/**
* Method to check if all the subsets of size k-1 of a candidate of size k are freuqnet
*
* @param candidate a candidate itemset of size k
* @param levelK_1 the frequent itemsets of size k-1
* @return true if all the subsets are frequet
*/
protected boolean allSubsetsOfSizeK_1AreFrequent(int[] candidate, List<Itemset> levelK_1) {
// generate all subsets by always each item from the candidate, one by one
for (int posRemoved = 0; posRemoved < candidate.length; posRemoved++) {
// perform a binary search to check if the subset appears in level k-1.
int first = 0;
int last = levelK_1.size() - 1;
// variable to remember if we found the subset
boolean found = false;
// the binary search
while (first <= last) {
int middle = (first + last) >> 1; // >>1 means to divide by 2
int comparison = ArraysAlgos.sameAs(levelK_1.get(middle).getItems(), candidate, posRemoved);
if (comparison < 0) {
first =
middle
+ 1; // the itemset compared is larger than the subset according to the lexical
// order
} else if (comparison > 0) {
last =
middle
- 1; // the itemset compared is smaller than the subset is smaller according to
// the lexical order
} else {
found = true; // we have found it so we stop
break;
}
}
if (found
== false) { // if we did not find it, that means that candidate is not a frequent itemset
// because
// at least one of its subsets does not appear in level k-1.
return false;
}
}
return true;
}
/**
* The ApGenRules as described in p.14 of the paper by Agrawal. (see the Agrawal paper for more
* details).
*
* @param k the size of the first itemset used to generate rules
* @param m the recursive depth of the call to this method (first time 1, then 2...)
* @param lk the itemset that is used to generate rules
* @param Hm a set of itemsets that can be used with lk to generate rules
* @throws IOException exception if error while writing output file
*/
private void apGenrules(int k, int m, Itemset lk, List<int[]> Hm) throws IOException {
// if the itemset "lk" that is used to generate rules is larger than the size of itemsets in
// "Hm"
if (k > m + 1) {
// Create a list that we will be used to store itemsets for the recursive call
List<int[]> Hm_plus_1_for_recursion = new ArrayList<int[]>();
// generate candidates using Hm
List<int[]> Hm_plus_1 = generateCandidateSizeK(Hm);
// for each such candidates
for (int[] hm_P_1 : Hm_plus_1) {
// We subtract the candidate from the itemset "lk"
int[] itemset_Lk_minus_hm_P_1 =
ArraysAlgos.cloneItemSetMinusAnItemset(lk.getItems(), hm_P_1);
// We will now calculate the support of the rule Lk/(hm_P_1) ==> hm_P_1
// we need it to calculate the confidence
int support = calculateSupport(itemset_Lk_minus_hm_P_1);
double supportAsDouble = (double) support;
// calculate the confidence of the rule Lk/(hm_P_1) ==> hm_P_1
double conf = lk.getAbsoluteSupport() / supportAsDouble;
// if the confidence is not enough than we don't need to consider
// the rule Lk/(hm_P_1) ==> hm_P_1 anymore so we continue
if (conf < minconf || Double.isInfinite(conf)) {
continue;
}
double lift = 0;
int supportHm_P_1 = 0;
// if the user is using the minlift threshold, then we will need to calculate the lift of
// the
// rule as well and check if the lift is higher or equal to minlift.
if (usingLift) {
// if we want to calculate the lift, we need the support of Hm+1
supportHm_P_1 = calculateSupport(hm_P_1);
// calculate the lift of the rule: Lk/(hm_P_1) ==> hm_P_1
double term1 = ((double) lk.getAbsoluteSupport()) / databaseSize;
double term2 = (supportAsDouble) / databaseSize;
lift = term1 / (term2 * ((double) supportHm_P_1 / databaseSize));
// if the lift is not enough
if (lift < minlift) {
continue;
}
}
// The rule has passed the confidence and lift threshold requirements,
// so we can output it
saveRule(
itemset_Lk_minus_hm_P_1,
support,
hm_P_1,
supportHm_P_1,
lk.getAbsoluteSupport(),
conf,
lift);
// if k == m+1, then we cannot explore further rules using Lk since Lk will be too small.
if (k != m + 1) {
Hm_plus_1_for_recursion.add(hm_P_1);
}
}
// recursive call to apGenRules to find more rules using "lk"
apGenrules(k, m + 1, lk, Hm_plus_1_for_recursion);
}
}
/**
* Run the algorithm for generating association rules from a set of itemsets.
*
* @param patterns the set of itemsets
* @param output the output file path. If null the result is saved in memory and returned by the
* method.
* @param databaseSize the number of transactions in the original database
* @return the set of rules found if the user chose to save the result to memory
* @throws IOException exception if error while writting to file
*/
private AssocRules runAlgorithm(Itemsets patterns, String output, int databaseSize)
throws IOException {
// if the user want to keep the result into memory
if (output == null) {
writer = null;
rules = new AssocRules("ASSOCIATION RULES");
} else {
// if the user want to save the result to a file
rules = null;
writer = new BufferedWriter(new FileWriter(output));
}
this.databaseSize = databaseSize;
// record the time when the algorithm starts
startTimestamp = System.currentTimeMillis();
// initialize variable to count the number of rules found
ruleCount = 0;
// save itemsets in a member variable
this.patterns = patterns;
// SORTING
// First, we sort all itemsets having the same size by lexical order
// We do this for optimization purposes. If the itemsets are sorted, it allows to
// perform two optimizations:
// 1) When we need to calculate the support of an itemset (in the method
// "calculateSupport()") we can use a binary search instead of browsing the whole list.
// 2) When combining itemsets to generate candidate, we can use the
// lexical order to avoid comparisons (in the method "generateCandidates()").
// For itemsets of the same size
for (List<Itemset> itemsetsSameSize : patterns.getLevels()) {
// Sort by lexicographical order using a Comparator
Collections.sort(
itemsetsSameSize,
new Comparator<Itemset>() {
@Override
public int compare(Itemset o1, Itemset o2) {
// The following code assume that itemsets are the same size
return ArraysAlgos.comparatorItemsetSameSize.compare(o1.getItems(), o2.getItems());
}
});
}
// END OF SORTING
// Now we will generate the rules.
// For each frequent itemset of size >=2 that we will name "lk"
for (int k = 2; k < patterns.getLevels().size(); k++) {
for (Itemset lk : patterns.getLevels().get(k)) {
// create a variable H1 for recursion
List<int[]> H1_for_recursion = new ArrayList<int[]>();
// For each itemset "itemsetSize1" of size 1 that is member of lk
for (int item : lk.getItems()) {
int itemsetHm_P_1[] = new int[] {item};
// make a copy of lk without items from hm_P_1
int[] itemset_Lk_minus_hm_P_1 = ArraysAlgos.cloneItemSetMinusOneItem(lk.getItems(), item);
// Now we will calculate the support and confidence
// of the rule: itemset_Lk_minus_hm_P_1 ==> hm_P_1
int support = calculateSupport(itemset_Lk_minus_hm_P_1); // THIS COULD BE
// OPTIMIZED ?
double supportAsDouble = (double) support;
// calculate the confidence of the rule : itemset_Lk_minus_hm_P_1 ==> hm_P_1
double conf = lk.getAbsoluteSupport() / supportAsDouble;
// if the confidence is lower than minconf
if (conf < minconf || Double.isInfinite(conf)) {
continue;
}
double lift = 0;
int supportHm_P_1 = 0;
// if the user is using the minlift threshold, we will need
// to also calculate the lift of the rule: itemset_Lk_minus_hm_P_1 ==> hm_P_1
if (usingLift) {
// if we want to calculate the lift, we need the support of hm_P_1
supportHm_P_1 =
calculateSupport(
itemsetHm_P_1); // if we want to calculate the lift, we need to add this.
// calculate the lift
double term1 = ((double) lk.getAbsoluteSupport()) / databaseSize;
double term2 = supportAsDouble / databaseSize;
double term3 = ((double) supportHm_P_1 / databaseSize);
lift = term1 / (term2 * term3);
// if the lift is not enough
if (lift < minlift) {
continue;
}
}
// If we are here, it means that the rule respect the minconf and minlift parameters.
// Therefore, we output the rule.
saveRule(
itemset_Lk_minus_hm_P_1,
support,
itemsetHm_P_1,
supportHm_P_1,
lk.getAbsoluteSupport(),
conf,
lift);
// Then we keep the itemset hm_P_1 to find more rules using this itemset and lk.
H1_for_recursion.add(itemsetHm_P_1);
// ================ END OF WHAT I HAVE ADDED
}
// Finally, we make a recursive call to continue explores rules that can be made with "lk"
apGenrules(k, 1, lk, H1_for_recursion);
}
}
// close the file if we saved the result to a file
if (writer != null) {
writer.close();
}
// record the end time of the algorithm execution
endTimeStamp = System.currentTimeMillis();
// Return the rules found if the user chose to save the result to memory rather than a file.
// Otherwise, null will be returned
return rules;
}
/**
* Try to expand a rule by right expansion only.
*
* @param ruleG the rule
*/
private void expandR(RuleG ruleG) {
// map to record the potential item to expand the right side of the rule
// Key: item Value: bitset indicating the IDs of the transaction containing the item
// from the transactions containing the rule.
Map<Integer, BitSet> mapCountRight = new HashMap<Integer, BitSet>();
// for each transaction containing the rule
for (int tid = ruleG.common.nextSetBit(0); tid >= 0; tid = ruleG.common.nextSetBit(tid + 1)) {
// iterate over the items in this transaction
Iterator<Integer> iter = database.getTransactions().get(tid).getItems().iterator();
while (iter.hasNext()) {
Integer item = iter.next();
// if that item is not frequent, then remove it from the transaction
if (tableItemCount[item] < minsuppRelative) {
iter.remove();
continue;
}
// If the item is smaller than the largest item in the right side
// of the rule, we can stop this loop because items
// are sorted in lexicographical order.
if (item < ruleG.maxRight) {
break;
}
// if the item is larger than the maximum item in the right side
// and is not contained in the left side of the rule
if (item > ruleG.maxRight
&& !ArraysAlgos.containsLEX(ruleG.getItemset1(), item, ruleG.maxLeft)) {
// update the tidset of the item
BitSet tidsItem = mapCountRight.get(item);
if (tidsItem == null) {
tidsItem = new BitSet();
mapCountRight.put(item, tidsItem);
}
tidsItem.set(tid);
}
}
}
// for each item c found in the previous step, we create a rule
// I ==> J U {c} if the support is enough
for (Entry<Integer, BitSet> entry : mapCountRight.entrySet()) {
BitSet tidsRule = entry.getValue();
int ruleSupport = tidsRule.cardinality();
// if the support is enough
if (ruleSupport >= minsuppRelative) {
Integer itemC = entry.getKey();
// create new right part of rule
Integer[] newRightItemset = new Integer[ruleG.getItemset2().length + 1];
System.arraycopy(ruleG.getItemset2(), 0, newRightItemset, 0, ruleG.getItemset2().length);
newRightItemset[ruleG.getItemset2().length] = itemC;
// recompute maxRight
int maxRight = itemC >= ruleG.maxRight ? itemC : ruleG.maxRight;
// calculate confidence
double confidence = ((double) ruleSupport) / ruleG.tids1.cardinality();
// create the rule
RuleG candidate =
new RuleG(
ruleG.getItemset1(),
newRightItemset,
ruleSupport,
ruleG.tids1,
tidsRule,
ruleG.maxLeft,
maxRight);
// if the confidence is enough
if (confidence >= minConfidence) {
// save the rule to the current top-k rules
save(candidate, ruleSupport);
}
// register the rule as a candidate for future expansion(s)
registerAsCandidate(false, candidate);
}
}
}
/**
* Try to expand a rule by left and right expansions.
*
* @param ruleG the rule
*/
private void expandLR(RuleG ruleG) {
// Maps to record the potential item to expand the left/right sides of the rule
// Key: item Value: bitset indicating the IDs of the transaction containing the item
// from the transactions containing the rule.
Map<Integer, BitSet> mapCountLeft = new HashMap<Integer, BitSet>();
Map<Integer, BitSet> mapCountRight = new HashMap<Integer, BitSet>();
for (int tid = ruleG.common.nextSetBit(0); tid >= 0; tid = ruleG.common.nextSetBit(tid + 1)) {
Iterator<Integer> iter = database.getTransactions().get(tid).getItems().iterator();
while (iter.hasNext()) {
Integer item = iter.next();
// CAN DO THIS BECAUSE TRANSACTIONS ARE SORTED BY DESCENDING
// ITEM IDS (see Database.Java)
if (item < ruleG.maxLeft && item < ruleG.maxRight) { //
break;
}
if (tableItemCount[item] < minsuppRelative) {
iter.remove();
continue;
}
if (item > ruleG.maxLeft
&& !ArraysAlgos.containsLEX(ruleG.getItemset2(), item, ruleG.maxRight)) {
BitSet tidsItem = mapCountLeft.get(item);
if (tidsItem == null) {
tidsItem = new BitSet();
mapCountLeft.put(item, tidsItem);
}
tidsItem.set(tid);
}
if (item > ruleG.maxRight
&& !ArraysAlgos.containsLEX(ruleG.getItemset1(), item, ruleG.maxLeft)) {
BitSet tidsItem = mapCountRight.get(item);
if (tidsItem == null) {
tidsItem = new BitSet();
mapCountRight.put(item, tidsItem);
}
tidsItem.set(tid);
}
}
}
// for each item c found in the previous step, we create a rule
// I ==> J U {c} if the support is enough
for (Entry<Integer, BitSet> entry : mapCountRight.entrySet()) {
BitSet tidsRule = entry.getValue();
int ruleSupport = tidsRule.cardinality();
// if the support is enough
if (ruleSupport >= minsuppRelative) {
Integer itemC = entry.getKey();
// create new right part of rule
Integer[] newRightItemset = new Integer[ruleG.getItemset2().length + 1];
System.arraycopy(ruleG.getItemset2(), 0, newRightItemset, 0, ruleG.getItemset2().length);
newRightItemset[ruleG.getItemset2().length] = itemC;
// recompute maxRight
int maxRight = (itemC >= ruleG.maxRight) ? itemC : ruleG.maxRight;
// calculate the confidence of the rule
double confidence = ((double) ruleSupport) / ruleG.tids1.cardinality();
// create the rule
RuleG candidate =
new RuleG(
ruleG.getItemset1(),
newRightItemset,
ruleSupport,
ruleG.tids1,
tidsRule,
ruleG.maxLeft,
maxRight);
// if the confidence is enough
if (confidence >= minConfidence) {
// save the rule in current top-k rules
save(candidate, ruleSupport);
}
// register the rule as a candidate for future expansion
registerAsCandidate(false, candidate);
}
}
// for each item c found in the previous step, we create a rule
// I U {c} ==> J if the support is enough
for (Entry<Integer, BitSet> entry : mapCountLeft.entrySet()) {
BitSet tidsRule = entry.getValue();
int ruleSupport = tidsRule.cardinality();
// if the support is enough
if (ruleSupport >= minsuppRelative) {
Integer itemC = entry.getKey();
// The tidset of the left itemset is calculated
BitSet tidsLeft = (BitSet) ruleG.tids1.clone();
tidsLeft.and(tableItemTids[itemC]);
// create new left part of rule
Integer[] newLeftItemset = new Integer[ruleG.getItemset1().length + 1];
System.arraycopy(ruleG.getItemset1(), 0, newLeftItemset, 0, ruleG.getItemset1().length);
newLeftItemset[ruleG.getItemset1().length] = itemC;
// recompute maxLeft
int maxLeft = itemC >= ruleG.maxLeft ? itemC : ruleG.maxLeft;
// calculate the confidence of the rule
double confidence = ((double) ruleSupport) / tidsLeft.cardinality();
// create the rule
RuleG candidate =
new RuleG(
newLeftItemset,
ruleG.getItemset2(),
ruleSupport,
tidsLeft,
tidsRule,
maxLeft,
ruleG.maxRight);
// if the confidence is high enough
if (confidence >= minConfidence) {
// save the rule to the top-k rules
save(candidate, ruleSupport);
}
// register the rule as a candidate for further expansions
registerAsCandidate(true, candidate);
}
}
}
