Data mining applications place special requirements on clustering algorithms including: the ability to find clusters embedded in subspaces of high dimensional data, scalability, end-user comprehensibility of the results, non-presumption of any canonical data distribution, and insensitivity to the order of input records. We present CLIQUE, a clustering algorithm that satisfies each of these requirements. CLIQUE identifies dense clusters in subspaces of maximum dimensionality. It generates cluster descriptions in the form of DNF expressions that are minimized for ease of comprehension. It produces identical results irrespective of the order in which input records are presented and does not presume any specific mathematical form for data distribution. Through experiments, we show that CLIQUE efficiently finds accurate clusters in large high dimensional datasets.

We present a pattern-mining algorithm that scales roughly linearly in the number of maximal patterns embedded in a database irrespective of the length of the longest pattern. In comparison, previous algorithms based on Apriori scale exponentially with longest pattern length. Experiments on real data show that when the patterns are long, our algorithm is more efficient by an order of magnimaximal frequent itemset, Max-Miner’s output implicitly and concisely represents all frequent itemsets. Max-Miner is shown to result in two or more orders of magnitude in performance improvements over Apriori on some data-sets. On other data-sets where the patterns are not so long, the gains are more modest. In practice, Max-Miner is demonstrated to run in time that is roughly linear in the number of maximal frequent itemsets and the size of the database, irrespective of the size of the longest frequent itemset. tude or more. 1.

In this paper, we address the problem of finding frequent itemsets in a database. Using the closed itemset lattice framework, we show that this problem can be reduced to the problem of finding frequent closed itemsets. Based on this statement, we can construct efficient data mining algorithms by limiting the search space to the closed itemset lattice rather than the subset lattice. Moreover, we show that the set of all frequent closed itemsets suffices to determine a reduced set of association rules, thus addressing another important data mining problem: limiting the number of rules produced without information loss. We propose a new algorithm, called A-Close, using a closure mechanism to find frequent closed itemsets. We realized experiments to compare our approach to the commonly used frequent itemset search approach. Those experiments showed that our approach is very valuable for dense and/or correlated data that represent an important part of existing databases.

The set of frequent closed itemsets uniquely determines the exact frequency of all itemsets, yet it can be orders of magnitude smaller than the set of all frequent itemsets. In this paper we present CHARM, an efficient algorithm for mining all frequent closed itemsets. It enumerates closed sets using a dual itemset-tidset search tree, using an efficient hybrid search that skips many levels. It also uses a technique called diffsets to reduce the memory footprint of intermediate computations. Finally it uses a fast hash-based approach to remove any “non-closed” sets found during computation. An extensive experimental evaluation on a number of real and synthetic databases shows that CHARM significantly outperforms previous methods. It is also linearly scalable in the number of transactions.

We present a new algorithm for mining maximal frequent itemsets from a transactional database. Our algorithm is especially efficient when the itemsets in the database are very long. The search strategy of our algorithm integrates a depth-first traversal of the itemset lattice with effective pruning mechanisms. Our implementation of the search strategy combines a vertical bitmap representation of the database with an efficient relative bitmap compression schema. In a thorough experimental analysis of our algorithm on real data, we isolate the effect of the individual components of the algorithm. Our performance numbers show that our algorithm outperforms previous work by a factor of three to five. 1

The traditional association rule mining framework produces many redundant rules. The extent of redundancy is a lot larger than previously suspected. We present a new framework for associations based on the novel concept of closed frequent itemsets. The number of non-redundant rules produced by the new approach is exponentially (in the length of the longest frequent itemset) smaller than the rule set from the traditional approach. Experiments using several "hard" real and synthetic databases confirm the utility of our framework in terms of reduction in the number of rules presented to the user, and in terms of time.

Association rule discovery has emerged as an important problem in knowledge discovery and data mining. The association mining task consists of identifying the frequent itemsets, and then forming conditional implication rules among them. In this paper we present efficient algorithms for the discovery of frequent itemsets, which forms the compute intensive phase of the task. The algorithms utilize the structural properties of frequent itemsets to facilitate fast discovery. The items are organized into a subset lattice search space, which is decomposed into small independent chunks or sub-lattices, which can be solved in memory. Ecient lattice traversal techniques are presented, which quickly identify all the long frequent itemsets, and their subsets if required. We also present the effect of using different database layout schemes combined with the proposed decomposition and traversal techniques. We experimentally compare the new algorithms against the previous approaches, obtaining ...

Constraint-based rule miners find all rules in a given dataset meeting user-specified constraints such as minimum support and confidence. We describe a new algorithm that directly exploits all user-specified constraints including minimum support, minimum confidence, and a new constraint that ensures every mined rule offers a predictive advantage over any of its simplifications. Our algorithm maintains efficiency even at low supports on data that is dense (e.g. relational data). Previous approaches such as Apriori and its variants exploit only the minimum support constraint, and as a result are ineffective on dense data due to a combinatorial explosion of “frequent itemsets”.

In this paper we propose algorithms for generation of frequent itemsets by successive construction of the nodes of a lexicographic tree of itemsets. We discuss di erent strategies in generation and traversal of the lexicographic tree such as breadth- rst search, depth- rst search or a combination of the two. These techniques provide di erent trade-o s in terms of the I/O, memory and computational time requirements. We use the hierarchical structure of the lexicographic tree to successively project transactions at each node of the lexicographic tree, and use matrix counting on this reduced set of transactions for nding frequent itemsets. We tested our algorithm on both real and synthetic data. We provide an implementation of the tree projection method which is up to one order of magnitude faster than other recent techniques in the literature. The algorithm has a well structured data access pattern which provides data locality and reuse of data for multiple levels of the cache. We also discuss methods for parallelization of the

This paper presents a simple unsupervised learning algorithm for recognizing synonyms, based on statistical data acquired by querying a Web search engine. The algorithm, called PMI-IR, uses Pointwise Mutual Information (PMI) and Information Retrieval (IR) to measure the similarity of pairs of words. PMI-IR is empirically evaluated using 80 synonym test questions from the Test of English as a Foreign Language (TOEFL) and 50 synonym test questions from a collection of tests for students of English as a Second Language (ESL). On both tests, the algorithm obtains a score of 74%. PMI-IR is contrasted with Latent Semantic Analysis (LSA), which achieves a score of 64% on the same 80 TOEFL questions. The paper discusses potential applications of the new unsupervised learning algorithm and some implications of the results for LSA and LSI (Latent Semantic Indexing).