带间隔约束的Top-k对比序列模式挖掘

对比序列模式能够表达序列数据集合间的差异,在商品推荐、用户行为分析和电力供应预测等领域有广泛的应用.已有的对比序列模式挖掘算法需要用户设定正例支持度阈值和负例支持度阈值.在不具备足够先验知识的情况下,用户难以设定恰当的支持度阈值,从而可能错失一些对比显著的模式.为此,提出了带间隔约束的top-k对比序列模式挖掘算法kDSP-Miner(top-k distinguishing sequential patterns with gap constraint miner).kDSP-Miner中用户只需设置期望发现的对比最显著的模式个数,从而避免了直接设置对比支持度阈值.相应地,挖掘算法更容易使用,并且结果更易于解释.同时,为了提高算法执行效率,设计了若干剪枝策略和启发策略.进一步设计了kDSP-Miner的多线程版本,以提高其对高维序列元素情况的处理能力.通过在真实世界数据集上的详实实验,验证了算法的有效性和执行效率.     

Prefix-projection global constraint and top-<Emphasis Type="Italic">k</Emphasis> approach for sequential pattern mining

Sequential pattern mining (SPM) is an important data mining problem with broad applications. SPM is a hard problem due to the huge number of intermediate subsequences to be considered. State of the art approaches for SPM (e.g., PrefixSpan Pei et al. 2001) are largely based on the pattern-growth approach, where for each frequent prefix subsequence, only its related suffix subsequences need to be considered, and the database is recursively projected into smaller ones. Many authors have promoted the use of constraints to focus on the most promising patterns according to the interests of the end user. The top-k SPM problem is also used to cope with the difficulty of thresholding and to control the number of solutions. State of the art methods developed for SPM and top-k SPM, though efficient, are locked into a rather rigid search strategy, and suffer from the lack of declarativity and flexibility. Indeed, adding new constraints usually amounts to changing the data-structures used in the core of the algorithm, and combining these new constraints often require new developments. Recent works (e.g. Kemmar et al. 2014; Négrevergne and Guns 2015) have investigated the use of Constraint Programming (CP) for SPM. However, despite their nice declarative aspects, all these modelings have scaling problems, due to the huge size of their constraint networks. To address this issue, we propose the Prefix-Projection global constraint, which encapsulates both the subsequence relation as well as the frequency constraint. Its filtering algorithm relies on the principle of projected databases which allows to keep in the variables domain, only values leading to a frequent pattern in the database. Prefix-Projection filtering algorithm enforces domain consistency on the variable succeeding the current frequent prefix in polynomial time. This global constraint also allows for a straightforward implementation of additional constraints such as size, item membership, regular expressions and any combination of them. Experimental results show that our approach clearly outperforms existing CP approaches and competes well with the state-of-the-art methods on large datasets for mining frequent sequential patterns, sequential patterns under various constraints, and top-k sequential patterns. Unlike existing CP methods, our approach achieves a better scalability.     

An efficient algorithm for mining top-<Emphasis Type="Italic">k</Emphasis> on-shelf high utility itemsets

High on-shelf utility itemset (HOU) mining is an emerging data mining task which consists of discovering sets of items generating a high profit in transaction databases. The task of HOU mining is more difficult than traditional high utility itemset (HUI) mining, because it also considers the shelf time of items, and items having negative unit profits. HOU mining can be used to discover more useful and interesting patterns in real-life applications than traditional HUI mining. Several algorithms have been proposed for this task. However, a major drawback of these algorithms is that it is difficult for users to find a suitable value for the minimum utility threshold parameter. If the threshold is set too high, not enough patterns are found. And if the threshold is set too low, too many patterns will be found and the algorithm may use an excessive amount of time and memory. To address this issue, we propose to address the problem of top-k on-shelf high utility itemset mining, where the user directly specifies k, the desired number of patterns to be output instead of specifying a minimum utility threshold value. An efficient algorithm named KOSHU (fast top-K on-shelf high utility itemset miner) is proposed to mine the top-k HOUs efficiently, while considering on-shelf time periods of items, and items having positive and/or negative unit profits. KOSHU introduces three novel strategies, named efficient estimated co-occurrence maximum period rate pruning, period utility pruning and concurrence existing of a pair 2-itemset pruning to reduce the search space. KOSHU also incorporates several novel optimizations and a faster method for constructing utility-lists. An extensive performance study on real-life and synthetic datasets shows that the proposed algorithm is efficient both in terms of runtime and memory consumption and has excellent scalability.     

Skopus: Mining top-<Emphasis Type="Italic">k</Emphasis> sequential patterns under leverage

This paper presents a framework for exact discovery of the top-k sequential patterns under Leverage. It combines (1) a novel definition of the expected support for a sequential pattern—a concept on which most interestingness measures directly rely—with (2) Skopus: a new branch-and-bound algorithm for the exact discovery of top-k sequential patterns under a given measure of interest. Our interestingness measure employs the partition approach. A pattern is interesting to the extent that it is more frequent than can be explained by assuming independence between any of the pairs of patterns from which it can be composed. The larger the support compared to the expectation under independence, the more interesting is the pattern. We build on these two elements to exactly extract the k sequential patterns with highest leverage, consistent with our definition of expected support. We conduct experiments on both synthetic data with known patterns and real-world datasets; both experiments confirm the consistency and relevance of our approach with regard to the state of the art.     

Mining top-k co-occurrence items with sequential pattern

Frequent sequential pattern mining has become one of the most important tasks in data mining. It has many applications, such as sequential analysis, classification, and prediction. How to generate candidates and how to control the combinatorically explosive number of intermediate subsequences are the most difficult problems. Intelligent systems such as recommender systems, expert systems, and business intelligence systems use only a few patterns, namely those that satisfy a number of defined conditions. Challenges include the mining of top-k patterns, top-rank-k patterns, closed patterns, and maximal patterns. In many cases, end users need to find itemsets that occur with a sequential pattern. Therefore, this paper proposes approaches for mining top-k co-occurrence items usually found with a sequential pattern. The Naive Approach Mining (NAM) algorithm discovers top-k co-occurrence items by directly scanning the sequence database to determine the frequency of items. The Vertical Approach Mining (VAM) algorithm is based on vertical database scanning. The Vertical with Index Approach Mining (VIAM) algorithm is based on a vertical database with index scanning. VAM and VIAM use pruning strategies to reduce the search space, thus improving performance. VAM and VIAM are especially effective in mining the co-occurrence items of a long input pattern. The three algorithms were evaluated using real-world databases. The experimental results show that these algorithms perform well, especially VAM and VIAM.     

On Multifold MDS and Perfect Codes That Are Not Splittable into Onefold Codes

The union of disjoint MDS (or perfect) codes with distance 2 (respectively, 3) is always an -fold MDS (perfect) code. The converse is shown to be incorrect. Moreover, if k is a multiple of 4 and n + 1 16 is a power of two, then a k/2-fold k-ary MDS code of length m 3 and an (n + 1)/8-fold perfect code of length n exist from which no MDS (perfect) code can be isolated.     

带通配符和One-Off条件的序列模式挖掘

很多应用领域产生大量的序列数据。如何从这些序列数据中挖掘具有重要价值的模式,已成为序列模式挖掘研究的主要任务。研究这样一个问题：给定序列S、支持度阈值和间隔约束,从序列S中挖掘所有出现次数不小于给定支持度阈值的频繁序列模式,并且要求模式中任意两个相邻元素在序列中的出现位置满足用户定义的间隔约束。设计了一种有效的带有通配符的模式挖掘算法One-Off Mining,模式在序列中的出现满足One-Off条件,即模式的任意两次出现都不共享序列中同一位置的字符。在生物DNA序列上的实验结果表明,One-Off Mining比相关的序列模式挖掘算法具有更好的时间性能和完备性。     

Mining top-k frequent patterns over data streams sliding window

Frequent pattern mining in data streams is an important research topic in the data mining community. In previous studies, a minimum support threshold was assumed to be available for mining frequent patterns. However, setting such a threshold is typically difficult. Hence, it is more reasonable to ask users to set a bound on the result size. The present study considers mining top-k frequent patterns from data streams using a sliding window technique. A single-pass algorithm, called MSWTP, is developed for the generation of top-k frequent patterns without a threshold. In the method, the content of the transactions in the sliding window is incrementally maintained in a summary data structure, named SWTP-tree, by scanning the stream only once. To make the mining operation efficient, insignificant patterns are distinguished from others by applying the Chernoff bound. Two kinds of obsolete pattern and one kind of insignificant pattern are periodically pruned from the pattern tree. Whenever necessary, the k most frequent patterns can be selected from SWTP-tree in order of their descending frequency. The performance of the proposed technique is evaluated via simulation experiments. The results show that the proposed method is both efficient and scalable, and that it outperforms comparable algorithms.     

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.     

Mining top-k maximal reference sequences from streaming web click-sequences with a damped sliding window

Online mining of path traversal patterns from continuous Web click streams is one of the challenging research problems of Web usage mining. Most of previous works focus on mining path traversal patterns over the entire history of Web click streams. Mining the recent changes of Web click streams can provide valuable information for the analysis of the Web click streams. In this paper, we propose a new, online mining algorithm, called Top-DSW (top-k path traversal patterns of stream Damped Sliding Window), to discover the set of top-k path traversal patterns from streaming maximal forward references, where k is the desired number of path traversal patterns to be mined. An effective summary data structure, called TKP-DSW-list (a list of top-k path traversal patterns of stream Damped Sliding Windows) is developed to maintain the essential information about the top-k path traversal patterns from the maximal forward references within a stream damped sliding window. An effective space pruning mechanism, called TKR-list-maintain, is developed to control the memory requirement of the TKP-DSW-list. Experimental studies show that the proposed Top-DSW algorithm is an efficient, single-pass algorithm for online mining of the set of top-k path traversal patterns over stream damped sliding windows.     

Efficient mining of maximal frequent itemsets from databases on a cluster of workstations

In this paper, we propose two parallel algorithms for mining maximal frequent itemsets from databases. A frequent itemset is maximal if none of its supersets is frequent. One parallel algorithm is named distributed max-miner (DMM), and it requires very low communication and synchronization overhead in distributed computing systems. DMM has the local mining phase and the global mining phase. During the local mining phase, each node mines the local database to discover the local maximal frequent itemsets, then they form a set of maximal candidate itemsets for the top-down search in the subsequent global mining phase. A new prefix tree data structure is developed to facilitate the storage and counting of the global candidate itemsets of different sizes. This global mining phase using the prefix tree can work with any local mining algorithm. Another parallel algorithm, named parallel max-miner (PMM), is a parallel version of the sequential max-miner algorithm (Proc of ACM SIGMOD Int Conf on Management of Data, 1998, pp 85–93). Most of existing mining algorithms discover the frequent k-itemsets on the kth pass over the databases, and then generate the candidate (k + 1)-itemsets for the next pass. Compared to those level-wise algorithms, PMM looks ahead at each pass and prunes more candidate itemsets by checking the frequencies of their supersets. Both DMM and PMM were implemented on a cluster of workstations, and their performance was evaluated for various cases. They demonstrate very good performance and scalability even when there are large maximal frequent itemsets (i.e., long patterns) in databases.

Linear Models of Circuits Based on the Multivalued Components

Linearization and planarization of the circuit models is pivotal to the submicron technologies. On the other hand, the characteristics of the VLSI circuits can be sometimes improved by using the multivalued components. It was shown that any -level circuit based on the multivalued components is representable as an algebraic model based on linear arithmetic polynomials mapped correspondingly into decision diagrams that are linear and planar by nature. Complexity of representing a circuit as the linear decision diagram was estimated as O(G) with G for the number of multivalued components in the circuit. The results of testing the LinearDesignMV algorithm on circuits of more than 8000 LGSynth 93 multivalued components were presented.     

Discovering top-k patterns with differential privacy-an accurate approach

Frequent pattern mining discovers sets of items that frequently appear together in a transactional database; these can serve valuable economic and research purposes. However, if the database contains sensitive data (e.g., user behavior records, electronic health records), directly releasing the discovered frequent patterns with support counts will carry significant risk to the privacy of individuals. In this paper, we study the problem of how to accurately find the top-k frequent patterns with noisy support counts on transactional databases while satisfying differential privacy. We propose an algorithm, called differentially private frequent pattern (DFP-Growth), that integrates a Laplace mechanism and an exponential mechanism to avoid privacy leakage. We theoretically prove that the proposed method is (λ, δ)-useful and differentially private. To boost the accuracy of the returned noisy support counts, we take consistency constraints into account to conduct constrained inference in the post-processing step. Extensive experiments, using several real datasets, confirm that our algorithm generates highly accurate noisy support counts and top-k frequent patterns.     

Efficient top-k similarity join processing over multi-valued objects

The top-k similarity joins have been extensively studied and used in a wide spectrum of applications such as information retrieval, decision making, spatial data analysis and data mining. Given two sets of objects $\mathcal U$ and $\mathcal V$ , a top-k similarity join returns k pairs of most similar objects from $\mathcal U \times \mathcal V$ . In the conventional model of top-k similarity join processing, an object is usually regarded as a point in a multi-dimensional space and the similarity is measured by some simple distance metrics like Euclidean distance. However, in many applications an object may be described by multiple values (instances) and the conventional model is not applicable since it does not address the distributions of object instances. In this paper, we study top-k similarity join over multi-valued objects. We apply two types of quantile based distance measures, ?-quantile distance and ?-quantile group-base distance, to explore the relative instance distribution among the multiple instances of objects. Efficient and effective techniques to process top-k similarity joins over multi-valued objects are developed following a filtering-refinement framework. Novel distance, statistic and weight based pruning techniques are proposed. Comprehensive experiments on both real and synthetic datasets demonstrate the efficiency and effectiveness of our techniques.     

Finite Computation of the ℓ1 Estimator from Huber’s M-Estimator in Linear Regression

We review and extend previous work on the approximation of the linear ₁ estimator by the Huber M-estimator based on the algorithms proposed by Clark and Osborne [7], and Madsen and Nielsen [12]. Although the Madsen-Nielsen algorithm is a promising one, it is guaranteed to terminate finitely under certain assumptions. We describe a variant of the Madsen-Nielsen algorithm to compute the ₁ estimator from the Huber M-estimator in a finite number of steps without any restrictive steps nor assumptions. Summary computational results are given.     

Scalable and efficient processing of top-<Emphasis Type="Italic">k</Emphasis> multiple-type integrated queries

In this paper, we define a new class of queries, the top-k multiple-type integrated query (simply, top-k MULTI query). It deals with multiple data types and finds the information in the order of relevance between the query and the object. Various data types such as spatial, textual, and relational data types can be used for the top-k MULTI query. The top-k MULTI query distinguishes itself from the traditional top-k query in that the component scores to calculate final scores are determined dependent of the query. Hence, each component score is calculated only when the query is given for each data type rather than being calculated apriori as in the top-k query. As a representative instance, the traditional top-k spatial keyword query is an instance of the top-k MULTI query. It deals with the spatial data type and text data type and finds the information based on spatial proximity and textual relevance between the query and the object, which is determined only when the query is given. In this paper, we first define the top-k MULTI query formally and define a new specific instance for the top-k MULTI query, the top-k spatial-keyword-relational(SKR) query, by integrating the relational data type into the traditional top-k spatial keyword query. Then, we investigate the processing approaches for the top-k MULTI query. We discuss the scalability of those approaches as new data types are integrated. We also devise the processing methods for the top-k SKR query. Finally, through extensive experiments on the top-k SKR query using real and synthetic data sets, we compare efficiency of the methods in terms of the query performance and storage.     

Approximate Continuous Top-<Emphasis Type="Italic">k</Emphasis> Query over Sliding Window

Continuous top-k query over sliding window is a fundamental problem in database, which retrieves k objects with the highest scores when the window slides. Existing studies mainly adopt exact algorithms to tackle this type of queries, whose key idea is to maintain a subset of objects in the window, and try to retrieve answers from it. However, all the existing algorithms are sensitive to query parameters and data distribution. In addition, they suffer from expensive overhead for incremental maintenance, and thus cannot satisfy real-time requirement. In this paper, we define a novel query named (ε, δ)-approximate continuous top-k query, which returns approximate answers for top-k query. In order to efficiently support this query, we propose an efficient framework, named PABF (Probabilistic Approximate Based Framework), to support approximate top-k query over sliding window. We firstly maintain a self-adaptive pruning value, which could filter out newly arrived objects who have a probability less than 1 ? δ of being a query result. For those objects that are not filtered, we combine them together, if the score difference among them is less than a threshold. To efficiently maintain these combined results, the framework PABF also proposes a multi-phase merging algorithm. Theoretical analysis indicates that even in the worst case, we require only logarithmic complexity for maintaining each candidate.     

TopPI: An efficient algorithm for item-centric mining

In this paper, we introduce item-centric mining, a new semantics for mining long-tailed datasets. Our algorithm, TopPI, finds for each item its top-k most frequent closed itemsets. While most mining algorithms focus on the globally most frequent itemsets, TopPI guarantees that each item is represented in the results, regardless of its frequency in the database.TopPI allows users to efficiently explore Web data, answering questions such as “what are the k most common sets of songs downloaded together with the ones of my favorite artist?”. When processing retail data consisting of 55 million supermarket receipts, TopPI finds the itemset “milk, puff pastry” that appears 10,315 times, but also “frangipane, puff pastry” and “nori seaweed, wasabi, sushi rice” that occur only 1120 and 163 times, respectively. Our experiments with analysts from the marketing department of our retail partner demonstrate that item-centric mining discover valuable itemsets. We also show that TopPI can serve as a building-block to approximate complex itemset ranking measures such as the p-value.Thanks to efficient enumeration and pruning strategies, TopPI avoids the search space explosion induced by mining low support itemsets. We show how TopPI can be parallelized on multi-cores and distributed on Hadoop clusters. Our experiments on datasets with different characteristics show the superiority of TopPI when compared to standard top-k solutions, and to Parallel FP-Growth, its closest competitor.     

Answering why-not and why questions on reverse top-<Emphasis Type="Italic">k</Emphasis> queries

Why-not and why questions can be posed by database users to seek clarifications on unexpected query results. Specifically, why-not questions aim to explain why certain expected tuples are absent from the query results, while why questions try to clarify why certain unexpected tuples are present in the query results. This paper systematically explores the why-not and why questions on reverse top-k queries, owing to its importance in multi-criteria decision making. We first formalize why-not questions on reverse top-k queries, which try to include the missing objects in the reverse top-k query results, and then, we propose a unified framework called WQRTQ to answer why-not questions on reverse top-k queries. Our framework offers three solutions to cater for different application scenarios. Furthermore, we study why questions on reverse top-k queries, which aim to exclude the undesirable objects from the reverse top-k query results, and extend the framework WQRTQ to efficiently answer why questions on reverse top-k queries, which demonstrates the flexibility of our proposed algorithms. Extensive experimental evaluation with both real and synthetic data sets verifies the effectiveness and efficiency of the presented algorithms under various experimental settings.