Question

Apply the Apriori algorithm to the following data set. $$\begin{array}{ll} \text { Trans ID } & \text { Items Purchased } \\ \hline 101 & \text { milk, bread, eggs } \\ 102 & \text { milk, juice } \\ 103 & \text { juice, butter } \\ 104 & \text { milk, bread, eggs } \\ 105 & \text { coffee, eggs } \\ 106 & \text { coffee } \\ 107 & \text { coffee, juice } \\ 108 & \text { milk, bread, cookies, eggs } \\ 109 & \text { cookies, butter } \\ 110 & \text { milk, bread } \end{array}$$ The set of items is \(\\{\text { milk, bread, cookies, eggs, butter, coffee, juice }\\}\). Use 0.2 for the minimum support value.

Short answer

The process continues until there are no more new itemsets. After applying the Apriori algorithm, the final items and item sets are the ones that meet the minimum support value.

Step-by-step solution

List individual items

Make a list of individual items and determine the frequency (count) of each item: \[\{{\text{milk, bread, cookies, eggs, butter, coffee, juice}}\}\].

Determine support value

The support value for each item is determined by counting how many times the item shows up in the transactions and dividing by the total number of transactions. An itemset must have at least the minimum support of 0.2 value to be considered frequent.

Eliminate items with less than minimum support value

Remove all the items that fall below the minimum support value from the list.

Create the first itemset

Create the first itemset with the remaining items, and calculate their support values. If an itemset doesn't meet the minimum support, discard it.

Create the second itemset

Using the remaining items from the first itemset, create the second itemset, and calculate their support values. Discard the sets that do not meet the minimum support.

Repeat the process

Repeat the process of creating itemsets and eliminating those that do not meet the minimum support until no more new itemsets can be created.

Key concepts

Data Mining

Data mining is like a treasure hunt where the treasure is hidden knowledge within large datasets. It employs sophisticated algorithms to discover patterns and relationships that were previously unknown.

Imagine you own a grocery store and want to understand your customers better. Data mining would allow you to analyze purchase histories to identify trends, such as which items are frequently bought together. This forms the basis for association rules, which can help in marketing strategies, like what products to place near each other, or identifying which items are popular so you can keep them in stock.

It involves multiple steps including data cleaning, integration, selection, transformation, data mining, pattern evaluation, and knowledge presentation. In the Apriori algorithm exercise, data mining helps discover which items are commonly purchased together in the dataset of transactions provided.

Association Rule Learning

Association rule learning is a key technique in data mining focused on finding interesting relationships, frequently called 'association rules', within large sets of data.

For instance, in the context of a grocery store - a classic example of an association rule is the 'milk and bread' rule. This rule suggests that customers who buy milk are also likely to buy bread.

These rules are helpful for cross-selling, inventory management, and store layout. The algorithms like Apriori not only find these associations but also quantify them with metrics such as 'support' and 'confidence', ensuring the rules are statistically significant and not due to random chance.

Support Value Calculation

The support value calculation is a critical step in association rule learning. It quantifies how frequently an item or an itemset appears in the dataset of transactions.

To calculate the support value, divide the number of transactions featuring the item or itemset by the total number of transactions. For example, if 'milk' appears in 7 out of 10 transactions, the support value for 'milk' is 0.7.

This measure helps to identify which items are popular across all transactions. In the Apriori exercise, we use a minimum support value to filter out the itemsets that are not frequently purchased together, enabling a focus on more potentially profitable associations.

Frequent Itemset Generation

Frequent itemset generation is the process of identifying all itemsets in the dataset that meet a specified minimum support threshold.

Initially, all individual items' support counts are calculated, and items failing to meet the minimum support are discarded. Iteratively, larger itemsets are then considered, building upon the previous itemsets that met the support criterion.

The Apriori algorithm uses a 'bottom up' approach, where you start with single items and expand to larger sets, while also utilizing the 'Apriori property'—the idea that all subsets of a frequent itemset must also be frequent. This step is essential for narrowing down the sizeable list of possible itemsets to those most relevant for generating association rules.