Para Miner: a generic pattern mining algorithm for multi-core architectures

In this paper, we present Para Miner which is a generic and parallel algorithm for closed pattern mining. Para Miner is built on the principles of pattern enumeration in strongly accessible set systems. Its efficiency is due to a novel dataset reduction technique (that we call EL-reduction), combined with novel technique for performing dataset reduction in a parallel execution on a multi-core architecture. We illustrate Para Miner’s genericity by using this algorithm to solve three different pattern mining problems: the frequent itemset mining problem, the mining frequent connected relational graphs problem and the mining gradual itemsets problem. In this paper, we prove the soundness and the completeness of Para Miner. Furthermore, our experiments show that despite being a generic algorithm, Para Miner can compete with specialized state of the art algorithms designed for the pattern mining problems mentioned above. Besides, for the particular problem of gradual itemset mining, Para Miner outperforms the state of the art algorithm by two orders of magnitude.     

Mining frequent subgraphs over uncertain graph databases under probabilistic semantics

Frequent subgraph mining has been extensively studied on certain graph data. However, uncertainty is intrinsic in graph data in practice, but there is very few work on mining uncertain graph data. This paper focuses on mining frequent subgraphs over uncertain graph data under the probabilistic semantics. Specifically, a measure called ${\varphi}$ -frequent probability is introduced to evaluate the degree of recurrence of subgraphs. Given a set of uncertain graphs and two real numbers ${0 < \varphi, \tau < 1}$ , the goal is to quickly find all subgraphs with ${\varphi}$ -frequent probability at least τ. Due to the NP-hardness of the problem and to the #P-hardness of computing the ${\varphi}$ -frequent probability of a subgraph, an approximate mining algorithm is proposed to produce an ${(\varepsilon, \delta)}$ -approximate set Π of “frequent subgraphs”, where ${0 < \varepsilon < \tau}$ is error tolerance, and 0 <?δ?< 1 is a confidence bound. The algorithm guarantees that (1) any frequent subgraph S is contained in Π with probability at least ((1 ? δ) /2) ^s , where s is the number of edges in S; (2) any infrequent subgraph with ${\varphi}$ -frequent probability less than ${\tau - \varepsilon}$ is contained in Π with probability at most δ/2. The theoretical analysis shows that to obtain any frequent subgraph with probability at least 1 ? Δ, the input parameter δ of the algorithm must be set to at most ${1 - 2 (1 - \Delta)^{1 / \ell_{\max}}}$ , where 0 <?Δ <?1, and ? _max is the maximum number of edges in frequent subgraphs. Extensive experiments on real uncertain graph data verify that the proposed algorithm is practically efficient and has very high approximation quality. Moreover, the difference between the probabilistic semantics and the expected semantics on mining frequent subgraphs over uncertain graph data has been discussed in this paper for the first time.     

Mining constrained frequent itemsets from distributed uncertain data

Nowadays, high volumes of massive data can be generated from various sources (e.g., sensor data from environmental surveillance). Many existing distributed frequent itemset mining algorithms do not allow users to express the itemsets to be mined according to their intention via the use of constraints. Consequently, these unconstrained mining algorithms can yield numerous itemsets that are not interesting to users. Moreover, due to inherited measurement inaccuracies and/or network latencies, the data are often riddled with uncertainty. These call for both constrained mining and uncertain data mining. In this journal article, we propose a data-intensive computer system for tree-based mining of frequent itemsets that satisfy user-defined constraints from a distributed environment such as a wireless sensor network of uncertain data.     

Hyper-structure mining of frequent patterns in uncertain data streams

Data uncertainty is inherent in many real-world applications such as sensor monitoring systems, location-based services, and medical diagnostic systems. Moreover, many real-world applications are now capable of producing continuous, unbounded data streams. During the recent years, new methods have been developed to find frequent patterns in uncertain databases; nevertheless, very limited work has been done in discovering frequent patterns in uncertain data streams. The current solutions for frequent pattern mining in uncertain streams take a FP-tree-based approach; however, recent studies have shown that FP-tree-based algorithms do not perform well in the presence of data uncertainty. In this paper, we propose two hyper-structure-based false-positive-oriented algorithms to efficiently mine frequent itemsets from streams of uncertain data. The first algorithm, UHS-Stream, is designed to find all frequent itemsets up to the current moment. The second algorithm, TFUHS-Stream, is designed to find frequent itemsets in an uncertain data stream in a time-fading manner. Experimental results show that the proposed hyper-structure-based algorithms outperform the existing tree-based algorithms in terms of accuracy, runtime, and memory usage.     

Crowdsourcing for data management

The discovery of informative itemsets is a fundamental building block in data analytics and information retrieval. While the problem has been widely studied, only few solutions scale. This is particularly the case when (1) the data set is massive, calling for large-scale distribution, and/or (2) the length k of the informative itemset to be discovered is high. In this paper, we address the problem of parallel mining of maximally informative k-itemsets (miki) based on joint entropy. We propose PHIKS (Parallel Highly Informative \(\underline{K}\)-ItemSet), a highly scalable, parallel miki mining algorithm. PHIKS renders the mining process of large-scale databases (up to terabytes of data) succinct and effective. Its mining process is made up of only two efficient parallel jobs. With PHIKS, we provide a set of significant optimizations for calculating the joint entropies of miki having different sizes, which drastically reduces the execution time, the communication cost and the energy consumption, in a distributed computational platform. PHIKS has been extensively evaluated using massive real-world data sets. Our experimental results confirm the effectiveness of our proposal by the significant scale-up obtained with high itemsets length and over very large databases.     

不确定数据频繁闭项集挖掘算法

由于不确定数据的向下封闭属性,挖掘全部频繁项集的方法会得到一个指数级的结果。为获得一个较小的合适的结果集,研究了在不确定数据上挖掘频繁闭项集,并提出了一种新的频繁闭项集挖掘算法——NA-PFCIM。该算法将项集挖掘过程看作一个概率分布函数,考虑到基于正态分布模型的方法提取的频繁项集精确度较高,而且支持大型数据库,采用了正态分布模型提取频繁项集。同时,为了减少搜索空间以及避免冗余计算,利用基于深度优先搜索的策略来获得所有的概率频繁闭项集。该算法还设计了两个剪枝策略:超集修剪和子集修剪。最后,在常用的数据集(T10I4D100K、Accidents、Mushroom、Chess)上,将提出的NA-PFCIM算法和基于泊松分布的A-PFCIM算法进行比较。实验结果表明,NA-PFCIM算法能够减少所要扩展的项集,同时减少项集频繁概率的计算,其性能优于对比算法。     

Summary queries for frequent itemsets mining

There are many advanced techniques that can efficiently mine frequent itemsets using a minimum-support. However, the question that remains unanswered is whether the minimum-support can really help decision makers to make decisions. In this paper, we study four summary queries for frequent itemsets mining, namely, (1) finding a support-average of itemsets, (2) finding a support-quantile of itemsets, (3) finding the number of itemsets that greater/less than the support-average, i.e., an approximated distribution of itemsets, and (4) finding the relative frequency of an itemset (compared its frequency with that of other itemsets in the same dataset). With these queries, a decision maker will know whether an itemset in question is greater/less than the support-quantile; the distribution of itemsets; and the frequentness of an itemset. Processing these summary queries is challenging, because the minimum-support constraint cannot be used to prune infrequent itemsets. In this paper, we propose several simple yet effective approximation solutions. We conduct extensive experiments for evaluating our strategy, and illustrate that the proposed approaches can well model and capture the statistical parameters (summary queries) of itemsets in a database.     

A false negative approach to mining frequent itemsets from high speed transactional data streams

Mining frequent itemsets from transactional data streams is challenging due to the nature of the exponential explosion of itemsets and the limit memory space required for mining frequent itemsets. Given a domain of I unique items, the possible number of itemsets can be up to 2^I − 1. When the length of data streams approaches to a very large number N, the possibility of an itemset to be frequent becomes larger and difficult to track with limited memory. The existing studies on finding frequent items from high speed data streams are false-positive oriented. That is, they control memory consumption in the counting processes by an error parameter ?, and allow items with support below the specified minimum support s but above s − ? counted as frequent ones. However, such false-positive oriented approaches cannot be effectively applied to frequent itemsets mining for two reasons. First, false-positive items found increase the number of false-positive frequent itemsets exponentially. Second, minimization of the number of false-positive items found, by using a small ?, will make memory consumption large. Therefore, such approaches may make the problem computationally intractable with bounded memory consumption. In this paper, we developed algorithms that can effectively mine frequent item(set)s from high speed transactional data streams with a bound of memory consumption. Our algorithms are based on Chernoff bound in which we use a running error parameter to prune item(set)s and use a reliability parameter to control memory. While our algorithms are false-negative oriented, that is, certain frequent itemsets may not appear in the results, the number of false-negative itemsets can be controlled by a predefined parameter so that desired recall rate of frequent itemsets can be guaranteed. Our extensive experimental studies show that the proposed algorithms have high accuracy, require less memory, and consume less CPU time. They significantly outperform the existing false-positive algorithms.     

基于不确定性数据的频繁闭项集挖掘算法

对于不确定性数据,传统判断项集是否频繁的方法并不能准确表达项集的频繁性,同样对于大型数据,频繁项集显得庞大和冗余。针对上述不足,在水平挖掘算法Apriori的基础上,提出一种基于不确定性数据的频繁闭项集挖掘算法UFCIM。利用置信度概率表达项集频繁的准确性,置信度越高,项集为频繁的准确性也越高,且由于频繁闭项集是频繁项集的一种无损压缩表示,因此利用压缩形式的频繁闭项集替代庞大的频繁项集。实验结果表明,该算法能够快速地挖掘出不确定性数据中的频繁闭项集,在减少项集冗余的同时保证项集的准确性和完整性。     

A new mining approach for uncertain databases using CUFP trees

In the past, many algorithms have been proposed to mine frequent itemsets from transactional databases, in which the presence or absence of items in transactions was certainly known. In some applications, items may also be uncertain in transactions with their existential probabilities ranging from 0 to 1 in the uncertain dataset. Apparently, the processing in uncertain datasets is quite different from those in certain datasets. The UF-tree algorithm was proposed to construct the UF-tree structure from an uncertain dataset and mine frequent itemsets from the tree. In the UF-tree construction process, however, only the same items with the same existential probabilities in transactions were merged together in the tree, thus causing many redundant nodes in the tree. In this paper, a new tree structure called the compressed uncertain frequent-pattern tree (CUFP tree) is designed to efficiently keep the related information in the mining process. In the CUFP tree, the same items will be merged in a branch of the tree even when the existential probabilities in transactions are not the same. A mining algorithm called the CUFP-mine algorithm is then proposed based on the tree structure to find uncertain frequent patterns. Experimental results show that the proposed approach has a better performance than UF-tree algorithm both in the execution time and in the number of tree nodes.     

A survey of queries over uncertain data

Uncertain data have already widely existed in many practical applications recently, such as sensor networks, RFID networks, location-based services, and mobile object management. Query processing over uncertain data as an important aspect of uncertain data management has received increasing attention in the field of database. Uncertain query processing poses inherent challenges and demands non-traditional techniques, due to the data uncertainty. This paper surveys this interesting and still evolving research area in current database community, so that readers can easily obtain an overview of the state-of-the-art techniques. We first provide an overview of data uncertainty, including uncertainty types, probability representation models, and sources of probabilities. We next outline the current major types of uncertain queries and summarize the main features of uncertain queries. Particularly, we present and analyze several typical uncertain queries in detail, such as skyline queries, top- $k$ queries, nearest-neighbor queries, aggregate queries, join queries, range queries, and threshold queries over uncertain data. Finally, we present many interesting research topics on uncertain queries that have not yet been explored.     

UV-diagram: a voronoi diagram for uncertain spatial databases

The Voronoi diagram is an important technique for answering nearest-neighbor queries for spatial databases. We study how the Voronoi diagram can be used for uncertain spatial data, which are inherent in scientific and business applications. Specifically, we propose the Uncertain-Voronoi diagram (or UV-diagram), which divides the data space into disjoint “UV-partitions”. Each UV-partition $P$ is associated with a set $S$ of objects, such that any point $q$ located in $P$ has the set $S$ as its nearest neighbor with nonzero probabilities. The UV-diagram enables queries that return objects with nonzero chances of being the nearest neighbor (NN) of a given point $q$ . It supports “continuous nearest-neighbor search”, which refreshes the set of NN objects of $q$ , as the position of $q$ changes. It also allows the analysis of nearest-neighbor information, for example, to find out the number of objects that are the nearest neighbors of any point in a given area. A UV-diagram requires exponential construction and storage costs. To tackle these problems, we devise an alternative representation of a UV-diagram, by using a set of UV-cells. A UV-cell of an object $o$ is the extent $e$ for which $o$ can be the nearest neighbor of any point $q \in e$ . We study how to speed up the derivation of UV-cells by considering its nearby objects. We also use the UV-cells to design the UV-index, which supports different queries, and can be constructed in polynomial time. We have performed extensive experiments on both real and synthetic data to validate the efficiency of our approaches.     

QUBLE: towards blending interactive visual subgraph search queries on large networks

In a previous paper, we laid out the vision of a novel graph query processing paradigm where instead of processing a visual query graph after its construction, it interleaves visual query formulation and processing by exploiting the latency offered by the gui to filter irrelevant matches and prefetch partial query results [8]. Our recent attempts at implementing this vision [8, 9] show significant improvement in system response time (srt) for subgraph queries. However, these efforts are designed specifically for graph databases containing a large collection of small or medium-sized graphs. In this paper, we propose a novel algorithm called quble (QUery Blender for Large nEtworks) to realize this visual subgraph querying paradigm on very large networks (e.g., protein interaction networks, social networks). First, it decomposes a large network into a set of graphlets and supergraphlets using a minimum cut-based graph partitioning technique. Next, it mines approximate frequent and small infrequent fragments (sifs) from them and identifies their occurrences in these graphlets and supergraphlets. Then, the indexing framework of [9] is enhanced so that the mined fragments can be exploited to index graphlets for efficient blending of visual subgraph query formulation and query processing. Extensive experiments on large networks demonstrate effectiveness of quble.     

Mining non-derivable hypercliques

A hyperclique (Xiong et al. in Proceedings of the IEEE international conference on data mining, pp 387–394, 2003) is an itemset containing items that are strongly correlated with each other, based on a user-specified threshold. Hypercliques (HCs) have been successfully used in a number of applications, for example, clustering (Xiong et al. in Proceedings of the 4th SIAM international conference on data mining, pp 279–290, 2004) and noise removal (Xiong et al. in IEEE Trans Knowl Data Eng 18(3):304–319, 2006). Even though HC has been shown to respond well to datasets with skewed support distribution and low support threshold, it may still grow very large for dense datasets and lower h-confidence threshold. In this paper, we propose a new pruning method based on combining HCs and non-derivable itemsets (NDIs) (Calders and Goethals in Proceedings of the PKDD international conference on principles of data mining and knowledge discovery, pp 74–85, 2002) in order to substantially reduce the amount of generated HCs. Specifically, we propose a new collection of HCs, called non-derivable hypercliques (NDHCs). The NDHC collection is a lossless representation of HCs, that is, given the itemsets in NDHCs, we can generate the complete HC collection and their support, without additional scanning of the dataset. We present an efficient algorithm to mine all NDHC sets, NDHCMiner, and an algorithm to derive all HC sets and their support from NDHCs, NDHCDeriveAll. We experimentally compare our collection, NDHC with HC, with respect to runtime performance as well as total number of generated sets, using real and artificial data. We also show comparisons with another condensed representation of HCs, maximal hyperclique patterns (MHPs). Our experiments show that the NDHC collection offers substantial advantages over HCs, and even MHPs, especially for dense datasets and lower h-confidence values.     

Time-weighted counting for recently frequent pattern mining in data streams

How can we discover interesting patterns from time-evolving high-speed data streams? How to analyze the data streams quickly and accurately, with little space overhead? How to guarantee the found patterns to be self-consistent? High-speed data stream has been receiving increasing attention due to its wide applications such as sensors, network traffic, social networks, etc. The most fundamental task on the data stream is frequent pattern mining; especially, focusing on recentness is important in real applications. In this paper, we develop two algorithms for discovering recently frequent patterns in data streams. First, we propose TwMinSwap to find top-k recently frequent items in data streams, which is a deterministic version of our motivating algorithm TwSample providing theoretical guarantees based on item sampling. TwMinSwap improves TwSample in terms of speed, accuracy, and memory usage. Both require only O(k) memory spaces and do not require any prior knowledge on the stream such as its length and the number of distinct items in the stream. Second, we propose TwMinSwap-Is to find top-k recently frequent itemsets in data streams. We especially focus on keeping self-consistency of the discovered itemsets, which is the most important property for reliable results, while using O(k) memory space with the assumption of a constant itemset size. Through extensive experiments, we demonstrate that TwMinSwap outperforms all competitors in terms of accuracy and memory usage, with fast running time. We also show that TwMinSwap-Is is more accurate than the competitor and discovers recently frequent itemsets with reasonably large sizes (at most 5–7) depending on datasets. Thanks to TwMinSwap and TwMinSwap-Is, we report interesting discoveries in real world data streams, including the difference of trends between the winner and the loser of U.S. presidential candidates, and temporal human contact patterns.     

Diverse dimension decomposition for itemset spaces

We introduce the problem of diverse dimension decomposition in transactional databases, where a dimension is a set of mutually exclusive itemsets. The problem we consider requires to find a decomposition of the itemset space into dimensions, which are orthogonal to each other and which provide high coverage of the input database. The mining framework we propose can be interpreted as a dimensionality-reducing transformation from the space of all items to the space of orthogonal dimensions. Relying on information-theoretic concepts, we formulate the diverse dimension decomposition problem with a single objective function that simultaneously captures constraints on coverage, exclusivity, and orthogonality. We show that our problem is NP-hard, and we propose a greedy algorithm exploiting the well-known FP-tree data structure. Our algorithm is equipped with strategies for pruning the search space deriving directly from the objective function. We also prove a property that allows assessing the level of informativeness for newly added dimensions, thus allowing to define criteria for terminating the decomposition. We demonstrate the effectiveness of our solution by experimental evaluation on synthetic datasets with known dimension and three real-world datasets, flickr, del.icio.us and dblp. The problem we study is largely motivated by applications in the domain of collaborative tagging; however, the mining task we introduce in this paper is useful in other application domains as well.     

Uncertain minimum cost flow problem

The aim of this paper is to give an uncertainty distribution of the least cost of shipment of a commodity through a network with uncertain capacities. Uncertainty theory is used to deal with uncertain capacities, and an \(\alpha \) -minimum cost flow problem model is proposed. After defining the \(\alpha \) -minimum cost flow, the properties of the model are analyzed, and then an algorithm for uncertain minimum cost flow problem is developed. The algorithm can be considered as a general solution to the uncertain minimum cost flow problem. To demonstrate the efficiency of the proposed algorithm, a numerical example is illustrated.     

不确定数据流最大频繁项集挖掘算法研究

对于大型数据,频繁项集挖掘显得庞大而冗余,挖掘最大频繁项集可以减少挖出的频繁项集的个数。可是对于不确定性数据流,传统判断项集是否频繁的方法已不能准确表达项集的频繁性,而且目前还没有在不确定数据流上挖掘最大频繁项集的相关研究。因此,针对上述不足,提出了一种基于衰减模型的不确定性数据流最大频繁项集挖掘算法TUFSMax。该算法采用标记树结点的方法,使得算法不需要超集检测就可挖掘出所有的最大频繁项集,节约了超集检测时间。实验证明了提出的算法在时间和空间上具有高效性。     

Mining frequent itemsets in large databases: The hierarchical partitioning approach

Although many methods have been proposed to enhance the efficiencies of data mining, little research has been devoted to the issue of scalability – that is, the problem of mining frequent itemsets when the size of the database is very large. This study proposes a methodology, hierarchical partitioning, for mining frequent itemsets in large databases, based on a novel data structure called the Frequent Pattern List (FPL). One of the major features of the FPL is its ability to partition the database, and thus transform the database into a set of sub-databases of manageable sizes. As a result, a divide-and-conquer approach can be developed to perform the desired data-mining tasks. Experimental results show that hierarchical partitioning is capable of mining frequent itemsets and frequent closed itemsets in very large databases.     

An adaptive approach to mining frequent itemsets efficiently

The mining of frequent itemsets is a fundamental and important task of data mining. To improve the efficiency in mining frequent itemsets, many researchers developed smart data structures to represent the database, and designed divide-and-conquers approaches to generate frequent itemsets from these data structures. However, the features of real databases are diversified and the features of local databases in the mining process may also change. Consequently, different data structures may be utilized in the mining process to enhance efficiency. This study presents an adaptive mechanism to select suitable data structures depending on database densities: the Frequent Pattern List (FPL) for sparse databases, and the Transaction Pattern List (TPL) for dense databases. Experimental results verified the effectiveness of this approach.