[MUSIC] Now we study another interesting issue called Mining Closed Sequential Patterns. The algorithm mining this is called CloSpan, so what is closed sequential patterns, similar to closed frequent item sets? The closed sequential pattern s means, if there exists no superpattern s prime and this s prime and s have the same support. Then s is a closed sequential pattern, in another word, closed pattern means for the same support, you will find the longest one. That's the closed pattern, the other ones probably does not really matter, okay, for example, let's look at this example. Supposed we find three sequences, abc with support 20, abcd with support 20 and the abcde with support of 15. Which ones are closed, abcd is closed in the sense for support 20, abcd is a longest one. Then abcde is also closed because the support at 15, there is no longer 1 and 15 which is a super sequence of abcde. So there are two ways to mine closed sequential patterns, one way is you first mine all the sequential patterns. Then you find which one is closed to like this abc, you can knock it down, then you'll get set of closed sequential patterns. But this is not a very efficient, what we want is directly mine closed sequential patterns. This will reduce a number of redundant patterns to be generated in the middle. But it will attain the same expressive power because it's last it's compression, so there's a one interesting property like this. If s is the superset of s1, s is closed if and only if two projected database have the same size. Let's look at this, for example, for this sequence database, if you find f the project database and another sequence is af. This is the project database, if these project database have exactly same size, then this actually means af is closed. Essentially, you only need to mine one, that means you can merge them, so you will be able to develop two kinds of pruning. One called backward subpattern pruning, this is a subpattern, you can prune it, another is backward superpattern pruning, so you probably see. That you can use superpattern to chop up the subpattern you will get into this, okay? So with this spirit we can develop an efficient algorithm called CloSpan. It greatly enhance the processing efficiency, I'm not going to discuss very detailed. But details you can read this paper, it gives you all the detail on the CloSpan. [MUSIC]