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

An efficient closed frequent itemset miner for the MOA stream mining system

Mining itemsets is a central task in data mining, both in the batch and the streaming paradigms. While robust, efficient, and well-tested implementations exist for batch mining, hardly any publicly available equivalent exists for the streaming scenario. The lack of an efficient, usable tool for the task hinders its use by practitioners and makes it difficult to assess new research in the area. To alleviate this situation, we review the algorithms described in the literature, and implement and evaluate the IncMine algorithm by Cheng, Ke, and Ng (2008) for mining frequent closed itemsets from data streams. Our implementation works on top of the MOA (Massive Online Analysis) stream mining framework to ease its use and integration with other stream mining tasks. We provide a PAC-style rigorous analysis of the quality of the output of IncMine as a function of its parameters; this type of analysis is rare in pattern mining algorithms. As a by-product, the analysis shows how one of the user-provided parameters in the original description can be removed entirely while retaining the performance guarantees. Finally, we experimentally confirm both on synthetic and real data the excellent performance of the algorithm, as reported in the original paper, and its ability to handle concept drift.Postprint (published version

Mining data quality rules based on T-dependence

Since their introduction in 1976, edit rules have been a standard tool in statistical analysis. Basically, edit rules are a compact representation of non-permitted combinations of values in a dataset. In this paper, we propose a technique to automatically find edit rules by use of the concept of T-dependence. We first generalize the traditional notion of lift, to that of T-lift, where stochastic independence is generalized to T-dependence. A combination of values is declared as an edit rule under a t-norm T if there is a strong negative correlation under T-dependence. We show several interesting properties of this approach. In particular, we show that under the minimum t-norm, edit rules can be computed efficiently by use of frequent pattern trees. Experimental results show that there is a weak to medium correlation in the rank order of edit rules obtained under T_M and T_P, indicating that the semantics of these kinds of dependencies are different

Efficient Discovery of Association Rules and Frequent Itemsets through Sampling with Tight Performance Guarantees

The tasks of extracting (top-$K$) Frequent Itemsets (FI's) and Association Rules (AR's) are fundamental primitives in data mining and database applications. Exact algorithms for these problems exist and are widely used, but their running time is hindered by the need of scanning the entire dataset, possibly multiple times. High quality approximations of FI's and AR's are sufficient for most practical uses, and a number of recent works explored the application of sampling for fast discovery of approximate solutions to the problems. However, these works do not provide satisfactory performance guarantees on the quality of the approximation, due to the difficulty of bounding the probability of under- or over-sampling any one of an unknown number of frequent itemsets. In this work we circumvent this issue by applying the statistical concept of \emph{Vapnik-Chervonenkis (VC) dimension} to develop a novel technique for providing tight bounds on the sample size that guarantees approximation within user-specified parameters. Our technique applies both to absolute and to relative approximations of (top-$K$) FI's and AR's. The resulting sample size is linearly dependent on the VC-dimension of a range space associated with the dataset to be mined. The main theoretical contribution of this work is a proof that the VC-dimension of this range space is upper bounded by an easy-to-compute characteristic quantity of the dataset which we call \emph{d-index}, and is the maximum integer $d$ such that the dataset contains at least $d$ transactions of length at least $d$ such that no one of them is a superset of or equal to another. We show that this bound is strict for a large class of datasets.Comment: 19 pages, 7 figures. A shorter version of this paper appeared in the proceedings of ECML PKDD 201