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.
Mining frequent itemsets is an essential problem in data mining and plays an important role in many data mining applications. In recent years, some itemset representations based on node sets have been proposed, which have shown to be very efficient for mining frequent itemsets. In this paper, we propose DiffNodeset, a novel and more efficient itemset representation, for mining frequent itemsets. Based on the DiffNodeset structure, we present an efficient algorithm, named dFIN, to mining frequent itemsets. To achieve high efficiency, dFIN finds frequent itemsets using a set-enumeration tree wit…
In this paper we present a new error bound on sampling algorithms for frequent itemsets mining. We show that the new bound is asymptotically tighter than the state-of-art bounds, i.e., given the chosen samples, for small enough error probability, the new error bound is roughly half of the existing bounds. Based on the new bound, we give a new approximation algorithm, which is much simpler compared to the existing approximation algorithms, but can also guarantee the worst approximation error with precomputed sample size. We also give an algorithm which can approximate the top-$k$ frequent items…
National University of Computer and Emerging Sciences（国家计算机与新兴科学大学）
Mining frequent itemset using bit-vector representation approach is very efficient for dense type datasets, but highly inefficient for sparse datasets due to lack of any efficient bit-vector projection technique. In this paper we present a novel efficient bit-vector projection technique, for sparse and dense datasets. To check the efficiency of our bit-vector projection technique, we present a new frequent itemset mining algorithm Ramp (Real Algorithm for Mining Patterns) build upon our bit-vector projection technique. The performance of the Ramp is compared with the current best (all, maximal…
Association rules is a very important part of data mining. It is used to find the interesting patterns from transaction databases. Apriori algorithm is one of the most classical algorithms of association rules, but it has the bottleneck in efficiency. In this article, we proposed a prefixed-itemset-based data structure for candidate itemset generation, with the help of the structure we managed to improve the efficiency of the classical Apriori algorithm.
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 a…
Brown University（布朗大学）；University of Southern Denmark（南丹麦大学）
Frequent Itemsets (FIs) mining is a fundamental primitive in data mining. It requires to identify all itemsets appearing in at least a fraction $θ$ of a transactional dataset $\mathcal{D}$. Often though, the ultimate goal of mining $\mathcal{D}$ is not an analysis of the dataset \emph{per se}, but the understanding of the underlying process that generated it. Specifically, in many applications $\mathcal{D}$ is a collection of samples obtained from an unknown probability distribution $π$ on transactions, and by extracting the FIs in $\mathcal{D}$ one attempts to infer itemsets that are frequent…
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 spec…
FAST-National University of Computer and Emerging Sciences（FAST-国立计算机与新兴科学大学）
In this paper we present a novel hybrid (arraybased layout and vertical bitmap layout) database representation approach for mining complete Maximal Frequent Itemset (MFI) on sparse and large datasets. Our work is novel in terms of scalability, item search order and two horizontal and vertical projection techniques. We also present a maximal algorithm using this hybrid database representation approach. Different experimental results on real and sparse benchmark datasets show that our approach is better than previous state of art maximal algorithms.
FAST-National University of Computer and Emerging Science（FAST-国家计算机与新兴科学大学）
Real world datasets are sparse, dirty and contain hundreds of items. In such situations, discovering interesting rules (results) using traditional frequent itemset mining approach by specifying a user defined input support threshold is not appropriate. Since without any domain knowledge, setting support threshold small or large can output nothing or a large number of redundant uninteresting results. Recently a novel approach of mining only N-most/Top-K interesting frequent itemsets has been proposed, which discovers the top N interesting results without specifying any user defined support thre…
BESTMOD Laboratory（BESTMOD实验室）；Institut Supérieur de Gestion（高等管理学院）
Mining association rules is a task of data mining, which extracts knowledge in the form of significant implication relation of useful items (objects) from a database. Mining multilevel association rules uses concept hierarchies, also called taxonomies and defined as relations of type 'is-a' between objects, to extract rules that items belong to different levels of abstraction. These rules are more useful, more refined and more interpretable by the user. Several algorithms have been proposed in the literature to discover the multilevel association rules. In this article, we are interested in th…
Frequent itemset mining has emerged as a fundamental problem in data mining and plays an important role in many data mining tasks, such as association analysis, classification, etc. In the framework of frequent itemset mining, the results are itemsets that are frequent in the whole database. However, in some applications, such recommendation systems and social networks, people are more interested in finding out the items that occur with some user-specified itemsets (query itemsets) most frequently in a database. In this paper, we address the problem by proposing a new mining task named top-k c…
The monotone duality problem is defined as follows: Given two monotone formulas f and g in iredundant DNF, decide whether f and g are dual. This problem is the same as duality testing for hypergraphs, that is, checking whether a hypergraph H consists of precisely all minimal transversals of a simple hypergraph G. By exploiting a recent problem-decomposition method by Boros and Makino (ICALP 2009), we show that duality testing for hypergraphs, and thus for monotone DNFs, is feasible in DSPACE[log^2 n], i.e., in quadratic logspace. As the monotone duality problem is equivalent to a number of pro…
Mining association rules is a popular and well researched method for discovering interesting relations between variables in large databases. A practical problem is that at medium to low support values often a large number of frequent itemsets and an even larger number of association rules are found in a database. A widely used approach is to gradually increase minimum support and minimum confidence or to filter the found rules using increasingly strict constraints on additional measures of interestingness until the set of rules found is reduced to a manageable size. In this paper we describe a…
Here, we present a novel algorithm for frequent itemset mining for streaming data (FIM-SD). For the past decade, various FIM-SD methods in one-pass approximation settings have been developed to approximate the frequency of each itemset. These approaches can be categorized into two approximation types: parameter-constrained (PC) mining and resource-constrained (RC) mining. PC methods control the maximum error that can be included in the frequency based on a pre-defined parameter. In contrast, RC methods limit the maximum memory consumption based on resource constraints. However, the existing PC…
National University of Computer and Emerging Sciences（国立计算机与新兴科学大学）
Maximal frequent patterns superset checking plays an important role in the efficient mining of complete Maximal Frequent Itemsets (MFI) and maximal search space pruning. In this paper we present a new indexing approach, FastLMFI for local maximal frequent patterns (itemset) propagation and maximal patterns superset checking. Experimental results on different sparse and dense datasets show that our work is better than the previous well known progressive focusing technique. We have also integrated our superset checking approach with an existing state of the art maximal itemsets algorithm Mafia, …
Set intersection is the core in a variety of problems, e.g. frequent itemset mining and sparse boolean matrix multiplication. It is well-known that large speed gains can, for some computational problems, be obtained by using a graphics processing unit (GPU) as a massively parallel computing device. However, GPUs require highly regular control flow and memory access patterns, and for this reason previous GPU methods for intersecting sets have used a simple bitmap representation. This representation requires excessive space on sparse data sets. In this paper we present a novel data layout, "BatM…
While there has been a lot of work on finding frequent itemsets in transaction data streams, none of these solve the problem of finding similar pairs according to standard similarity measures. This paper is a first attempt at dealing with this, arguably more important, problem. We start out with a negative result that also explains the lack of theoretical upper bounds on the space usage of data mining algorithms for finding frequent itemsets: Any algorithm that (even only approximately and with a chance of error) finds the most frequent k-itemset must use space Omega(min{mb,n^k,(mb/phi)^k}) bi…
Given a database, a common problem is to find the pairs or $k$-tuples of items that frequently co-occur. One specific problem is to create a small space "sketch" of the data that records which $k$-tuples appear in more than an $ε$ fraction of rows of the database. We improve the lower bound of Liberty, Mitzenmacher, and Thaler [LMT14], showing that $Ω(\frac{1}εd \log (εd))$ bits are necessary even in the case of $k=2$. This matches the sampling upper bound for all $ε\geq 1/d^{.99}$, and (in the case of $k=2$) another trivial upper bound for $ε= 1/d$.
In the last few years, the amount of collected data, in various computer science applications, has grown considerably. These large volumes of data need to be analyzed in order to extract useful hidden knowledge. This work focuses on association rule extraction. This technique is one of the most popular in data mining. Nevertheless, the number of extracted association rules is often very high, and many of them are redundant. In this paper, we propose a new algorithm, called PRINCE. Its main feature is the construction of a partially ordered structure for extracting subsets of association rules,…
