From https://www.hackerearth.com/blog/machine-learning/beginners-tutorial-apriori-algorithm-data-mining-r-implementation/
With the quick growth in e-commerce applications, there is an accumulation vast quantity of data in months not in years. Data Mining, also known as Knowledge Discovery in Databases(KDD), to find anomalies, correlations, patterns, and trends to predict outcomes. Apriori algorithm is a classical algorithm in data mining. It is used for mining frequent itemsets and relevant association rules. It is devised to operate on a database containing a lot of transactions, for instance, items brought by customers in a store. It is very important for effective Market Basket Analysis and it helps the customers in purchasing their items with more ease which increases the sales of the markets. It has also been used in the field of healthcare for the detection of adverse drug reactions. It produces association rules that indicates what all combinations of medications and patient characteristics lead to ADRs.
Association rule learning is a prominent and a well-explored method for determining relations among variables in large databases. Let us take a look at the formal definition of the problem of association rules given by Rakesh Agrawal, the President and Founder of the Data Insights Laboratories. Let I={i1,i2,i3,…,in} be a set of n attributes called items and D={t1,t2,…,tn} be the set of transactions. It is called database. Every transaction, ti in D has a unique transaction ID, and it consists of a subset of itemsets in I. A rule can be defined as an implication, X⟶Y where X and Y are subsets of I(X,Y⊆I), and they have no element in common, i.e., X∩Y. X and Y are the antecedent and the consequent of the rule, respectively. Let’s take an easy example from the supermarket sphere. The example that we are considering is quite small and in practical situations, datasets contain millions or billions of transactions. The set of itemsets, I ={Onion, Burger, Potato, Milk, Beer} and a database consisting of six transactions. Each transaction is a tuple of 0’s and 1’s where 0 represents the absence of an item and 1 the presence. An example for a rule in this scenario would be {Onion, Potato} => {Burger}, which means that if onion and potato are bought, customers also buy a burger.