Yun Chi

Moment: maintaining closed frequent itemsets over a stream sliding window

This paper considers the problem of mining closed frequent itemsets over a sliding window using limited memory space. We design a synopsis data structure to monitor transactions in the sliding window so that we can output the current closed frequent itemsets at any time. Due to time and memory constraints, the synopsis data structure cannot monitor all possible itemsets. However, monitoring only frequent itemsets make it impossible to detect new itemsets when they become frequent. In this paper, we introduce a compact data structure, the closed enumeration tree (CET), to maintain a dynamically selected set of item-sets over a sliding-window. The selected itemsets consist of a boundary between closed frequent itemsets and the rest of the itemsets. Concept drifts in a data stream are reflected by boundary movements in the CET. In other words, a status change of any itemset (e.g., from non-frequent to frequent) must occur through the boundary. Because the boundary is relatively stable, the cost of mining closed frequent item-sets over a sliding window is dramatically reduced to that of mining transactions that can possibly cause boundary movements in the CET. Our experiments show that our algorithm performs much better than previous approaches.

Catch the moment: maintaining closed frequent itemsets over a data stream sliding window

This paper considers the problem of mining closed frequent itemsets over a data stream sliding window using limited memory space. We design a synopsis data structure to monitor transactions in the sliding window so that we can output the current closed frequent itemsets at any time. Due to time and memory constraints, the synopsis data structure cannot monitor all possible itemsets. However, monitoring only frequent itemsets will make it impossible to detect new itemsets when they become frequent. In this paper, we introduce a compact data structure, the closed enumeration tree (CET), to maintain a dynamically selected set of itemsets over a sliding window. The selected itemsets contain a boundary between closed frequent itemsets and the rest of the itemsets. Concept drifts in a data stream are reflected by boundary movements in the CET. In other words, a status change of any itemset (e.g., from non-frequent to frequent) must occur through the boundary. Because the boundary is relatively stable, the cost of mining closed frequent itemsets over a sliding window is dramatically reduced to that of mining transactions that can possibly cause boundary movements in the CET. Our experiments show that our algorithm performs much better than representative algorithms for the sate-of-the-art approaches.

Mining closed and maximal frequent subtrees from databases of labeled rooted trees

Tree structures are used extensively in domains such as computational biology, pattern recognition, XML databases, computer networks, and so on. One important problem in mining databases of trees is to find frequently occurring subtrees. Because of the combinatorial explosion, the number of frequent subtrees usually grows exponentially with the size of frequent subtrees and, therefore, mining all frequent subtrees becomes infeasible for large tree sizes. We present CMTreeMiner, a computationally efficient algorithm that discovers only closed and maximal frequent subtrees in a database of labeled rooted trees, where the rooted trees can be either ordered or unordered. The algorithm mines both closed and maximal frequent subtrees by traversing an enumeration tree that systematically enumerates all frequent subtrees. Several techniques are proposed to prune the branches of the enumeration tree that do not correspond to closed or maximal frequent subtrees. Heuristic techniques are used to arrange the order of computation so that relatively expensive computation is avoided as much as possible. We study the performance of our algorithm through extensive experiments, using both synthetic data and data sets from real applications. The experimental results show that our algorithm is very efficient in reducing the search space and quickly discovers all closed and maximal frequent subtrees.

Indexing and mining free trees

Tree structures are used extensively in domains such as computational biology, pattern recognition, computer networks, and so on. We present an indexing technique for free trees and apply this indexing technique to the problem of mining frequent subtrees. We first define a novel representation, the canonical form, for rooted trees and extend the definition to free trees. We also introduce another concept, the canonical string, as a simpler representation for free trees in their canonical forms. We then apply our tree indexing technique to the frequent subtree mining problem and present FreeTreeMiner, a computationally efficient algorithm that discovers all frequently occurring subtrees in a database of free trees. We study the performance and the scalability of our algorithms through extensive experiments based on both synthetic data and datasets from two real applications: a dataset of chemical compounds and a dataset of Internet multicast trees.

HybridTreeMiner: an efficient algorithm for mining frequent rooted trees and free trees using canonical forms

Tree structures are used extensively in domains such as computational biology, pattern recognition, XML databases, computer networks, and so on. In this paper, we present HybridTreeMiner, a computationally efficient algorithm that discovers all frequently occurring subtrees in a database of rooted unordered trees. The algorithm mines frequent subtrees by traversing an enumeration tree that systematically enumerates all subtrees. The enumeration tree is defined based on a novel canonical form for rooted unordered trees - the breadth-first canonical form (BFCF). By extending the definitions of our canonical form and enumeration tree to free trees, our algorithm can efficiently handle databases of free trees as well. We study the performance of our algorithms through extensive experiments based on both synthetic data and datasets from real applications. The experiments show that our algorithm is competitive in comparison to known rooted tree mining algorithms and is faster by one to two orders of magnitudes compared to a known algorithm for mining frequent free trees.

Canonical forms for labelled trees and their applications in frequent subtree mining

Tree structures are used extensively in domains such as computational biology, pattern recognition, XML databases, computer networks, and so on. In this paper, we first present two canonical forms for labelled rooted unordered trees–the breadth-first canonical form (BFCF) and the depth-first canonical form (DFCF). Then the canonical forms are applied to the frequent subtree mining problem. Based on the BFCF, we develop a vertical mining algorithm, RootedTreeMiner, to discover all frequently occurring subtrees in a database of labelled rooted unordered trees. The RootedTreeMiner algorithm uses an enumeration tree to enumerate all (frequent) labelled rooted unordered subtrees. Next, we extend the definition of the DFCF to labelled free trees and present an Apriori-like algorithm, FreeTreeMiner, to discover all frequently occurring subtrees in a database of labelled free trees. Finally, we study the performance and the scalability of our algorithms through extensive experiments based on both synthetic data and datasets from real applications.

Correction to "Mining Closed and Maximal Frequent Subtrees from Databases of Labeled Rooted Trees"

Tree structures are used extensively in domains such as computational biology, pattern recognition, XML databases, computer networks, and so on. One important problem in mining databases of trees is to find frequently occurring subtrees. Because of the combinatorial explosion, the number of frequent subtrees usually grows exponentially with the size of frequent subtrees and, therefore, mining all frequent subtrees becomes infeasible for large tree sizes. We present CMTreeMiner, a computationally efficient algorithm that discovers only closed and maximal frequent subtrees in a database of labeled rooted trees, where the rooted trees can be either ordered or unordered. The algorithm mines both closed and maximal frequent subtrees by traversing an enumeration tree that systematically enumerates all frequent subtrees. Several techniques are proposed to prune the branches of the enumeration tree that do not correspond to closed or maximal frequent subtrees. Heuristic techniques are used to arrange the order of computation so that relatively expensive computation is avoided as much as possible. We study the performance of our algorithm through extensive experiments, using both synthetic data and data sets from real applications. The experimental results show that our algorithm is very efficient in reducing the search space and quickly discovers all closed and maximal frequent subtrees.