Explain the steps in mining frequent itemsets using vertical data format using a suitable example.Explain what is meant by mining closed frequent itemsets

Mining frequent itemsets using vertical data format involves several steps. Here is a step-by-step explanation using a simple example:

1. Data Preparation: The first step is to prepare your data in a vertical format. This means that each transaction is represented as a column, and each row represents an item. For example, consider a small grocery store with three transactions: T1 = {bread, milk}, T2 = {bread, diaper, beer}, and T3 = {milk, diaper, beer, cola}. The vertical data format would look like this:

2. Identify Frequent Itemsets: The next step is to identify the frequent itemsets. This is done by counting the number of transactions that contain each item. In our example, the item 'bread' appears in 2 transactions, 'milk' in 2 transactions, 'diaper' in 2 transactions, 'beer' in 2 transactions, and 'cola' in 1 transaction. If we set our minimum support threshold to 2, then all items except 'cola' are considered frequent.

3. Generate Candidate Itemsets: Now, we generate candidate itemsets of size 2 by combining the frequent items. In our example, the candidate itemsets would be {bread, milk}, {bread, diaper}, {bread, beer}, {milk, diaper}, {milk, beer}, and {diaper, beer}.

4. Identify Frequent Itemsets: We then identify the frequent itemsets of size 2 by counting the number of transactions that contain each itemset. In our example, the itemset {bread, milk} appears in 1 transaction, {bread, diaper} in 1 transaction, {bread, beer} in 1 transaction, {milk, diaper} in 1 transaction, {milk, beer} in 1 transaction, and {diaper, beer} in 2 transactions. If we set our minimum support threshold to 2, then only the itemset {diaper, beer} is considered frequent.

5. Repeat Steps 3 and 4: We repeat steps 3 and 4 for itemsets of size 3, 4, etc., until no more frequent itemsets can be found.

Mining closed frequent itemsets is a variation of frequent itemset mining. A closed itemset is a frequent itemset for which there is no immediate superset that has the same support count. In other words, a closed itemset is a maximal set of items that appear together in the same number of transactions. The advantage of mining closed frequent itemsets is that it can significantly reduce the number of itemsets that need to be considered, while still preserving the same amount of information.