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

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

Model-based probabilistic frequent itemset mining

Data uncertainty is inherent in emerging applications such as location-based services, sensor monitoring systems, and data integration. To handle a large amount of imprecise information, uncertain databases have been recently developed. In this paper, we study how to efficiently discover frequent itemsets from large uncertain databases, interpreted under the Possible World Semantics. This is technically challenging, since an uncertain database induces an exponential number of possible worlds. To tackle this problem, we propose a novel methods to capture the itemset mining process as a probability distribution function taking two models into account: the Poisson distribution and the normal distribution. These model-based approaches extract frequent itemsets with a high degree of accuracy and support large databases. We apply our techniques to improve the performance of the algorithms for (1) finding itemsets whose frequentness probabilities are larger than some threshold and (2) mining itemsets with the {Mathematical expression} highest frequentness probabilities. Our approaches support both tuple and attribute uncertainty models, which are commonly used to represent uncertain databases. Extensive evaluation on real and synthetic datasets shows that our methods are highly accurate and four orders of magnitudes faster than previous approaches. In further theoretical and experimental studies, we give an intuition which model-based approach fits best to different types of data sets. © 2012 The Author(s).published_or_final_versio

An Efficient Rigorous Approach for Identifying Statistically Significant Frequent Itemsets

As advances in technology allow for the collection, storage, and analysis of vast amounts of data, the task of screening and assessing the significance of discovered patterns is becoming a major challenge in data mining applications. In this work, we address significance in the context of frequent itemset mining. Specifically, we develop a novel methodology to identify a meaningful support threshold s* for a dataset, such that the number of itemsets with support at least s* represents a substantial deviation from what would be expected in a random dataset with the same number of transactions and the same individual item frequencies. These itemsets can then be flagged as statistically significant with a small false discovery rate. We present extensive experimental results to substantiate the effectiveness of our methodology.Comment: A preliminary version of this work was presented in ACM PODS 2009. 20 pages, 0 figure

Mining Frequent Itemsets over Uncertain Databases

In recent years, due to the wide applications of uncertain data, mining frequent itemsets over uncertain databases has attracted much attention. In uncertain databases, the support of an itemset is a random variable instead of a fixed occurrence counting of this itemset. Thus, unlike the corresponding problem in deterministic databases where the frequent itemset has a unique definition, the frequent itemset under uncertain environments has two different definitions so far. The first definition, referred as the expected support-based frequent itemset, employs the expectation of the support of an itemset to measure whether this itemset is frequent. The second definition, referred as the probabilistic frequent itemset, uses the probability of the support of an itemset to measure its frequency. Thus, existing work on mining frequent itemsets over uncertain databases is divided into two different groups and no study is conducted to comprehensively compare the two different definitions. In addition, since no uniform experimental platform exists, current solutions for the same definition even generate inconsistent results. In this paper, we firstly aim to clarify the relationship between the two different definitions. Through extensive experiments, we verify that the two definitions have a tight connection and can be unified together when the size of data is large enough. Secondly, we provide baseline implementations of eight existing representative algorithms and test their performances with uniform measures fairly. Finally, according to the fair tests over many different benchmark data sets, we clarify several existing inconsistent conclusions and discuss some new findings.Comment: VLDB201