Anti-monotone Property Research Articles

Mining Spatial Co-Location Patterns With a Mixed Prevalence Measure.

A co-location pattern indicates a subset of spatial features whose instances are frequently located together in proximate geographical space. Most previous studies of spatial co-location pattern mining concern what percentage of instances per feature are involved in the table instance of a pattern, but neglect the heterogeneity in the number of feature instances and the distribution of instances. As a result, the deviation may be occurred in the interest measure of co-locations. In this article, we propose a novel mixed prevalence index (MPI) incorporating the effect of feature-level and instance-level heterogeneity on the prevalence measure, which can address some dilemmas in existing interest measures. Luckily, MPI possesses the partial antimonotone property. In virtue of this property, a branch-based search algorithm equipped with some optimizing strategies of MPI calculation is proposed, namely, Branch-Opt-MPI. Comprehensive experiments are conducted on both real and synthetic spatial datasets. Experimental results reveal the superiority of MPI compared to other interest measures and also validate the efficiency and scalability of the Branch-Opt-MPI. Particularly, the Branch-Opt-MPI performs more efficiently than baselines for several times or even orders of magnitude in dense data.

Totally-ordered Sequential Rules for Utility Maximization

High-utility sequential pattern mining (HUSPM) is a significant and valuable activity in knowledge discovery and data analytics with many real-world applications. In some cases, HUSPM can not provide an excellent measure to predict what will happen. High-utility sequential rule mining (HUSRM) discovers high utility and high confidence sequential rules, so it can solve the issue in HUSPM. However, all existing HUSRM algorithms aim to find high-utility partially-ordered sequential rules (HUSRs), which are not consistent with reality and may generate fake HUSRs. Therefore, in this article, we formulate the problem of high-utility totally-ordered sequential rule mining and propose a novel algorithm, called TotalSR, which aims to identify all high-utility totally-ordered sequential rules (HTSRs). TotalSR introduces a left-first expansion strategy that can utilize the anti-monotonic property to use a confidence pruning strategy. TotalSR also designs a new utility upper bound: RSPEU , which is tighter than the existing upper bounds. TotalSR can drastically reduce the search space with the help of utility upper bounds pruning strategies, avoiding much more meaningless computation. To effectively compute the information, TotalSR proposes an auxiliary antecedent record table that can efficiently calculate the antecedent’s support and a utility prefix sum list that can compute the upper bound in O (1) time for a sequence. Finally, there are numerous experimental results on both real and synthetic datasets demonstrating that TotalSR is more efficient than the existing algorithms.

Effective Community Search on Large Attributed Bipartite Graphs

Community search over bipartite graphs has attracted significant interest recently. In many applications such as the user–item bipartite graph in e-commerce and customer–movie bipartite graph in movie rating website, nodes tend to have attributes. However, the previous community search algorithms on bipartite graphs ignore attributes, thus making them to return results with poor cohesion with respect to their node attributes. In this paper, we study the community search problem on attributed bipartite graphs. Given a query vertex [Formula: see text], we aim to find the attributed [Formula: see text]-communities of [Formula: see text], where the structure cohesiveness of the community is described by the [Formula: see text]-core model, and the attribute similarity of two groups of nodes in the subgraph is maximized. In order to retrieve attributed communities from bipartite graphs, we first propose a basic algorithm composed of two steps: the generation and verification of candidate keyword sets, and then two improved query algorithms Inc and Dec are proposed. Inc is proposed considering the anti-monotonicity property of attributed bipartite graphs, then we adopt different generating methods and verify the order of candidate keyword sets and propose the Dec algorithm. After evaluating our solutions on eight large graphs, the experimental results demonstrate that our methods are effective and efficient in querying the attributed communities on bipartite graphs.

SCPM-CR: A Novel Method for Spatial Co-Location Pattern Mining With Coupling Relation Consideration

Spatial co-location pattern mining (SCPM) aims to discover subsets of spatial features frequently located together in proximate areas. Previous studies of SCPM solely concern the inter-features association of a pattern, but neglect the interesting intra-feature behavior. In this paper, we propose the task of spatial co-location pattern mining with coupling relation consideration (SCPM-CR) to capture complex relations embedded in a co-location. Specifically, InterPCI measure is designed to capture the inter-features coupling by considering the comprehensive interaction of objects for the features in a pattern, and luckily it possesses the anti-monotone property. Another measure, IntraCAI, is proposed to capture the congregating behavior of intra-feature objects under the restriction of a co-location. A general framework is designed for SCPM-CR task and experiments show that a large fraction of computation time is devoted to identifying the participating objects of a candidate pattern. To tackle this calculation bottleneck, a novel candidate-and-search algorithm is suggested, CS-HBS, equipped with heuristic backtracking search. Extensive experiments are conducted on real and synthetic datasets to demonstrate the superiority of SCPM-CR compared with traditional SCPM methods, and also to validate the efficiency and scalability of CS-HBS. Experimental results show that CS-HBS outperforms the baselines by several times or even orders of magnitude.

Discovering Periodic Patterns in Time Series from Twitter Data Set

The important class of regularities that exist in a time series is nothing but the Partial periodic patterns. These patterns have key properties such as starting, stopping, and restartinganywhere− within a series. Partial periodic patterns areclassifiedinto two types: (i) regular patterns− exhibiting periodic behavior throughout a series with some exceptions and( ii) periodic patterns exhibiting periodic behavior only for particular time intervals within a series. We have focused primarily on finding regular patterns during past studies on partial periodic search. The knowledge pertaining to periodic patterns cannot be ignored. This is because useful information pertaining to seasonal or time-based associations between events is provided bythem. Because of the foll o wi n g two main reasons, finding periodic patterns is a non-trivial task. (i) Each periodic pattern is associated with time-based information pertaining to its durations of periodic appearances in a series. Since the information can vary within and across patterns, obtaining this information ischallenging. (ii) As they do not satisfy the anti-monotonic property, finding all periodic patterns is a computationally expensive process. In this paper, periodic pattern model is proposed by addressing the above issues. Periodic Pattern growth algorithm along with an efficient pruning technique is also proposed to discover these patterns. The results through Experimentation have shown that Periodic patterns canbe really useful and it has also proven that our algorithm isnoteworthy.

Effective community search over large star-schema heterogeneous information networks

Community search (CS) enables personalized community discovery and has found a wide spectrum of emerging applications such as setting up social events and friend recommendation. While CS has been extensively studied for conventional homogeneous networks, the problem for heterogeneous information networks (HINs) has received attention only recently. However, existing studies suffer from several limitations, e.g., they either require users to specify a meta-path or relational constraints, which pose great challenges to users who are not familiar with HINs. To address these limitations, in this paper, we systematically study the problem of CS over large star-schema HINs without asking users to specify these constraints; that is, given a set Q of query vertices with the same type, find the most-likely community from a star-schema HIN containing Q , in which all the vertices are with the same type and close relationships. To capture the close relationships among vertices of the community, we employ the meta-path-based core model, and maximize the number of shared meta-paths such that each of them results in a cohesive core containing Q. To enable efficient CS, we first develop online algorithms via exploiting the anti-monotonicity property of shared meta-paths. We further boost the efficiency by proposing a novel index and an efficient index-based algorithm with elegant pruning techniques. Extensive experiments on four real large star-schema HINs show that our solutions are effective and efficient for searching communities, and the index-based algorithm is much faster than the online algorithms.

A chaotic system with attractor coexistence and its synchronization circuit implementation

We construct a three-dimensional chaotic system based on TANG chaotic system and analyze the system dynamics based on the equilibrium points, phase diagram, Lyapunov exponential spectrum, bifurcation diagram, and complexity. The more complexly dynamic behaviors indicate that our designed system has different topology, bifurcation anti-monotonic property and attractor coexistence phenomenon from TANG system. The system has the coexistence of chaotic attractor and point attractor and can select the initial value that is suitable for chaotic secure communication by analyzing the coexistence attractor. The actual digital circuit is implemented with field programmable gate array (FPGA). The system is extremely sensitive to the selections of initial values and system parameters and has good and rich dynamic behavior, which is suitable for the field of chaotic confidential communication. The linear feedback method is used to control the system synchronous and the simulation of synchronous circuit is realized by Multisim software. The simulation results are consistent with the numerical analysis, which lays a theoretical foundation for the application of the system in the field of synchronized confidential communication.

Finding Route Hotspots in Large Labeled Networks

In many advanced network analysis applications, like social networks, e-commerce, and network security, hotspots are generally considered as a group of vertices that are tightly connected owing to the similar characteristics, such as common habits and location proximity. In this article, we investigate the formation of hotspots from an alternative perspective that considers the routes along the network paths as the auxiliary information, and attempt to find the route hotspots in large labeled networks. A route hotspot is a cohesive subgraph that is covered by a set of routes, and these routes correspond to the same sequential pattern consisting of vertices' labels. To the best of our knowledge, the problem of Finding Route Hotspots in Large Labeled Networks has not been tackled in the literature. However, it is challenging as counting the number of hotspots in a network is #P-hard. Inspired by the observation that the sizes of hotspots decrease with the increasing lengths of patterns, we prove several anti-monotonicity properties of hotspots, and then develop a scalable algorithm called FastRH that can use these properties to effectively prune the patterns that cannot form any hotspots. In addition, to avoid the duplicate computation overhead, we judiciously design an effective index structure called RH-Index for storing the hotspot and pattern information collectively, which also enables incremental updating and efficient query processing. Our experimental results on real-world datasets clearly demonstrate the effectiveness and scalability of our proposed methods.

Efficient discovery of co-location patterns from massive spatial datasets with or without rare features

A co-location pattern indicates a group of spatial features whose instances are frequently located together in proximate geographic area. Spatial co-location pattern mining (SCPM) is valuable for many practical applications. Numerous previous SCPM studies emphasize the equal participation per feature. As a result, the interesting co-locations with rare features cannot be captured. In this paper, we propose a novel interest measure, i.e., the weighted participation index (WPI), to identify co-locations with or without rare features. The WPI measure possesses a conditional anti-monotone property which can be utilized to prune the search space. In addition, a fast row instance identification mechanism based on the ordered NR-tree is proposed to enhance efficiency. Subsequently, the ordered NR-tree-based algorithm is developed. To further improve efficiency and process massive spatial data, we break the ordered NR-tree into multiple independent subtrees, and parallelize the ordered NR-tree-based algorithm on MapReduce framework. Extensive experiments are conducted on both real and synthetic datasets to verify the effectiveness, efficiency and scalability of our techniques.

Efficient list based mining of high average utility patterns with maximum average pruning strategies

High average utility pattern mining is the concept proposed to complement drawbacks of high utility pattern mining by considering lengths of patterns along with the utilities of the patterns. High average utility pattern mining should be able to gratify the anti-monotone property like other pattern mining techniques. Many high average utility pattern mining studies to satisfy the anti-monotone property have been proposed in order to improve various upper-bounds because the performance of pattern mining can be improved efficiently by satisfying the anti-monotone property. Although those upper-bounds can effectively reduce the search space, they still take a lot of cost to calculate all unpromising patterns or cannot find them in advance. Therefore, in this paper, a novel high average utility pattern mining approach is proposed by employing two novel upper-bounds called tight maximum average utility upper-bound and maximum remaining average utility upper-bound. Moreover, a newly suggested list-based structure, TA-List, is designed to adopt two pruning strategies. The proposed technique can efficiently extract high average utility patterns by reducing search space. To evaluate the performance of the proposed method, various experiments using real and synthetic datasets are conducted in terms of runtime, memory usage and scalability and the proposed approach is compared with the state-of-the-art high average utility pattern mining algorithms. The results of experiments show that the suggested algorithm has better performance with regard to runtime, memory usage and scalability.

Route to Chaos in an Electrostatic Ion Cyclotron with Higher-Order Source Term

Many conventional experimental analyses have helped us to understand most of the properties of plasma wave interactions and its behavior; nonlinear dynamics has helped us to enhance our analysis. In this paper we have tried to analyze a plasma jerk system for an ion cyclotron plasma oscillation in a magnetic field by including a higher-order source term caused by large-amplitude fluctuations. The multistability and antimonotonicity properties of the plasma system are discussed which were not explored earlier. We have also shown that the large-amplitude limit cycle in the original jerk system model of plasma is now reduced to a much smaller chaotic cycle for the new proposed system with higher-order source term.

Fracmemristor chaotic oscillator with multistable and antimonotonicity properties

Memristor is a non-linear circuit element in which voltage-current relationship is determined by the previous values of the voltage and current, generally the history of the circuit. The nonlinearity in this component can be considered as a fractional-order form, which yields a fractional memristor (fracmemristor). In this paper, a fractional-order memristor in a chaotic oscillator is applied, while the other electronic elements are of integer order. The fractional-order range is determined in a way that the circuit has chaotic solutions. Also, the statistical and dynamical features of this circuit are analyzed. Tools like Lyapunov exponents and bifurcation diagram show the existence of multistability and antimonotonicity, two less common properties in chaotic circuits.

UWFP-Outlier: an efficient frequent-pattern-based outlier detection method for uncertain weighted data streams

In this paper, we propose an efficient frequent-pattern-based outlier detection method, namely, UWFP-Outlier, for identifying the implicit outliers from uncertain weighted data streams. For reducing the time cost of the UWFP-Outlier method, in the weighted frequent pattern mining phase, we introduce the concepts of the maximal weight and maximal probability to form a compact anti-monotonic property, thereby reducing the scale of potential extensible patterns. For accurately detecting the outliers, in the outlier detection phase, we design two deviation indices to measure the deviation degree of each transaction in the uncertain weighted data streams by considering more factors that may influence its deviation degree; then, the transactions which have large deviation degrees are judged as outliers. The experimental results indicate that the proposed UWFP-Outlier method can accurately detect the outliers from uncertain weighted data streams with a lower time cost.

Cohesive Subgraph Search Using Keywords in Large Networks

Keyword search has been widely studied to retrieve relevant substructures from graphs for a given set of keywords. However, existing well-studied approaches aim at finding compact trees/subgraphs containing the keywords, and ignore a critical measure, density, to represent how strongly and stably the keyword nodes are connected in the substructure. In this paper, given a set of keywords <inline-formula><tex-math notation="LaTeX">$Q = \lbrace w_1, w_2, \ldots, w_l\rbrace$</tex-math></inline-formula> , we study the problem of finding a cohesive subgraph containing <inline-formula><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> with high density and compactness from a graph <inline-formula><tex-math notation="LaTeX">$G$</tex-math></inline-formula> . We model the cohesive subgraph based on a carefully chosen <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -truss model, and formulate the problem of finding cohesive subgraphs for keyword queries as <i>minimal dense truss</i> search problem, i.e., finding minimal subgraph that maximizes the trussness covering <inline-formula><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> . However, unlike <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -truss based community search that can be efficiently done based on the local search from a given set of nodes, <i>minimal dense truss</i> search for keyword queries is a nontrivial task as the subset of keyword nodes to be included in the retrieved substructure is previously unknown. To tackle this problem, we first design a novel hybrid KT-Index to keep the keyword and truss information compacly, and then propose an efficient algorithm that carries the search on KT-Index directly to find the dense truss with the maximum trussness <inline-formula><tex-math notation="LaTeX">$G_{den}$</tex-math></inline-formula> without repeated accesses to the original graph. Then, we develop a novel refinement approach to extract minimal dense truss from the dense truss <inline-formula><tex-math notation="LaTeX">$G_{den}$</tex-math></inline-formula> , by checking each node at most once based on the anti-monotonicity property derived from <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -truss, together with several optimization strategies including batch based deletion, early-stop based deletion, and local exploration. Moreover, we also extend the proposed method to deal with the top- <inline-formula><tex-math notation="LaTeX">$r$</tex-math></inline-formula> search. Extensive experimental studies on real-world networks validated the effectiveness and efficiency of our approaches.

Efficient Discovery of Weighted Frequent Neighborhood Itemsets in Very Large Spatiotemporal Databases

Weighted Frequent Itemset (WFI) mining is an important model in data mining. It aims to discover all itemsets whose weighted sum in a transactional database is no less than the user-specified threshold value. Most previous works focused on finding WFIs in a transactional database and did not recognize the spatiotemporal characteristics of an item within the data. This paper proposes a more flexible model of Weighted Frequent Neighborhood Itemsets (WFNI) that may exist in a spatiotemporal database. The recommended patterns may be found very useful in many real-world applications. For instance, an WFNI generated from an air pollution database indicates a geographical region where people have been exposed to high levels of an air pollutant, say $PM2.5$ . The generated WFNIs do not satisfy the anti-monotonic property. Two new measures have been presented to effectively reduce the search space and the computational cost of finding the desired patterns. A pattern-growth algorithm, called Spatial Weighted Frequent Pattern-growth , has also been presented to find all WFNIs in a spatiotemporal database. Experimental results demonstrate that the proposed algorithm is efficient. We also describe a case study in which our model has been used to find useful information in air pollution database.

WMFP-Outlier: An Efficient Maximal Frequent-Pattern-Based Outlier Detection Approach for Weighted Data Streams

Since outliers are the major factors that affect accuracy in data science, many outlier detection approaches have been proposed for effectively identifying the implicit outliers from static datasets, thereby improving the reliability of the data. In recent years, data streams have been the main form of data, and the data elements in a data stream are not always of equal importance. However, the existing outlier detection approaches do not consider the weight conditions; hence, these methods are not suitable for processing weighted data streams. In addition, the traditional pattern-based outlier detection approaches incur a high time cost in the outlier detection phase. Aiming at overcoming these problems, this paper proposes a two-phase pattern-based outlier detection approach, namely, WMFP-Outlier, for effectively detecting the implicit outliers from a weighted data stream, in which the maximal frequent patterns are used instead of the frequent patterns to accelerate the process of outlier detection. In the process of maximal frequent-pattern mining, the anti-monotonicity property and MFP-array structure are used to accelerate the mining operation. In the process of outlier detection, three deviation indices are designed for measuring the degree of abnormality of each transaction, and the transactions with the highest degrees of abnormality are judged as outliers. Last, several experimental studies are conducted on a synthetic dataset to evaluate the performance of the proposed WMFP-Outlier approach. The results demonstrate that the accuracy of the WMFP-Outlier approach is higher compared to the existing pattern-based outlier detection approaches, and the time cost of the outlier detection phase of WMFP-Outlier is lower than those of the other four compared pattern-based outlier detection approaches.

Antimonotonicity and multistability in a fractional order memristive chaotic oscillator

A memristor diode bridge chaotic circuit is proposed in this paper. The proposed oscillator has only one nonlinear element in the form of memristor. Dynamical properties of the proposed oscillator are investigated. The fractional order model of the oscillator is designed using Grünwald–Letnikov (GL) method. Bifurcation diagrams are plotted which shows that the proposed oscillator exhibits multistability. Finally, the antimonotonicity property of the fractional order oscillator is discussed in detail with two control parameters. Such property has not been explored for fractional order systems before.

Efficiently mining cohesion-based patterns and rules in event sequences

Discovering patterns in long event sequences is an important data mining task. Traditionally, research focused on frequency-based quality measures that allow algorithms to use the anti-monotonicity property to prune the search space and efficiently discover the most frequent patterns. In this work, we step away from such measures, and evaluate patterns using cohesion — a measure of how close to each other the items making up the pattern appear in the sequence on average. We tackle the fact that cohesion is not an anti-monotonic measure by developing an upper bound on cohesion in order to prune the search space. By doing so, we are able to efficiently unearth rare, but strongly cohesive, patterns that existing methods often fail to discover. Furthermore, having found the occurrences of cohesive itemsets in the input sequence, we use them to discover the representative sequential patterns and the dominant partially ordered episodes, without going through the computationally expensive candidate generation procedures typically associated with sequential pattern and episode mining. Experiments show that our method efficiently discovers important patterns that existing state-of-the-art methods fail to discover.

Efficiently Approximating Top-$k$ Sequential Patterns in Transactional Graphs

In real-world networks, an edge (or vertex) may be associated with a transaction database, where each transaction consists of a set of items to describe the attributes or behaviors of the edge (or vertex). This type of graph is named as a transactional graph, and the problem of mining sequential patterns from transactional graphs is to discover the subsequences of transaction sequences that frequently appear in many paths of the graph. Solving this problem can facilitate broad applications ranging from social network analysis to urban computing. However, this task is not trivial due to a large number of sequences existed in the graph. In particular, each path of the graph may induce multiple sequences of transactions, and gathering the transaction sequences induced by all the paths may lead to an extremely large volume. To efficiently approximate the top-k patterns, we propose a Parallelized Sampling-based Approach For Mining Top-k Sequential Patterns, PSMSP, which involves two key techniques: (a) a parallelized unbiased sequence sampling approach based on a sequence balanced graph partition strategy, and (b) a novel PSP-Tree structure to efficiently mine the patterns based on the anti-monotonicity properties. The experimental results on synthetic and real-world datasets demonstrate that the PSMSP can successfully find the sequential patterns with superior efficiency.

Selective Database Projections Based Approach for Mining High-Utility Itemsets

High-utility itemset mining (HilIM) is an emerging area of data mining and is widely used. HilIM differs from the frequent itemset mining (FIM), as the latter considers only the frequency factor, whereas the former has been designed to address both quantity and profit factors to reveal the most profitable products. The challenges of generating the HilI include exponential complexity in both time and space. Moreover, the pruning techniques of reducing the search space, which is available in FIM because of their monotonic and anti-monotonic properties, cannot be used in HilIM. In this paper, we propose a novel selective database projection-based HilI mining algorithm (SPHilI-Miner). We introduce an efficient data format, named HilI-RTPL, which is an optimum and compact representation of data requiring low memory. We also propose two novel data structures, viz, selective database projection utility list and Tail-Count list to prune the search space for HilI mining. Selective projections of the database reduce the scanning time of the database making our proposed approach more efficient. It creates unique data instances and new projections for data having less dimensions thereby resulting in faster HilI mining. We also prove upper bounds on the amount of memory consumed by these projections. Experimental comparisons on various benchmark data sets show that the SPHilI-Miner algorithm outperforms the state-of-the-art algorithms in terms of computation time, memory usage, scalability, and candidates generation.