/**
* 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);
}
}
/**
* Calculate the support of an itemset by looking at the frequent patterns of the same size.
* Because patterns are sorted by lexical order, we use a binary search. This is MUCH MORE
* efficient than just browsing the full list of patterns. An alternative would be to use a trie
* to store patterns but it may require a bit more memory.
*
* @param itemset the itemset.
* @return the support of the itemset
*/
private int calculateSupport(int[] itemset) {
// We first get the list of patterns having the same size as "itemset"
List<Itemset> patternsSameSize = patterns.getLevels().get(itemset.length);
//
// We perform a binary search to find the position of itemset in this list
int first = 0;
int last = patternsSameSize.size() - 1;
while (first <= last) {
int middle = (first + last) >> 1; // >>1 means to divide by 2
int[] itemsetMiddle = patternsSameSize.get(middle).getItems();
int comparison = ArraysAlgos.comparatorItemsetSameSize.compare(itemset, itemsetMiddle);
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 {
// we have found the itemset, so we return its support.
return patternsSameSize.get(middle).getAbsoluteSupport();
}
}
// If the itemset is not found in this list, it means that the itemset
// is not closed, so we need to find the smallest superset (its closure) to
// determine its support.
// We start from itemset of length |itemset|+1 and increase the size of itemset after each
// while loop.
int size = itemset.length;
loop:
while (true) {
size++;
List<Itemset> patternsList = patterns.getLevels().get(size);
// For each pattern of a given size
for (Itemset pattern : patternsList) {
int[] patternArray = pattern.getItems();
// If the first item of the pattern is larger than the first item of the itemset,
// we don't need to compare with following patterns.
if (patternArray[0] > itemset[0]) {
continue loop;
}
// Otherwise, we check if itemset is contained in pattern
int posItemset = 0;
int posPattern = 0;
while (posPattern < patternArray.length) {
if (patternArray[posPattern] == itemset[posItemset]) {
posItemset++;
// if it is contained completely
if (posItemset == itemset.length) {
return pattern.getAbsoluteSupport();
}
} else if (patternArray[posPattern] >= itemset[posItemset]) {
// if the current item of pattern is larger than the current item in pattern,
// then itemset cannot be contained in pattern so we stop considering it
break;
}
posPattern++;
}
}
}
}
/**
* 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;
}
