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Post: #1

APRIORI Algorithm

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The Apriori Algorithm: Basics

The Apriori Algorithm is an influential algorithm for
mining frequent itemsets for boolean association rules.
Key Concepts :
• Frequent Itemsets: The sets of item which has minimum
support (denoted by Li for ith-Itemset).
• Apriori Property: Any subset of frequent itemset must be
• Join Operation: To find L
k , a set of candidate k-itemsets
is generated by joining Lk-1 with itself.

The Apriori Algorithm in a

• Find the frequent itemsets: the sets of items that have
minimum support
– A subset of a frequent itemset must also be a
frequent itemset
• i.e., if {AB} is a frequent itemset, both {
A} and {
should be a frequent itemset
– Iteratively find frequent itemsets with cardinality
from 1 to k (k-itemset)
• Use the frequent itemsets to generate association rules.

Generating 2-itemset Frequent Pattern

• To discover the set of frequent 2-itemsets, L2 , the
algorithm uses L1 Join L1 to generate a candidate set of
2-itemsets, C2.
• Next, the transactions in D are scanned and the support
count for each candidate itemset in C2 is accumulated
(as shown in the middle table).
• The set of frequent 2-itemsets, L2 , is then determined,
consisting of those candidate 2-itemsets in C2 having
minimum support.
• Note: We haven’t used Apriori Property yet.Step 3: Generating 3-itemset Frequent Pattern
{I1, I2, I3}
{I1, I2, I5}
Itemset Sup.
{I1, I2, I3} 2
{I1, I2, I5} 2
Itemset Sup
{I1, I2, I3} 2
{I1, I2, I5} 2
C3 C3 L3
Scan D for
count of

Generating 3-itemset Frequent Pattern[/b]

• Based on the Apriori property that all subsets of a frequent itemset must
also be frequent, we can determine that four latter candidates cannot
possibly be frequent. How ?
• For example , lets take {I1, I2, I3}. The 2-item subsets of it are {I1, I2}, {I1,
I3} & {I2, I3}. Since all 2-item subsets of {I1, I2, I3} are members of L2, We
will keep {I1, I2, I3} in C3.
• Lets take another example of {I2, I3, I5} which shows how the pruning is
performed. The 2-item subsets are {I2, I3}, {I2, I5} & {I3,I5}.
• BUT, {I3, I5} is not a member of L2 and hence it is not frequent violating
Apriori Property. Thus We will have to remove {I2, I3, I5} from C3.
• Therefore, C3 = {{I1, I2, I3}, {I1, I2, I5}} after checking for all members of
result of Join operation for Pruning.
• Now, the transactions in D are scanned in order to determine L3, consisting
of those candidates 3-itemsets in C3 having minimum support.

Methods to Improve Apriori’s Efficiency

• Hash-based itemset counting: A
k-itemset whose corresponding
hashing bucket count is below the threshold cannot be frequent.
• Transaction reduction: A transaction that does not contain any
frequent k-itemset is useless in subsequent scans.
• Partitioning: Any itemset that is potentially frequent in DB must be
frequent in at least one of the partitions of DB.
• Sampling: mining on a subset of given data, lower support threshold
+ a method to determine the completeness.
• Dynamic itemset counting: add new candidate itemsets only when
all of their subsets are estimated to be frequent.

Why Frequent Pattern Growth Fast ?

• Performance study shows
– FP-growth is an order of magnitude faster than Apriori,
and is also faster than tree-projection
• Reasoning
– No candidate generation, no candidate test
– Use compact data structure
– Eliminate repeated database scan
– Basic operation is counting and FP-tree building
Post: #2
Apriori is an algorithm for mining frequent sets of elements and learning association rules on transactional databases. It proceeds by identifying the common individual elements in the database and extending them to ever larger sets of articles, as long as those sets of elements appear frequently enough in the database. Frequent item sets determined by Apriori can be used to determine association rules that highlight general trends in the database: this has applications in domains such as market basket analysis.

The Apriori algorithm was proposed by Agrawal and Srikant in 1994. Apriori is designed to operate on databases that contain transactions (for example, collections of items purchased by customers, or details of a website visitation). Other algorithms are designed to find association rules in data that have no transactions (Winepi and Minepi), or that have no time stamps (DNA sequencing). Each transaction is viewed as a set of elements (a set of elements).

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