Itemset mining is one of the most studied tasks in knowledge discovery. In this paper we analyze the computational complexity of three central itemset mining problems. We prove that mining confident rules with a given item in the head is NP-hard. We prove that mining high utility itemsets is NP-hard. We finally prove that mining maximal or closed itemsets is coNP-hard as soon as the users can specify constraints on the kind of itemsets they are interested in.
CNRS（法国国家科学研究中心）；University of Montpellier（蒙彼利埃大学）；University of Oran 1（奥兰第一大学）；CRIL, University of Artois（阿尔图瓦大学CRIL实验室）
Discovering significant itemsets is one of the fundamental problems in data mining. It has recently been shown that constraint programming is a flexible way to tackle data mining tasks. With a constraint programming approach, we can easily express and efficiently answer queries with users constraints on items. However, in many practical cases it is possible that queries also express users constraints on the dataset itself. For instance, asking for a particular itemset in a particular part of the dataset. This paper presents a general constraint programming model able to handle any kind of quer…
Simula Research Laboratory（西穆拉研究实验室）；LIRMM, University of Montpellier, CNRS（蒙彼利埃大学法国国家科学研究中心蒙彼利埃信息与机器人学实验室）
The problem of discovering frequent itemsets including rare ones has received a great deal of attention. The mining process needs to be flexible enough to extract frequent and rare regularities at once. On the other hand, it has recently been shown that constraint programming is a flexible way to tackle data mining tasks. In this paper, we propose a constraint programming approach for mining itemsets with multiple minimum supports. Our approach provides the user with the possibility to express any kind of constraints on the minimum item supports. An experimental analysis shows the practical ef…
Ramp: Fast Frequent Itemset Mining with Efficient Bit-Vector Projection Technique
National University of Computer and Emerging Sciences（国家计算机与新兴科学大学）
基于位向量表示的频繁项集挖掘方法对于密集数据集是非常有效的，但对于稀疏数据集，由于缺乏有效的位向量投影技术，挖掘效率很低。在本文中，我们提出了一种新的有效的位向量投影技术，稀疏和密集的数据集。为了检验我们的位向量投影技术的效率，我们提出了一个新的频繁项集挖掘算法Ramp（Real Algorithm for Mining Patterns）。在基准数据集上将Ramp算法与目前最好的频繁项集挖掘算法（全频繁项集、最大频繁项集和闭频繁项集）进行了性能比较。在稀疏数据集和密集数据集上的不同实验结果表明，使用Ramp挖掘频繁项集的速度比目前最好的算法都要快，这表明了位向量投影思想的有效性。我们还提出了一个新的本地最大频繁项集传播和最大项集超集检查方法FastLMFI，建立在我们的PBR位向量投影技术。我们不同的计算实验表明，使用FastLMFI的项集最大值检查是快速和有效的比以前将已知的渐进聚焦方法。
So far, most of association rule minings have considered about positive association rules based on frequent itemsets in databases[2,5-7], but they have not considered the problem of mining negative association rules correlated with frequent and infrequent itemsets. Negative association rule mining is much more difficult than positive association rule mining because it needs infrequent itemsets, and only the rare association rule mining which is a kind of negative association rule minings has been studied. This paper presents a mathematical model to mine positive and negative association rules …
In this paper we propose a R-step approximation to solve frequent itemset mining on quantum hardware like quantum annealing or QAOA. The idea is to search for the set of items where the minimal 2-item frequency is maximal. This can be represented as a maximum clique problem.
University of Oran 1（奥兰第一大学）；University of Montpellier（蒙彼利埃大学）；University of Caen（卡昂大学）
Discovering the set of closed frequent patterns is one of the fundamental problems in Data Mining. Recent Constraint Programming (CP) approaches for declarative itemset mining have proven their usefulness and flexibility. But the wide use of reified constraints in current CP approaches raises many difficulties to cope with high dimensional datasets. This paper proposes CLOSED PATTERN global constraint which does not require any reified constraints nor any extra variables to encode efficiently the Closed Frequent Pattern Mining (CFPM) constraint. CLOSED-PATTERN captures the particular semantics…
In this paper, we propose an algorithm of searching for both positive and negative itemsets of interest which should be given at the first stage for positive and negative association rules mining. Traditional association rule mining algorithms extract positive association rules based on frequent itemsets, for which the frequent itemsets, i.e. only positive itemsets of interest are searched. Further, there are useful itemsets among the frequent itemsets pruned from the traditional algorithms to reduce the search space, for mining of negative association rules. Therefore, the traditional algorit…
Frequent itemset mining is a popular data mining technique. Apriori, Eclat, and FP-Growth are among the most common algorithms for frequent itemset mining. Considerable research has been performed to compare the relative performance between these three algorithms, by evaluating the scalability of each algorithm as the dataset size increases. While scalability as data size increases is important, previous papers have not examined the performance impact of similarly sized datasets that contain different itemset characteristics. This paper explores the effects that two dataset characteristics can…
Jinan University（暨南大学）；Guangdong University of Technology（广东工业大学）
Traditional high-utility itemset mining (HUIM) aims to determine all high-utility itemsets (HUIs) that satisfy the minimum utility threshold (\textit{minUtil}) in transaction databases. However, in most applications, not all HUIs are interesting because only specific parts are required. Thus, targeted mining based on user preferences is more important than traditional mining tasks. This paper is the first to propose a target-based HUIM problem and to provide a clear formulation of the targeted utility mining task in a quantitative transaction database. A tree-based algorithm known as Target-ba…
The Apriori algorithm is a classical algorithm for the frequent itemset mining problem. A significant bottleneck in Apriori is the number of I/O operation involved, and the number of candidates it generates. We investigate the role of LSH techniques to overcome these problems, without adding much computational overhead. We propose randomized variations of Apriori that are based on asymmetric LSH defined over Hamming distance and Jaccard similarity.
An Efficient Data Structure for Fast Mining High Utility Itemsets
在本文中，我们提出了一种新的数据结构称为PUN-list，它既保持了项目集的效用信息和效用上界，以方便挖掘高效用项目集的处理。基于PUN-Lists，提出了一种快速挖掘高效用项集的方法MIP（Mining high utility Itemset using PUN-Lists）。MIP的效率是通过三种技术来实现的。首先，项目集由一种高度压缩的数据结构PUN-列表表示，避免了代价高昂的重复效用计算。其次，通过扫描项集的PUN-列表可以有效地计算项集的效用，并且通过短项集的PUN-列表可以快速构造长项集的PUN-列表。第三，通过采用效用上界躺在PUN列表作为修剪策略，MIP直接发现高效用项目集的搜索空间，称为集合枚举树，而不产生大量的候选人。在各种合成数据集和真实数据集上的大量实验表明，PUN-list是非常有效的，因为MIP比最近报道的算法平均快至少一个数量级。
One of the biggest problems in itemset mining is the requirement of developing a data structure or algorithm, every time a user wants to extract a different type of itemsets. To overcome this, we propose a method, called Generic Itemset Mining based on Reinforcement Learning (GIM-RL), that offers a unified framework to train an agent for extracting any type of itemsets. In GIM-RL, the environment formulates iterative steps of extracting a target type of itemsets from a dataset. At each step, an agent performs an action to add or remove an item to or from the current itemset, and then obtains f…
Mining frequent itemsets from a transaction database has emerged as a fundamental problem in data mining and committed itself as a building block for many pattern mining tasks. In this paper, we present a general technique to reduce support checking time in existing depth-first search generate-and-test schemes such as Eclat/dEclat and PrePost+. Our technique allows infrequent candidate itemsets to be detected early. The technique is based on an early-stopping criterion and is general enough to be applicable in many frequent itemset mining algorithms. We have applied the technique to two TID-li…
This paper presents a study of the characteristics of transactional databases used in frequent itemset mining. Such characterizations have typically been used to benchmark and understand the data mining algorithms working on these databases. The aim of our study is to give a picture of how diverse and representative these benchmarking databases are, both in general but also in the context of particular empirical studies found in the literature. Our proposed list of metrics contains many of the existing metrics found in the literature, as well as new ones. Our study shows that our list of metri…
Data mining is a widely used technology for various real-life applications of data analytics and is important to discover valuable association rules in transaction databases. Interesting itemset mining plays an important role in many real-life applications, such as market, e-commerce, finance, and medical treatment. To date, various data mining algorithms based on frequent patterns have been widely studied, but there are a few algorithms that focus on mining infrequent or rare patterns. In some cases, infrequent or rare itemsets and rare association rules also play an important role in real-li…
Frequent Pattern Mining is a one field of the most significant topics in data mining. In recent years, many algorithms have been proposed for mining frequent itemsets. A new algorithm has been presented for mining frequent itemsets based on N-list data structure called Prepost algorithm. The Prepost algorithm is enhanced by implementing compact PPC-tree with the general tree. Prepost algorithm can only find a frequent itemsets with required (pre-order and post-order) for each node. In this chapter, we improved prepost algorithm based on Hadoop platform (HPrepost), proposed using the Mapreduce …
Finding high-importance patterns in data is an emerging data mining task known as High-utility itemset mining (HUIM). Given a minimum utility threshold, a HUIM algorithm extracts all the high-utility itemsets (HUIs) whose utility values are not less than the threshold. This can reveal a wealth of useful information, but the precise needs of users are not well taken into account. In particular, users often want to focus on patterns that have some specific items rather than find all patterns. To overcome that difficulty, targeted mining has emerged, focusing on user preferences, but only prelimi…
School of Computer Science, University of St Andrews（圣安德鲁斯大学计算机学院）；Vrije Universiteit Brussel（布鲁塞尔自由大学）
Finding interesting patterns is a challenging task in data mining. Constraint based mining is a well-known approach to this, and one for which constraint programming has been shown to be a well-suited and generic framework. Dominance programming has been proposed as an extension that can capture an even wider class of constraint-based mining problems, by allowing to compare relations between patterns. In this paper, in addition to specifying a dominance relation, we introduce the ability to specify an incomparability condition. Using these two concepts we devise a generic framework that can do…
Because of usefulness and comprehensibility, fuzzy data mining has been extensively studied and is an emerging topic in recent years. Compared with utility-driven itemset mining technologies, fuzzy utility mining not only takes utilities (e.g., profits) into account, but also considers quantities of items in each transaction for discovering high fuzzy utility itemsets (HFUIs). Thus, fuzziness can be regard as a key criterion to select high-utility itemsets, while the exiting algorithms are not efficient enough. In this paper, an efficient one-phase algorithm named Fuzzy-driven Utility Itemset …
It is generally well agreed that developing a unifying theory is one of the most important issues in Data Mining research. In the last two decades, a great deal of work has been devoted to the algorithmic aspects of the Frequent Itemset (FI) Mining problem. We are motivated by the need for formal modeling in the field. Thus, we introduce and analyze, in this theoretical study, a new model for the FI mining task. Indeed, we encode the itemsets as words over an ordered alphabet, and state this problem by a formal series over the counting semiring $(\mathbb{N},+,\times,0,1)$, whose range constitu…
Czech Technical University in Prague（布拉格捷克技术大学）；Institute of Computer Science（计算机科学研究所）
In the recent decade companies started collecting of large amount of data. Without a proper analyse, the data are usually useless. The field of analysing the data is called data mining. Unfortunately, the amount of data is quite large: the data do not fit into main memory and the processing time can become quite huge. Therefore, we need parallel data mining algorithms. One of the popular and important data mining algorithm is the algorithm for generation of so called frequent itemsets. The problem of mining of frequent itemsets can be explained on the following example: customers goes in a sto…
Association rules express implication formed relations among attributes in databases of itemsets. The apriori algorithm is presented, the basis for most association rule mining algorithms. It works by pruning away rules that need not be evaluated based on the user specified minimum support confidence. Additionally, variations of the algorithm are presented that enable it to handle quantitative attributes and to extract rules about generalizations of items, but preserve the downward closure property that enables pruning. Intertransformation of the extensions is proposed for special cases.
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…
High Utility Itemset (HUI) mining problem is one of the important problems in the data mining literature. The problem offers greater flexibility to a decision maker to incorporate her/his notion of utility into the pattern mining process. The problem, however, requires the decision maker to choose a minimum utility threshold value for discovering interesting patterns. This is quite challenging due to the disparate itemset characteristics and their utility distributions. In order to address this issue, Top-K High Utility Itemset (THUI) mining problem was introduced in the literature. THUI minin…
High-utility itemset mining finds itemsets from a transaction database with utility no less than a fixed user-defined threshold. The utility of an itemset is defined as the sum of the utilities of its item. Several algorithms were proposed to mine high-utility itemsets. However, no state-of-the-art algorithm performs consistently good across dense and sparse datasets. In this paper, we propose a novel data structure called Utility-Tree, and a tree-based algorithm called UT-Miner that mines high-utility itemsets in one-phase only without generating any candidates and uses a lightweight construc…
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…
Jinan University（暨南大学）；Guangdong University of Technology（广东工业大学）；Shenzhen University（深圳大学）
For applied intelligence, utility-driven pattern discovery algorithms can identify insightful and useful patterns in databases. However, in these techniques for pattern discovery, the number of patterns can be huge, and the user is often only interested in a few of those patterns. Hence, targeted high-utility itemset mining has emerged as a key research topic, where the aim is to find a subset of patterns that meet a targeted pattern constraint instead of all patterns. This is a challenging task because efficiently finding tailored patterns in a very large search space requires a targeted mini…
Quantum Computing and Data Processing for Frequent Itemset Mining
National Taiwan University（台湾大学）；National Chengchi University（国立政治大学）；Academia Sinica（中央研究院）；The Pennsylvania State University（宾夕法尼亚州立大学）；University of Illinois Chicago（伊利诺伊大学芝加哥分校）
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…
Data aggregation in the setting of local differential privacy (LDP) guarantees strong privacy by providing plausible deniability of sensitive data. Existing works on this issue mostly focused on discovering heavy hitters, leaving the task of frequent itemset mining (FIM) as an open problem. To the best of our knowledge, the-state-of-the-art LDP solution to FIM is the SVSM protocol proposed recently. The SVSM protocol is mainly based on the padding and sampling based frequency oracle (PSFO) protocol, and regarded an itemset as an independent item without considering the frequency consistency am…
High-utility Itemset Mining (HUIM) finds itemsets from a transaction database with utility no less than a user-defined threshold where the utility of an itemset is defined as the sum of the item-wise utilities. In this paper, we generalize this notion to utility functions that need not be a simple sum of individual utilities. In particular, we study generalized utility functions that are subadditive and monotone (SM). We also describe a novel function that allows us to include external information in the form of a relationship graph for computing utility. Next, we focus on algorithms for HUIM …
Guangdong University of Technology（广东工业大学）；Jinan University（暨南大学）；Pazhou Lab（琶洲实验室）
High utility itemset mining approaches discover hidden patterns from large amounts of temporal data. However, an inescapable problem of high utility itemset mining is that its discovered results hide the quantities of patterns, which causes poor interpretability. The results only reflect the shopping trends of customers, which cannot help decision makers quantify collected information. In linguistic terms, computers use mathematical or programming languages that are precisely formalized, but the language used by humans is always ambiguous. In this paper, we propose a novel one-phase temporal f…
