Lecture 5 Apriori algorithm

Summary

This video discusses association rules and the process of finding them in data, focusing on frequent item sets and how to generate association rules with support and confidence thresholds. It introduces the Apriori algorithm, which reduces computational complexity by pruning infrequent item sets using the Apriori principle. The principle states that if an item set is frequent, all of its subsets must also be frequent, and vice versa. This approach helps in efficiently identifying valid association rules, with future lectures exploring more advanced algorithms to further reduce complexity.

Takeaways

• 😀 Association rules are formed in the format X → Y, where X and Y are item sets satisfying support and confidence criteria.
• 😀 Support is defined as the number of transactions where both X and Y appear, while confidence is the fraction of transactions where both X and Y appear compared to only X appearing.
• 😀 The challenge of finding all association rules lies in the exponential growth of possible item sets as the number of items increases, making brute force infeasible.
• 😀 The two-step approach for association rule mining involves finding frequent item sets first and then generating rules from them.
• 😀 The number of candidate item sets grows exponentially, with 2^d possible combinations for d items, which leads to computationally expensive evaluations.
• 😀 A lattice structure can be used to represent all potential item sets, where each level corresponds to item sets of different sizes.
• 😀 The Apriori algorithm is used to reduce computational complexity by pruning infrequent item sets early on, based on the anti-monotone property.
• 😀 The anti-monotone property states that if an item set is not frequent, none of its supersets can be frequent either.
• 😀 By leveraging the Apriori principle, subsets of frequent item sets are guaranteed to be frequent, reducing the number of candidate item sets to evaluate.
• 😀 The process of identifying frequent item sets involves scanning the transaction database and counting occurrences to identify item sets that meet a minimum support threshold.
• 😀 The Apriori algorithm works recursively: after identifying frequent item sets of length 1, it combines them to form larger item sets and checks their support in subsequent iterations.

Q & A

What are the main criteria used to determine if an association rule is valid?

The two main criteria for an association rule to be valid are support and confidence. Support is the frequency with which both X and Y appear together in transactions, while confidence is the probability that Y appears given that X has appeared.

What is the computational challenge in discovering association rules?

The challenge in discovering association rules lies in the computational expense of finding all possible item sets. Since the number of possible item sets grows exponentially with the number of items, finding frequent item sets becomes computationally prohibitive.

What is the two-step approach to discovering association rules?

The two-step approach involves: 1) finding all frequent item sets, which meet a minimum support threshold, and 2) generating rules from these frequent item sets by checking if their confidence exceeds a minimum confidence threshold.

How does the lattice structure relate to association rules?

The lattice structure represents all possible item sets in a market basket, where each node is an item set. The structure shows how item sets of different sizes relate to each other, with lines indicating subset relationships. This helps in visualizing candidate item sets and their relationships.

How does the apriori principle aid in the discovery of frequent item sets?

The apriori principle states that if an item set is frequent, then all of its subsets must also be frequent. This helps in pruning candidate item sets, as if a subset is infrequent, its superset cannot be frequent either.

What is meant by the 'anti-monotone property' in association rule mining?

The anti-monotone property refers to the principle that if an item set is infrequent, all supersets of that item set will also be infrequent. This property allows us to eliminate candidate item sets early in the process.

What does pruning mean in the context of frequent item set mining?

Pruning refers to the process of eliminating item sets that are not frequent, reducing the number of candidate item sets to consider. This is based on the apriori principle and helps improve computational efficiency.

Why is it inefficient to evaluate all candidate item sets directly?

Evaluating all candidate item sets directly is inefficient because the number of possible item sets grows exponentially with the number of items in the database, making it computationally expensive to scan all transactions for each candidate set.

How do we use confidence in generating association rules?

Confidence is used to evaluate the strength of an association rule. If the confidence of a rule, defined as the ratio of transactions containing both X and Y to those containing only X, exceeds the minimum confidence threshold, the rule is considered valid.

What steps are involved in the apriori algorithm for generating association rules?

The apriori algorithm involves generating frequent item sets of length one, then recursively generating larger item sets from the frequent ones. For each new item set, the algorithm checks if it meets the support threshold, and if not, it prunes it from further consideration.