Hi! In this final session of this lecture we're going to discuss mining closed pattern. As we already know before, closed pattern is a compact form but it's a last less compression of frequent patterns. So mining this closed itemsets, it's very interesting and useful. And with pattern-growth approach there's one interesting method developed called 'Closet+'. Let's look at this 'Closet+'. How to develop efficient directly mining of closed itemsets. So let's look at this transaction database, it contains only four transactions and these are the items in these transactions. Suppose the minimum support is two, we'll be able to get these as frequent itemsets. And based on this we can work out the F-list like the following. Now, we look at an interesting method developed called 'itemset merging'. The philosophy can be represented using this example. Let's look at these projective database. For these projective database, we will have ACF, EF, and ACF based on this. As you can see this project database will get ACEF and ACF. But the interesting thing is ACF happens in every transaction project in this database. ACF have the same support as D. In that case, we can grab ACF out form ACFD project database which contains only one item E, it is not frequent. Therefore, we will be able to get a ACFD support is two, it's the final result. This method called 'itemset merging' simply says if Y appears in every occurrence of X, then items of Y is merged with X. Now, the X is D and a Y is ACF. ECF occurs in every occurrence of X which is D, then we will merge ACFD together to form a more compressed form. That means, you can mine all these immediately. So this is more efficient. Actually, there are many tricks developed in Closet+. For example, hybrid tree projection, we use bottom-up physical tree projection, top-down pseudo tree projection. There's one technical sub-itemset pruning, itemset skipping, efficient subset testing. But I'm not going to get into the details. For details, you can read this paper. So finally I'll summarize the recommended readings. These are all classical papers. Apriori mining and the further improvement of Apriori mining. Then we have vertical methods, FP-growth methods, and we have Closet+ methods. So finally, there is an interesting survey article called 'Frequent Pattern Mining Algorithms', which contain many more algorithms covered in this lecture. If you're interested in, go ahead and read this chapter.