Mining Top-K Frequent Itemsets Through Progressive Sampling

We study the use of sampling for efficiently mining the top-K frequent itemsets of cardinality at most w. To this purpose, we define an approximation to the top-K frequent itemsets to be a family of itemsets which includes (resp., excludes) all very frequent (resp., very infrequent) itemsets, together with an estimate of these itemsets' frequencies with a bounded error. Our first result is an upper bound on the sample size which guarantees that the top-K frequent itemsets mined from a random sample of that size approximate the actual top-K frequent itemsets, with probability larger than a specified value. We show that the upper bound is asymptotically tight when w is constant. Our main algorithmic contribution is a progressive sampling approach, combined with suitable stopping conditions, which on appropriate inputs is able to extract approximate top-K frequent itemsets from samples whose sizes are smaller than the general upper bound. In order to test the stopping conditions, this approach maintains the frequency of all itemsets encountered, which is practical only for small w. However, we show how this problem can be mitigated by using a variation of Bloom filters. A number of experiments conducted on both synthetic and real bench- mark datasets show that using samples substantially smaller than the original dataset (i.e., of size defined by the upper bound or reached through the progressive sampling approach) enable to approximate the actual top-K frequent itemsets with accuracy much higher than what analytically proved.Comment: 16 pages, 2 figures, accepted for presentation at ECML PKDD 2010 and publication in the ECML PKDD 2010 special issue of the Data Mining and Knowledge Discovery journa

Conditional heavy hitters : detecting interesting correlations in data streams

The notion of heavy hitters—items that make up a large fraction of the population—has been successfully used in a variety of applications across sensor and RFID monitoring, network data analysis, event mining, and more. Yet this notion often fails to capture the semantics we desire when we observe data in the form of correlated pairs. Here, we are interested in items that are conditionally frequent: when a particular item is frequent within the context of its parent item. In this work, we introduce and formalize the notion of conditional heavy hitters to identify such items, with applications in network monitoring and Markov chain modeling. We explore the relationship between conditional heavy hitters and other related notions in the literature, and show analytically and experimentally the usefulness of our approach. We introduce several algorithm variations that allow us to efficiently find conditional heavy hitters for input data with very different characteristics, and provide analytical results for their performance. Finally, we perform experimental evaluations with several synthetic and real datasets to demonstrate the efficacy of our methods and to study the behavior of the proposed algorithms for different types of data

Exploring Decomposition for Solving Pattern Mining Problems

This article introduces a highly efficient pattern mining technique called Clustering-based Pattern Mining (CBPM). This technique discovers relevant patterns by studying the correlation between transactions in the transaction database based on clustering techniques. The set of transactions is first clustered, such that highly correlated transactions are grouped together. Next, we derive the relevant patterns by applying a pattern mining algorithm to each cluster. We present two different pattern mining algorithms, one applying an approximation-based strategy and another based on an exact strategy. The approximation-based strategy takes into account only the clusters, whereas the exact strategy takes into account both clusters and shared items between clusters. To boost the performance of the CBPM, a GPU-based implementation is investigated. To evaluate the CBPM framework, we perform extensive experiments on several pattern mining problems. The results from the experimental evaluation show that the CBPM provides a reduction in both the runtime and memory usage. Also, CBPM based on the approximate strategy provides good accuracy, demonstrating its effectiveness and feasibility. Our GPU implementation achieves significant speedup of up to 552× on a single GPU using big transaction databases.publishedVersio

SOTXTSTREAM: Density-based self-organizing clustering of text streams

A streaming data clustering algorithm is presented building upon the density-based selforganizing stream clustering algorithm SOSTREAM. Many density-based clustering algorithms are limited by their inability to identify clusters with heterogeneous density. SOSTREAM addresses this limitation through the use of local (nearest neighbor-based) density determinations. Additionally, many stream clustering algorithms use a two-phase clustering approach. In the first phase, a micro-clustering solution is maintained online, while in the second phase, the micro-clustering solution is clustered offline to produce a macro solution. By performing self-organization techniques on micro-clusters in the online phase, SOSTREAM is able to maintain a macro clustering solution in a single phase. Leveraging concepts from SOSTREAM, a new density-based self-organizing text stream clustering algorithm, SOTXTSTREAM, is presented that addresses several shortcomings of SOSTREAM. Gains in clustering performance of this new algorithm are demonstrated on several real-world text stream datasets