We are given a large database of customer transactions, where each transaction consists of customer-id, transaction time, and the items bought in the transaction. We introduce the problem of mining sequential patterns over such databases. We present three algorithms to solve this problem, and empirically evaluate their performance using synthetic data. Two of the proposed algorithms, AprioriSome and AprioriAll, have comparable performance, albeit AprioriSome performs a little better when the minimum number of customers that must support a sequential pattern is low. Scale-up experiments show that both AprioriSome and AprioriAll scale linearly with the number of customer transactions. They also have excellent scale-up properties with respect to the number of transactions per customer and the number of items in a transaction. 1 Introduction Database mining is motivated by the decision support problem faced by most large retail organizations. Progress in bar-code technology has made it po...

Abstract. The problem of mining sequential patterns was recently introduced in [3]. We are given a database of sequences, where each sequence is a list of transactions ordered by transaction-time, and each transaction is a set of items. The problem is to discover all sequential patterns with a user-speci ed minimum support, where the support of a pattern is the number of data-sequences that contain the pattern. An example of a sequential pattern is \5 % of customers bought `Foundation' and `Ringworld ' in one transaction, followed by `Second Foundation ' in a later transaction". We generalize the problem as follows. First, we add time constraints that specify a minimum and/or maximum time period between adjacent elements in a pattern. Second, we relax the restriction that the items in an element of a sequential pattern must come from the same transaction, instead allowing the items to be present in a set of transactions whose transaction-times are within a user-speci ed time window. Third, given a user-de ned taxonomy (is-a hierarchy) on items, we allow sequential patterns to include items across all levels of the taxonomy. We present GSP, a new algorithm that discovers these generalized sequential patterns. Empirical evaluation using synthetic and real-life data indicates that GSP is much faster than the AprioriAll algorithm presented in [3]. GSP scales linearly with the number of data-sequences, and has very good scale-up properties with respect to the average datasequence size. 1

We present an efficient indexing method to locate 1-dimensional subsequences witbin a collection of sequences, such that the subsequences match a given (query) pattern within a specified tolerance. The idea is to map each data sequence into a small set of multidimensional rectangles in feature space. Then, these rectangles can be readily indexed using traditional spatial access methods, like the R*-tree [9]. In more deteil, we use a sliding window over the data sequence and extract its features; the result is a trail in feature space. We propose an efficient and effective algorithm to divide such trails into sub-trails, which are subsequently represented by their Minimum Bounding Rectangles (MBRs). We also examine queries of varying lengths, and we show how to handle each case efficiently. We implemented our method and carried out experiments on synthetic and real data (stock price movements). We compared the method to sequential scanning, which is the only obvious competitor. The results were excellent: our method accelerated the search time from 3 times up to 100 times.

We propose an indexing method for time sequences for processing similarity queries. We use the Discrete Fourier Transform (DFT) to map time sequences to the frequency domain, the crucial observation being that, for most sequences of practical interest, only the first few frequencies are strong. Another important observation is Parseval's theorem, which specifies that the Fourier transform preserves the Euclidean distance in the time or frequency domain. Having thus mapped sequences to a lower-dimensionality space by using only the first few Fourier coe cients, we use R-trees to index the sequences and e ciently answer similarity queries. We provide experimental results which show that our method is superior to search based on sequential scanning. Our experiments show that a few coefficients (1-3) are adequate to provide good performance. The performance gain of our method increases with the number and length of sequences.

We survey the current techniques to cope with the problem of string matching allowing errors. This is becoming a more and more relevant issue for many fast growing areas such as information retrieval and computational biology. We focus on online searching and mostly on edit distance, explaining the problem and its relevance, its statistical behavior, its history and current developments, and the central ideas of the algorithms and their complexities. We present a number of experiments to compare the performance of the different algorithms and show which are the best choices according to each case. We conclude with some future work directions and open problems. 1

*To whom correspondence should be addressed. Running head: Composing and enacting workflows using Taverna Motivation: In silico experiments in bioinformatics involve the co-ordinated use of computational tools and information repositories. A growing number of these resources are being made available with programmatic access in the form of Web services. Bioinformatics scientists will need to orchestrate these Web services in workflows as part of their analyses. Results: The Taverna project has developed a tool for the composition and enactment of bioinformatics workflows for the life sciences community. The tool includes a workbench application which provides a graphical user interface for the composition of workflows. These workflows are written in a new language called the Simple conceptual unified flow language (Scufl), where by each step within a workflow represents one atomic task. Two examples are used to illustrate the ease by with which in silico experiments can be represented as Scufl workflows using the workbench application. Availability: The Taverna workflow system is available as open source and can be downloaded with example Scufl workflows from

A new hidden Markov model method (SAM-T98) for nding remote homologs of protein sequences is described and evaluated. The method begins with a single target sequence and iteratively builds a hidden Markov model (hmm) from the sequence and homologs found using the hmm for database search. SAM-T98 is also used to construct model libraries automatically from sequences in structural databases. We evaluate the SAM-T98 method with four datasets. Three of the test sets are fold-recognition tests, where the correct answers are determined by structural similarity. The fourth uses a curated database. The method is compared against wu-blastp and against double-blast, a two-step method similar to ISS, but using blast instead of fasta. Results SAM-T98 had the fewest errors in all tests| dramatically so for the fold-recognition tests. At the minimum-error point on the SCOP-domains test, SAM-T98 got 880 true positives and 68 false positives, double-blast got 533 true positives with 71 false positives, and wu-blastp got 353 true positives with 24 false positives. The method is optimized to recognize superfamilies, and would require parameter adjustment to be used to nd family or fold relationships. One key to the performance of the hmm method is a new score-normalization technique that compares the score to the score with a reversed model rather than to a uniform null model. Availability A World Wide Web server, as well as information on obtaining the Sequence Alignment and PREPRINT to appear in Bioinformatics, 1999

. We explore the effect of dimensionality on the "nearest neighbor " problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective, we present empirical results on both real and synthetic data sets that demonstrate that this effect can occur for as few as 10-15 dimensions. These results should not be interpreted to mean that high-dimensional indexing is never meaningful; we illustrate this point by identifying some high-dimensional workloads for which this effect does not occur. However, our results do emphasize that the methodology used almost universally in the database literature to evaluate high-dimensional indexing techniques is flawed, and should be modified. In particular, most such techniques proposed in the literature are not evaluated versus simple...

Motivation: Genomics and proteomics studies routinely depend on homology searches based on the strategy of finding short seed matches which are then extended. The exploding genomic data growth presents a dilemma for DNA homology search techniques: increasing seed size decreases sensitivity whereas decreasing seed size slows down computation. Results: We present a new homology search algorithm "PatternHunter" that uses a novel seed model for increased sensitivity and new hit-processing techniques for significantly increased speed. At Blast levels of sensitivity, PatternHunter is able to find homologies between sequences as large as human chromosomes, in mere hours on a desktop. Availability: PatternHunter is available at

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