I have this algorithm for mining frequent itemsets from a database. In that problem, a person may acquire a list of products bought in a grocery store, and he/she wishes to find out which product subsets tend to occur often, simply by coming out with a parameter of minimum support \$\mu \in [0, 1]\$, which designates the minimum frequency at which an itemset appeares in the entire database in order to be deemed frequent.What comes to demonstration data, I copied this data set from the book Introduction to Data Mining by Tan, Steinbach, Kumar:{a, b}{b, c, d}{a, c, d, e}{a, d, e}{a, b, c}{a, b, c, d}{a}{a, b, c}{a, b, d}{b, c, e}and I used the same minimum support of 0.2.Now, here is the code:AprioriFrequentItemsetGenerator.java:package net.coderodde.mining.arg;import java.util.ArrayList;import java.util.Collections;import java.util.Comparator;import java.util.HashMap;import java.util.HashSet;import java.util.List;import java.util.Map;import java.util.Objects;import java.util.Set;/** * This class implements the  * <a href=https://en.wikipedia.org/wiki/Apriori_algorithm>Apriori algorithm</a>  * for frequent itemset generation. *  * @author Rodion rodde Efremov * @version 1.6 (Sep 14, 2015) * @param <I> the actual item type. */public class AprioriFrequentItemsetGenerator<I> {    /**     * Generates the frequent itemset data.     *      * @param transactionList the list of transactions to mine.     * @param minimumSupport  the minimum support.     * @return the object describing the result of this task.     */    public FrequentItemsetData<I> generate(List<Set<I>> transactionList,                                            double minimumSupport) {        Objects.requireNonNull(transactionList, The itemset list is empty.);        checkSupport(minimumSupport);        if (transactionList.isEmpty()) {            return null;        }        // Maps each itemset to its support count. Support count is simply the         // number of times an itemset appeares in the transaction list.        Map<Set<I>, Integer> supportCountMap = new HashMap<>();        // Get the list of 1-itemsets that are frequent.        List<Set<I>> frequentItemList = findFrequentItems(transactionList,                                                          supportCountMap,                                                          minimumSupport);        // Maps each 'k' to the list of frequent k-itemsets.         Map<Integer, List<Set<I>>> map = new HashMap<>();        map.put(1, frequentItemList);        // 'k' denotes the cardinality of itemsets processed at each iteration        // of the following loop.        int k = 1;        do {            ++k;            // First generate the candidates.            List<Set<I>> candidateList =                     generateCandidates(map.get(k - 1));            for (Set<I> transaction : transactionList) {                List<Set<I>> candidateList2 = subset(candidateList,                                                     transaction);                for (Set<I> itemset : candidateList2) {                    supportCountMap.put(itemset,                                        supportCountMap.getOrDefault(itemset,                                                                      0) + 1);                }            }            map.put(k, getNextItemsets(candidateList,                                       supportCountMap,                                        minimumSupport,                                        transactionList.size()));        } while (!map.get(k).isEmpty());        return new FrequentItemsetData<>(extractFrequentItemsets(map),                                         supportCountMap,                                         minimumSupport,                                         transactionList.size());    }    /**     * This method simply concatenates all the lists of frequent itemsets into     * one list.     *      * @param  map the map mapping an itemset size to the list of frequent     *             itemsets of that size.     * @return the list of all frequent itemsets.     */    private List<Set<I>>        extractFrequentItemsets(Map<Integer, List<Set<I>>> map) {        List<Set<I>> ret = new ArrayList<>();        for (List<Set<I>> itemsetList : map.values()) {            ret.addAll(itemsetList);        }        return ret;    }    /**     * This method gathers all the frequent candidate itemsets into a single      * list.     *      * @param candidateList   the list of candidate itemsets.     * @param supportCountMap the map mapping each itemset to its support count.     * @param minimumSupport  the minimum support.     * @param transactions    the total number of transactions.     * @return a list of frequent itemset candidates.     */    private List<Set<I>> getNextItemsets(List<Set<I>> candidateList,                                         Map<Set<I>, Integer> supportCountMap,                                         double minimumSupport,                                         int transactions) {        List<Set<I>> ret = new ArrayList<>(candidateList.size());        for (Set<I> itemset : candidateList) {            if (supportCountMap.containsKey(itemset)) {                int supportCount = supportCountMap.get(itemset);                double support = 1.0 * supportCount / transactions;                if (support >= minimumSupport) {                    ret.add(itemset);                }            }        }        return ret;    }    /**     * Computes the list of itemsets that are all subsets of      * {@code transaction}.     *      * @param candidateList the list of candidate itemsets.     * @param transaction   the transaction to test against.     * @return the list of itemsets that are subsets of {@code transaction}     *         itemset.     */    private List<Set<I>> subset(List<Set<I>> candidateList,                                 Set<I> transaction) {        List<Set<I>> ret = new ArrayList<>(candidateList.size());        for (Set<I> candidate : candidateList) {            if (transaction.containsAll(candidate)) {                ret.add(candidate);            }        }        return ret;    }    /**     * Generates the next candidates. This is so called F_(k - 1) x F_(k - 1)      * method.     *      * @param itemsetList the list of source itemsets, each of size <b>k</b>.     * @return the list of candidates each of size <b>k + 1</b>.     */    private List<Set<I>> generateCandidates(List<Set<I>> itemsetList) {        List<List<I>> list = new ArrayList<>(itemsetList.size());        for (Set<I> itemset : itemsetList) {            List<I> l = new ArrayList<>(itemset);            Collections.<I>sort(l, ITEM_COMPARATOR);            list.add(l);        }        int listSize = list.size();        List<Set<I>> ret = new ArrayList<>(listSize);        for (int i = 0; i < listSize; ++i) {            for (int j = i + 1; j < listSize; ++j) {                Set<I> candidate = tryMergeItemsets(list.get(i), list.get(j));                if (candidate != null) {                    ret.add(candidate);                }            }        }        return ret;    }    /**     * Attempts the actual construction of the next itemset candidate.     * @param itemset1 the list of elements in the first itemset.     * @param itemset2 the list of elements in the second itemset.     *      * @return a merged itemset candidate or {@code null} if one cannot be      *         constructed from the input itemsets.     */    private Set<I> tryMergeItemsets(List<I> itemset1, List<I> itemset2) {        int length = itemset1.size();        for (int i = 0; i < length - 1; ++i) {            if (!itemset1.get(i).equals(itemset2.get(i))) {                return null;            }        }        if (itemset1.get(length - 1).equals(itemset2.get(length - 1))) {            return null;        }        Set<I> ret = new HashSet<>(length + 1);        for (int i = 0; i < length - 1; ++i) {            ret.add(itemset1.get(i));        }        ret.add(itemset1.get(length - 1));        ret.add(itemset2.get(length - 1));        return ret;    }    private static final Comparator ITEM_COMPARATOR = new Comparator() {        @Override        public int compare(Object o1, Object o2) {            return ((Comparable) o1).compareTo(o2);        }    };    /**     * Computes the frequent itemsets of size 1.     *      * @param itemsetList     the entire database of transactions.     * @param supportCountMap the support count map to which to write the      *                        support counts of each item.     * @param minimumSupport  the minimum support.     * @return                the list of frequent one-itemsets.     */    private List<Set<I>> findFrequentItems(List<Set<I>> itemsetList,                                           Map<Set<I>, Integer> supportCountMap,                                           double minimumSupport) {        Map<I, Integer> map = new HashMap<>();        // Count the support counts of each item.        for (Set<I> itemset : itemsetList) {            for (I item : itemset) {                Set<I> tmp = new HashSet<>(1);                tmp.add(item);                if (supportCountMap.containsKey(tmp)) {                    supportCountMap.put(tmp, supportCountMap.get(tmp) + 1);                } else {                    supportCountMap.put(tmp, 1);                }                map.put(item, map.getOrDefault(item, 0) + 1);            }        }        List<Set<I>> frequentItemsetList = new ArrayList<>();        for (Map.Entry<I, Integer> entry : map.entrySet()) {            if (1.0 * entry.getValue() / map.size() >= minimumSupport) {                Set<I> itemset = new HashSet<>(1);                itemset.add(entry.getKey());                frequentItemsetList.add(itemset);            }        }        return frequentItemsetList;    }    private void checkSupport(double support) {        if (Double.isNaN(support)) {            throw new IllegalArgumentException(The input support is NaN.);        }        if (support > 1.0) {            throw new IllegalArgumentException(                    The input support is too large:  + support + ,  +                    should be at most 1.0);        }        if (support < 0.0) {            throw new IllegalArgumentException(                    The input support is too small:  + support + ,  +                    should be at least 0.0);        }    }}FrequentItemsetData.java:package net.coderodde.mining.arg;import java.util.List;import java.util.Map;import java.util.Set;/** * This class holds the result information of a data-mining task. *  * @author Rodion rodde Efremov * @version 1.6 (Sep 14, 2015) */public class FrequentItemsetData<I> {    private final List<Set<I>> frequentItemsetList;    private final Map<Set<I>, Integer> supportCountMap;    private final double minimumSupport;    private final int numberOfTransactions;    FrequentItemsetData(List<Set<I>> frequentItemsetList,                        Map<Set<I>, Integer> supportCountMap,                        double minimumSupport,                        int transactionNumber) {        this.frequentItemsetList = frequentItemsetList;        this.supportCountMap = supportCountMap;        this.minimumSupport = minimumSupport;        this.numberOfTransactions = transactionNumber;    }    public List<Set<I>> getFrequentItemsetList() {        return frequentItemsetList;    }    public Map<Set<I>, Integer> getSupportCountMap() {        return supportCountMap;    }    public double getMinimumSupport() {        return minimumSupport;    }    public int getTransactionNumber() {        return numberOfTransactions;    }    public double getSupport(Set<I> itemset) {        return 1.0 * supportCountMap.get(itemset) / numberOfTransactions;    }}Demo.java:package net.coderodde.mining.arg;import java.util.ArrayList;import java.util.Arrays;import java.util.HashSet;import java.util.List;import java.util.Set;public class Demo {    public static void main(String[] args) {        AprioriFrequentItemsetGenerator<String> generator =                new AprioriFrequentItemsetGenerator<>();        List<Set<String>> itemsetList = new ArrayList<>();        itemsetList.add(new HashSet<>(Arrays.asList(a, b)));        itemsetList.add(new HashSet<>(Arrays.asList(b, c, d)));        itemsetList.add(new HashSet<>(Arrays.asList(a, c, d, e)));        itemsetList.add(new HashSet<>(Arrays.asList(a, d, e)));        itemsetList.add(new HashSet<>(Arrays.asList(a, b, c)));        itemsetList.add(new HashSet<>(Arrays.asList(a, b, c, d)));        itemsetList.add(new HashSet<>(Arrays.asList(a)));        itemsetList.add(new HashSet<>(Arrays.asList(a, b, c)));        itemsetList.add(new HashSet<>(Arrays.asList(a, b, d)));        itemsetList.add(new HashSet<>(Arrays.asList(b, c, e)));        FrequentItemsetData<String> data = generator.generate(itemsetList, 0.2);        int i = 1;        for (Set<String> itemset : data.getFrequentItemsetList()) {            System.out.printf(%2d: %9s, support: %1.1f\n,                              i++,                               itemset,                              data.getSupport(itemset));        }    }}Any chance of optimizing performance of the algorithm? What about overall design?
Apriori algorithm for frequent itemset generation in Java
java;algorithm;data mining
I'm not really a professional or an expert when it comes to coding, in fact I only know the basics of java since I'm still studying, but as an opinion, I love how you took advantage of Object Oriented Programming when you made this Apriori algorithm. You made use of Sets,Lists and HashMaps to make things easier especially when dealing with lots of transactions. You also used Generics!Although I've noticed that you can still make this code shorter: if (supportCountMap.containsKey(tmp)) {                supportCountMap.put(tmp, supportCountMap.get(tmp) + 1);            } else {                supportCountMap.put(tmp, 1);            }by:supportCountMap.put(tmp, supportCount.getOrDefault(tmp, 0)+1);Actually, I'm doing a project which includes Apriori algorithm. I've tried making one but I didn't really liked my code because it was not optimized and clean so I decided to search for Apriori codes to compare and learn from and luckily, I met this one! I really liked the idea, it can be understood easily and the code is clean!