We are given a large database of customer transactions. Each transaction consists of items purchased by a customer in a visit. We present an e cient algorithm that generates all signi cant association rules between items in the database. The algorithm incorporates bu er management and novel estimation and pruning techniques. We also present results of applying this algorithm to sales data obtained from a large retailing company, which shows the e ectiveness of the algorithm.

Abstract. 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 introduce the problem of mining association rules in large relational tables containing both quantitative and categorical attributes. An example of such an association might be "10% of married people between age 50 and 60 have at least 2 cars". We deal with quantitative attributes by fine-partitioning the values of the attribute and then combining adjacent partitions as necessary. We introduce measures of partial completeness which quantify the information lost due to partitioning. A direct application of this technique can generate too many similar rules. We tackle this problem by using a "greater-than-expected-value" interest measure to identify the interesting rules in the output. We give an algorithm for mining such quantitative association rules. Finally, we describe the results of using this approach on a real-life dataset.

Data mining on large data warehouses is becoming increasingly important. In support of this trend, we consider a spectrum of architectural alternatives for coupling mining with database systems. These alternatives include: loose-coupling through a SQL cursor interface; encapsulation of a mining algorithm in a stored procedure; caching the data to a file system on-the-fly and mining; tight-coupling using primarily user-defined functions; and SQL implementations for processing in the DBMS. We comprehensively study the option of expressing the mining algorithm in the form of SQL queries using Association rule mining as a case in point. We consider four options in SQL-92 and six options in SQL enhanced with object-relational extensions (SQL-OR). Our evaluation of the different architectural alternatives shows that from a performance perspective, the Cache-Mine option is superior, although the performance of the SQL-OR option is within a factor of two. Both the Cache-Mine and the SQL-OR approaches incur a higher storage penalty than the loose-coupling approach which performance-wise is a factor of 3 to 4 worse than Cache-Mine. The SQL-92 implementations were too slow to qualify as a competitive option. We also compare these alternatives on the basis of qualitative factors like automatic parallelization, development ease, portability and inter-operability.

A range query applies an aggregation operation over all selected cells of an OLAP data cube where the selection is specified by providing ranges of values for numeric dimensions. We present fast algorithms for range queries for two types of aggregation operations: SUM and MAX. These two operations cover techniques required for most popular aggregation operations, such as those supported by SQL. For range-sum queries, the essential idea is to precompute some auxiliary information (prefix sums) that is used to answer ad hoc queries at run-time. By maintaining auxiliary information which is of the same size as the data cube, all range queries for a given cube can be answered in constant time, irrespective of the size of the sub-cube circumscribed by a query. Alternatively, one can keep auxiliary information which is 1/ b d of the size of the d -dimensional data cube. Response to a range query may now require access to some cells of the data cube in addition to the access to the auxiliary information, but the overall time complexity is typically reduced significantly. We also discuss how the precomputed information is incrementally updated by batching updates to the data cube. Finally, we present algorithms for choosing the subset of the data cube dimensions for which the auxiliary information is computed and the blocking factor to use for each such subset. Our approach to answering range-max queries is based on precomputed max over balanced hierarchical tree structures. We use a branch-and-bound-like procedure to speed up the finding of max in a region. We also show that with a branch-and-bound procedure, the average-case complexity is much smaller than the worst-case complexity.