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

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

MCRapper: Monte-Carlo Rademacher Averages for Poset Families and Approximate Pattern Mining

We present MCRapper, an algorithm for efficient computation of Monte-Carlo Empirical Rademacher Averages (MCERA) for families of functions exhibiting poset (e.g., lattice) structure, such as those that arise in many pattern mining tasks. The MCERA allows us to compute upper bounds to the maximum deviation of sample means from their expectations, thus it can be used to find both statistically-significant functions (i.e., patterns) when the available data is seen as a sample from an unknown distribution, and approximations of collections of high-expectation functions (e.g., frequent patterns) when the available data is a small sample from a large dataset. This feature is a strong improvement over previously proposed solutions that could only achieve one of the two. MCRapper uses upper bounds to the discrepancy of the functions to efficiently explore and prune the search space, a technique borrowed from pattern mining itself. To show the practical use of MCRapper, we employ it to develop an algorithm TFP-R for the task of True Frequent Pattern (TFP) mining. TFP-R gives guarantees on the probability of including any false positives (precision) and exhibits higher statistical power (recall) than existing methods offering the same guarantees. We evaluate MCRapper and TFP-R and show that they outperform the state-of-the-art for their respective tasks

Knowledge discovery techniques for transactional data model

In this work we give solutions to two key knowledge discovery problems for the Transactional Data model: Cluster analysis and Itemset mining. By knowledge discovery in context of these two problems, we specifically mean novel and useful ways of extracting clusters and itemsets from transactional data. Transactional Data model is widely used in a variety of applications. In cluster analysis the goal is to find clusters of similar transactions in the data with the collective properties of each cluster being unique. We propose the first clustering algorithm for transactional data which uses the latest model definition. All previously proposed algorithms did not use the important utility information in the data. Our novel technique effectively solves this problem. We also propose two new cluster validation metrics based on the criterion of high utility patterns. When comparing our technique with competing algorithms, we miss much fewer high utility patterns of importance than them. Itemset mining is the problem of searching for repeating patterns of high importance in the data. We show that the current model for itemset mining leads to information loss. It ignores the presence of clusters in the data. We propose a new itemset mining model which incorporates the cluster structure information. This allows the model to make predictions for future itemsets. We show that our model makes accurate predictions successfully, by discovering 30-40% future itemsets in most experiments on two benchmark datasets with negligible inaccuracies. There are no other present itemset prediction models, so accurate prediction is an accomplishment of ours. We provide further theoretical improvements in our model by making it capable of giving predictions for specific future windows by using time series forecasting. We also perform a detailed analysis of various clustering algorithms and study the effect of the Big Data phenomenon on them. This inspired us to further refine our model based on a classification problem design. This addition allows the mining of itemsets based on maximizing a customizable objective function made of different prediction metrics. The final framework design proposed by us is the first of its kind to make itemset predictions by using the cluster structure. It is capable of adapting the predictions to a specific future window and customizes the mining process to any specified prediction criterion. We create an implementation of the framework on a Web analytics data set, and notice that it successfully makes optimal prediction configuration choices with a high accuracy of 0.895