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all items in the set are contained in the purchase For instance, if a purchase included items a, b, and c, counts would be incremented for {a}, {b}, {c}, {a, b}, {b, c}, {a, c}, and {a, b, c} Those sets with a suf ciently high count at the end of the pass correspond to items that have a high degree of association The number of sets grows exponentially, making the procedure just described infeasible if the number of items is large Luckily, almost all the sets would normally have very low support; optimizations have been developed to eliminate most such sets from consideration These techniques use multiple passes on the database, considering only some sets in each pass In the a priori technique for generating large itemsets, only sets with single items are considered in the rst pass In the second pass, sets with two items are considered, and so on At the end of a pass all sets with suf cient support are output as large itemsets Sets found to have too little support at the end of a pass are eliminated Once a set is eliminated, none of its supersets needs to be considered In other words, in pass i we need to count only supports for sets of size i such that all subsets of the set have been found to have suf ciently high support; it suf ces to test all subsets of size i 1 to ensure this property At the end of some pass i, we would nd that no set of size i has suf cient support, so we do not need to consider any set of size i + 1 Computation then terminates

ACLs are the most common method of allowing traffic to travel from a lower to higher interface, as well as restricting traffic from a higher to a lower interface ACLs are made up of two components: creating a list of filtering statements and applying the statements to an interface To help with the implementation of ACLs, in version 62 of the operating system, Cisco introduced a concept called object groups Basically an object group is a group of objects of a similar type, like IP addresses and network numbers, TCP and/or UDP port numbers, IP protocols, and ICMP message types You can create an object group and then reference it in a single ACL statement For example, if you need to allow web traffic to three different servers, without object groups, you would need three individual ACL statements Instead, you can create an object group that contains the three addresses, and in a single ACL statement, reference the object group Object groups thus greatly simplify the maintenance and understanding of ACL policies ACLs and object groups are discussed in 6 Cisco also supports the filtering of HTTP and FTP content, including ActiveX scripts, Java applets, and web URLs The last is only supported when used in combination with a web proxy server Currently only Websense and Smartfilter are supported as proxy servers With a traditional proxy, the user establishes a connection to the proxy, and the proxy connects to the actual destination, requiring the proxy to maintain two connections to transmit the data With Cisco s solution, the security appliance passes the URL to the proxy server, the proxy determines whether it is allowed, and the result is passed back to the appliance, which implements the policy This approach greatly increases throughput and supports more connections since the user s connection isn t being proxied in the traditional sense.

Using plain association rules has several shortcomings One of the major shortcomings is that many associations are not very interesting, since they can be predicted For instance, if many people buy cereal and many people buy bread, we can predict that a fairly large number of people would buy both, even if there is no connection between the two purchases What would be interesting is a deviation from the expected co-occurrence of the two In statistical terms, we look for correlations between items; correlations can be positive, in that the co-occurrence is higher than would have been expected, or negative, in that the items co-occur less frequently than predicted See a standard textbook on statistics for more information about correlations Another important class of data-mining applications is sequence associations (or correlations) Time-series data, such as stock prices on a sequence of days, form an example of sequence data Stock-market analysts want to nd associations among stock-market price sequences An example of such a association is the following rule: Whenever bond rates go up, the stock prices go down within 2 days Discovering such association between sequences can help us to make intelligent investment decisions See the bibliographical notes for references to research on this topic Deviations from temporal patterns are often interesting For instance, if a company has been growing at a steady rate each year, a deviation from the usual growth rate is surprising If sales of winter clothes go down in summer, it is not surprising, since we can predict it from past years; a deviation that we could not have predicted from past experience would be considered interesting Mining techniques can nd deviations from what one would have expected on the basis of past temporal/sequential patterns See the bibliographical notes for references to research on this topic