19, 25, 26, 33, 39 950, 7, 15, 16 951, 4, 29, 46 952, 14, 20, 40, 43 953, 7, 38 954, 3, 18, 45, 47 955, 19, 29, 43 956, 9, 16 957, 0, 20, 42 958, 5, 10, 32, 33, 39, 44 959, 27, 28 960, 5, 22, 25, 29, 37, 43 961, 19 962, 4, 16, 34 963, 9, 17, 44, 45 964, 7, 15, 29 965, 7, 11, 27, 37, 39, 45, 49 966, 12, 31, 36, 48 967, 34, 49 968, 31 969, 25, 33, 42, 45 970, 16, 27, 32, 45 971, 25, 41 972, 6, 9, 15, 24, 25, 40, 45 973, 7, 8, 9, 11, 29, 37, 45 974, 21, 36 975, 5, 7, 14, 17, 22 976, 38, 40 977, 2, 7, 15, 22, 25, 33, 41 978, 27, 28 979, 16, 32, 45 980, 8, 18, 28 981, 13 982, 41 983, 27, 28, 38, 48 984, 3, 18, 35 985, 16, 20, 32, 36 986, 16, 32, 45 987, 4, 9 988, 22, 31, 39 989, 0, 2, 46 990, 34 991, 0, 2, 46 992, 0 993, 3, 6, 13 994, 3, 29, 44 995, 9, 27, 28, 45 996, 2, 10, 22, 31, 33, 46 997, 2, 6, 22, 32 998, 0, 4, 9, 30, 33 999, 3, 18, 35 1000, 15, 34, 47
package second;
import java.io.BufferedReader;
import java.io.File;
import java.io.FileReader;
import java.io.IOException;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.Map;
import java.util.Set;
/*
* date:2015-06-10
* by wenbaoli
*
*/
public class Apriori {
private float min_sup;//minimum support
private float min_conf;//minimum confidence
private Map<Integer,Set<String>> TransDataBase;//transaction database
private Integer DBnum;
private Map<Integer,Map<Set<String>,Float>> freqItermSet;//frequent iterm set,from 1 to k...
private Map<Set<String>,Set<Map<Set<String>,Float>>> associationRules;//the final associate rules
public Apriori(Map<Integer,Set<String>> DB , float minSup, float minConf){
this.TransDataBase = DB;
this.min_conf = minConf;
this.min_sup = minSup;
this.DBnum = DB.size();
freqItermSet =new HashMap<Integer,Map<Set<String>,Float>>();
associationRules = new HashMap<Set<String>,Set<Map<Set<String>,Float>>>();
}
/**
* @param args
*/
public static void main(String[] args) {
// TODO Auto-generated method stub
//initial
String file = "data/data.txt";
String delimeter = ",";
//load data
Map<Integer,Set<String>> data = new HashMap<Integer,Set<String>>();
int num = 0;
try {
File mFile = new File(file);
FileReader fr = new FileReader(mFile);
BufferedReader br = new BufferedReader(fr);
String line;
while((line=br.readLine())!= null) {
line = line.trim();
String[] str = line.split(delimeter);
// int i = Integer.parseInt(str[0]);
Set<String> set = new HashSet<String>();
for (int i = 1; i < str.length; i++) {
set.add(str[i].trim());
}
num++;
data.put(num, set);
}
br.close();
} catch(IOException ex) {
ex.printStackTrace();
}
Apriori ap = new Apriori(data,0.005f,0.6f);
ap.findAllFreqItermSet();
ap.findAssociationRules();
}
public void findAllFreqItermSet(){
//找出频繁一项集
Map<Set<String>,Float> f1 = new HashMap<Set<String>,Float>();
Map<Set<String>,Integer> OneItermSet = new HashMap<Set<String>,Integer>();
Iterator<Map.Entry<Integer, Set<String>>> it = this.TransDataBase.entrySet().iterator();
while(it.hasNext()){
Map.Entry<Integer, Set<String>> entry = it.next();
Set<String> itermSet = entry.getValue();
for(String iterm:itermSet){
Set<String> key = new HashSet<String>();
key.add(iterm);
if(!OneItermSet.containsKey(key)){
OneItermSet.put(key, 1);
}else{
int value = 1 + OneItermSet.get(key);
OneItermSet.put(key, value);
}
}
}
//找出支持度大于minSup的频繁一项集
Iterator<Map.Entry<Set<String>,Integer>> iter = OneItermSet.entrySet().iterator();
while(iter.hasNext()){
Map.Entry<Set<String>,Integer> entry = iter.next();
//计算支持度
Float support = new Float(entry.getValue().toString())/new Float(this.DBnum);
if(support >= this.min_sup){
f1.put(entry.getKey(), support);
}
}
System.out.println("频繁1" + "项集:" + f1);//打印频繁1-项集
System.out.println("-------------------------------------------");
this.freqItermSet.put(1, f1);
//由频繁k项集得到频繁k+1项集
int k = 2;
while(true){
Set<Set<String>> candFreItermSets = this.apriori_gen(k,this.freqItermSet.get(k-1).keySet());
Map<Set<String>,Float> freqKItermSetMap = this.getFreqKItermSet(k,candFreItermSets);
if(!freqKItermSetMap.isEmpty()){
this.freqItermSet.put(k, freqKItermSetMap);
} else {
break;
}
System.out.println("频繁" + k + "项集：" + freqKItermSetMap);
System.out.println("-------------------------------------------");
k++;
}
}
public Map<Set<String>, Float> getFreqKItermSet(int k,
Set<Set<String>> candFreItermSets) {
Map<Set<String>,Integer> candFreqKItermSetMap = new HashMap<Set<String>,Integer>();
//扫描事物数据库
Iterator<Map.Entry<Integer, Set<String>>> it = this.TransDataBase.entrySet().iterator();
//统计支持度计数
while (it.hasNext()){
Map.Entry<Integer, Set<String>> entry = it.next();
Iterator<Set<String>> iter = candFreItermSets.iterator();
while(iter.hasNext()){
Set<String> set = iter.next();
if(entry.getValue().containsAll(set)){
if(!candFreqKItermSetMap.containsKey(set)){
candFreqKItermSetMap.put(set, 1);
}else {
int value = 1+ candFreqKItermSetMap.get(set);
candFreqKItermSetMap.put(set, value);
}
}
}
}
Iterator<Map.Entry<Set<String>, Integer>> iter = candFreqKItermSetMap.entrySet().iterator();
Map<Set<String>,Float> freqKIntermSet = new HashMap<Set<String>,Float>();
while(iter.hasNext()){
Map.Entry<Set<String>, Integer> entry = iter.next();
float support = new Float(entry.getValue().toString())/this.DBnum;
if(support < this.min_sup){
iter.remove();
} else {
freqKIntermSet.put(entry.getKey(), support);
}
}
return freqKIntermSet;
}
public Set<Set<String>> apriori_gen(int k, Set<Set<String>> fk){
Set<Set<String>> ck = new HashSet<Set<String>>();
Iterator<Set<String>> it1 = fk.iterator();
while (it1.hasNext()) {
Set<String> itermSet1 = it1.next();
Iterator<Set<String>> it2 = fk.iterator();
while (it2.hasNext()) {
Set<String> itermSet2 = it2.next();
if(!itermSet1.equals(itermSet2)) {
//连接步
Set<String> commIterms = new HashSet<String>();
commIterms.addAll(itermSet1);
commIterms.retainAll(itermSet2);
if(commIterms.size() == (k - 2)){
Set<String> candIterms = new HashSet<String>();
candIterms.addAll(itermSet1);
candIterms.removeAll(itermSet2);
candIterms.addAll(itermSet2);
//剪枝步骤
if(!this.has_infrequent_subset(candIterms, fk)){
ck.add(candIterms);
}
}
}
}
}
System.out.println(ck.size());
return ck;
}
public boolean has_infrequent_subset(Set<String> set,Set<Set<String>> fk){
Set<Set<String>> subItermSet = new HashSet<Set<String>>();
Iterator<String> itr = set.iterator();
while(itr.hasNext()){
//深拷贝
Set<String> subItem = new HashSet<String>();
Iterator<String> it = set.iterator();
while(it.hasNext()){
subItem.add(it.next());
}
//去掉一个项后为k-1子集
subItem.remove(itr.next());
subItermSet.add(subItem);
}
Iterator<Set<String>> it = subItermSet.iterator();
while(it.hasNext()){
if(!fk.contains(it.next())){
return true;
}
}
return false;
}
public void findAssociationRulesTemp(){
}
public void findAssociationRules(){
Iterator<Map.Entry<Integer, Map<Set<String>,Float>>> it = this.freqItermSet.entrySet().iterator();
while (it.hasNext()) {
Map.Entry<Integer, Map<Set<String>,Float>> entry = it.next();
for (Set<String> itemSet : entry.getValue().keySet()) {
int n = itemSet.size() / 2;
for (int i = 1; i <= n; i++) {
Set<Set<String>> subset = this.getProperSubset(i,itemSet);
for(Set<String> conditionSet:subset){
Set<String> conclusionSet = new HashSet<String>();
conclusionSet.addAll(itemSet);
conclusionSet.removeAll(conditionSet);
int s1 = conditionSet.size();
int s2 = conclusionSet.size();
float supF = this.freqItermSet.get(s1).get(conditionSet);
float supS = this.freqItermSet.get(s2).get(conclusionSet);
float sup = this.freqItermSet.get(s1+s2).get(itemSet);
float conf1 = sup/supF;
float conf2 = sup/supS;
if(conf1 >= this.min_conf){
if(this.associationRules.get(conditionSet) == null){
Set<Map<Set<String>,Float>> conclusionSetSet = new HashSet<Map<Set<String>,Float>>();
Map<Set<String>,Float> sets = new HashMap<Set<String>,Float>();
sets.put(conclusionSet, conf1);
conclusionSetSet.add(sets);
this.associationRules.put(conditionSet, conclusionSetSet);
} else {
Map<Set<String>,Float> sets = new HashMap<Set<String>,Float>();
sets.put(conclusionSet, conf1);
associationRules.get(conditionSet).add(sets);
}
}
if(conf2 >= this.min_conf){
if(this.associationRules.get(conditionSet) == null){
Set<Map<Set<String>,Float>> conclusionSetSet = new HashSet<Map<Set<String>,Float>>();
Map<Set<String>,Float> sets = new HashMap<Set<String>,Float>();
sets.put(conclusionSet, conf2);
conclusionSetSet.add(sets);
this.associationRules.put(conditionSet, conclusionSetSet);
} else {
Map<Set<String>,Float> sets = new HashMap<Set<String>,Float>();
sets.put(conclusionSet, conf2);
associationRules.get(conditionSet).add(sets);
}
}
}
}
}
}
System.out.println("关联规则（强规则）：" + associationRules);
}
private Set<Set<String>> getProperSubset(int i, Set<String> itemSet) {
Set<Set<String>> subset = new HashSet<Set<String>>();
if(itemSet.size() <= 1){
return null;
}else if(itemSet.size() == 2){
for(String s: itemSet){
Set<String> set = new HashSet<String>();
set.add(s);
if(!subset.contains(s)){
subset.add(set);
}
}
return subset;
}else {
Iterator<String> it = itemSet.iterator();
String s = it.next();
Set<String> temp = new HashSet<String>(itemSet);
temp.remove(s);
//包含s的子集
Set<Set<String>> subset0 = new HashSet<Set<String>>();
subset0 = this.getProperSubset(i-1, temp);
subset.addAll(subset0);
//不包含s的子集
Set<Set<String>> subset1 = new HashSet<Set<String>>();
subset1 = this.getProperSubset(i, temp);
subset.addAll(subset1);
return subset;
}
}
}