(Implementation project) Many techniques have been proposed to further improve the performance of frequent itemset mining algorithms. Taking FP-tree- based frequent pattern growth algorithms (e.g., FP-growth) as an example, implement one of the following optimization techniques. Compare the performance of your new implementation with the unoptimized version.

(a) The frequent pattern mining method of Section 6.2.4 uses an FP-tree to generate conditional pattern bases using a bottom-up projection technique (i.e., project onto the prefix path of an item p). However, one can develop a top down projection technique, that is, project onto the suffix path of an item p in the generation of a conditional pattern base. Design and implement such a top down FP-tree mining method. Compare its performance with the bottom-up projection method.

(b) Nodes and pointers are used uniformly in an FP-tree in the FP-growth algorithm design. However, such a structure may consume a lot of space when the data are sparse. One possible alternative design is to explore array- and pointer-based hybrid implementation, where a node may store multiple items when it contains no splitting point to multiple sub-branches. Develop such an implementation and compare it with the original one.

(c) It is time and space consuming to generate numerous conditional pattern bases during pattern-growth mining. An interesting alternative is to push right the branches that have been mined for a particular item p, that is, to push them to the remaining branch (es) of the FP-tree. This is done so that fewer conditional pattern bases have to be generated and additional sharing can be explored when mining the remaining FP-tree branches. Design and implement such a method and conduct a performance study on it.