A Novel Approach for Mining Time and Space Proximity-based Frequent Sequential Patterns from Trajectory Data

Mining frequent sequential patterns from sequence databases has been a central research topic in data mining and various efficient mining sequential patterns algorithms have been proposed and studied. Recently, a novel sequential pattern mining research, called mining repetitive gapped subsequences, has attracted the attention of many researchers. However, the number of repetitive gapped subsequences generated by even these closed mining algorithms may be too large to understand for users, especially when support threshold is low. In this paper, we propose the problem of how to compress repetitive gapped sequential patterns. A novel distance measure of repetitive gapped sequential patterns and an efficient representative pattern checking scheme, δ-dominate sequential pattern checking are proposed. We also develop an efficient algorithm, CRGSgrow ( Compressing Repetitive Gapped Sequential pattern grow), including an efficient pruning strategy, SyncScan. An empirical study with both real and synthetic data sets clearly shows that the CRGSgrow has good performance.Keywordsrepetitive gapped sequential patterncompressing frequent patterns

Sequential pattern mining is applicable in a wide range of applications since many types of data sets are in a time related format. Besides mining sequential patterns in a single dimension, mining multidimensional sequential patterns can give us more informative and useful patterns. Due to the huge increase in data volume and also quite large search space, efficient solutions for finding patterns in multidimensional sequence data are nowadays very important. For this reason, developing a parallel algorithm is necessary. In this paper, we present a multidimensional sequence model and a parallel algorithm follows the level-wise approach and all participating processors or workers generate candidate sequence and count their supports independently. Simulation experiments show good load balancing and scalable and acceptable speedup over different processors and problem sizes. dense data sets such as telecommunications, where there are many and long frequent patterns, performance of these algorithms degrades incredibly. On the one side, parallel and distributed computing is expected to relieve current mining methods from the sequential bottleneck, providing the ability to scale to massive datasets, and improving the response time. Achieving good performance on today's multiprocessor systems is a non-trivial task. The main challenges include synchronization and communication minimization, work-load balancing, find good data layout and data decomposition, and disk I/O minimization, which is especially important for data mining (4). On the other side, the basic single dimension can not satisfy the requirement of multi-attribute analysis, which is often the case in actual system practice. To address this problem, multidimensional sequence pattern mining is developed. The most time consuming operation in the discovery process of sequential patterns is the computation of the frequency of the occurrences of interesting subsequences in the sequence database. However, the number of sequential patterns grows exponentially and the task of finding all sequential patterns requires a lot of computational resources, which make it an ideal candidate for parallel processing. However, sequential pattern mining suffers from a scalability problem in both memory use and computational time when a dataset size is large. To perform mining on large datasets, we propose to parallelize this task. We demonstrate that our parallel algorithm can effectively alleviate the scalability problem. In this paper, we present a model for multidimensional sequence pattern and then propose a parallel algorithm for mining sequential patterns from multidimensional sequence data. The algorithm is based on the data parallelism strategy of pattern growth. The experimental results show that our parallel algorithms usually achieve good load balancing and scalability.

One hundred and sixty-eight genotypes of cotton from the same growing region were used as a germplasm group to study the validity of different genetic distances in constructing cotton core subset. Mixed linear model approach was employed to unbiasedly predict genotypic values of 20 traits for eliminating the environmental effect. Six commonly used genetic distances (Euclidean, standardized Euclidean, Mahalanobis, city block, cosine and correlation distances) combining four commonly used hierarchical cluster methods (single distance, complete distance, unweighted pair-group average and Ward's methods) were used in the least distance stepwise sampling (LDSS) method for constructing different core subsets. The analyses of variance (ANOVA) of different evaluating parameters showed that the validities of cosine and correlation distances were inferior to those of Euclidean, standardized Euclidean, Mahalanobis and city block distances. Standardized Euclidean distance was slightly more effective than Euclidean, Mahalanobis and city block distances. The principal analysis validated standardized Euclidean distance in the course of constructing practical core subsets. The covariance matrix of accessions might be ill-conditioned when Mahalanobis distance was used to calculate genetic distance at low sampling percentages, which led to bias in small-sized core subset construction. The standardized Euclidean distance is recommended in core subset construction with LDSS method.

Tremendous growth of Location-based technologies resulted in the generation of a huge volume of spatial data, which needs to be analyzed to get potentially important patterns. The spatial patterns extracted can be used to design a better infrastructure ensuring reliable service coverage. Trajectory data is one variant of spatial data that are generated by moving objects travelling across. It is represented as a sequence of spatial coordinates (latitude, longitude) of a location. Trajectory clustering tries to group similar spatial data points to extract the most common movement behaviors. Trajectory data poses major challenges including uncertainty, sampling rate, representation, relationships, spatial autocorrelation, serialization, redundancy, and triviality, which makes it hard to apply traditional clustering algorithms over trajectory data. In this paper, K-Means and DBSCAN (Density-based spatial clustering of applications with noise) clustering algorithms are analyzed using different similarity measures like Euclidean, Hausdorff and Haversine distances with the help of index measures say Adjusted Rand Index (ARI) and Fowlkes-Mallows scores (FMS). Experiment is carried out over two different trajectory datasets and it is proved that usage of Haversine distance for clustering is efficient than Euclidean and Hausdorff distances in terms of spatial trajectory data.

In a cloud environment, resources should be acquired quickly and automatically released at runtime. Traditional trajectory data partitions, indexing and query processing techniques are extended, so that they can take advantage of the cloud of large clusters of highly parallel processing capabilities. There are ways with trajectory data in the cloud database query processing. The advanced sensing techniques available today caused the existence of many types of trajectory datasets whose study can form a strong basis for decision making regarding a data context. Trajectory data generally includes trajectory classification, trajectory clustering, and trajectory associations and so on. All these tools need trajectory similarity measures to get comparisons in trajectory data. Some of the popular existing methods of trajectory similarity include Euclidean distance, semantic distance and there near variants. Each variant of these techniques exhibits notable differences in measurement of similarity and computational difficulty. This paper targeted to deal with this situation with the goal of lower computational efforts in trajectory similarity computations. A two‐phase trajectory similarity measure is defined. The first phase does point level analysis of trajectory points representing all trajectories and the following phase use the analysis to find the similarities. Using a hybrid similarity framework, new means for trajectory clustering and trajectory query processing are developed. From trajectory analysis followed by trajectory clustering, evaluation of cluster quality and processing of trajectory query are undertaken in this paper in different ways from the existing methods. All the proposed developments are tested with trajectory datasets with multiple attributes and the results are more favour to proposed framework than the existing ones.

Previous studies of Mining Closed Sequential Patterns suggested several heuristics and proposed some computationally effective techniques. Like, Bidirectional Extension with closure checking schemas, Back scan search space pruning, and scan skip optimization used in BIDE (BI-Directional Extension) algorithm. Many researchers were inspired with the efficiency of BIDE, have tried to apply the technique implied by BIDE to various kinds of databases; we toofelt that it can be applied over progressive databases. Without tailoring BIDE, it cannot be applied to dynamic databases. The concept of progressive databases explores the nature of incremental databases by defining the parameters like, Period of Interest (POI), user defined minimum support. An algorithm PISA (Progressive mIning Sequential pAttern mining) was proposed by Huang et al. for finding all sequential patterns over progressive databases. The structure of PISA helps in space utilization by limiting the height of the tree, to the length of POI and this issue is also a motivation for further improvement in this work. In this paper, a tree structure LCT (Label, Customer-id, and Time stamp) is proposed, and an approach formining closed sequential patterns using closure checking schemas across the progressive databases concept. The significance of LCT structure is, confining its height to a maximum of two levels. The algorithmic approach describes that the window size can be increased by one unit of time. The complexity of the proposed algorithmic approach is also analysed. The approach is validated using synthetic data sets available in Internet and shows a better performance in comparison to the existing methods.

Frequent pattern mining is a classic data mining technique, generally applicable to a wide range of application domains, and a mature area of research. The fundamental challenge arises from the combinatorial nature of frequent itemsets, scaling exponentially with respect to the number of unique items. Apriori-based and FPTree-based algorithms have dominated the space thus far. Initial phases of this research relied on the Apriori algorithm and utilized a distributed computing environment; we proposed the Cartesian Scheduler to manage Apriori's candidate generation process. To address the limitation of bottom-up frequent pattern mining algorithms such as Apriori and FPGrowth, we propose the Frequent Hierarchical Pattern Tree (FHPTree): a tree structure and new frequent pattern mining paradigm. The classic problem is redefined as frequent hierarchical pattern mining where the goal is to detect frequent maximal pattern covers. Under the proposed paradigm, compressed representations of maximal patterns are mined using a top-down FHPTree traversal, FHPGrowth, which detects large patterns before their subsets, thus yielding significant reductions in computation time. The FHPTree memory footprint is small; the number of nodes in the structure scales linearly with respect to the number of unique items. Additionally, the FHPTree serves as a persistent, dynamic data structure to index frequent patterns and enable efficient searches. When the search space is exponential, efficient targeted mining capabilities are paramount; this is one of the key contributions of the FHPTree. This dissertation will demonstrate the performance of FHPGrowth, achieving a 300x speed up over state-of-the-art maximal pattern mining algorithms and approximately a 2400x speedup when utilizing FHPGrowth in a distributed computing environment. In addition, we allude to future research opportunities, and suggest various modifications to further optimize the FHPTree and FHPGrowth. Moreover, the methods we offer will have an impact on other data mining research areas including contrast set mining as well as spatial and temporal mining.

The behavior of the users of a website may change so quickly that it becomes a real challenge to attempt to make predictions according to the frequent patterns coming from the analysis of an access log file. In order to reduce the obsolescence of behavioral patterns as much as possible, the ideal method would provide frequent patterns in real time, making the result immediately available. In this paper, we propose a method for finding frequent behavioral patterns in real time, whatever the number of connected users. Considering how fast frequent behavior patterns may have changed since the time the access log file was analyzed, this result thus provides completely appropriate navigation schemata for predicting user behavior. Based on a distributed heuristic, our method also tackles and provides answers to several problems within the framework of data mining: the discovery of ‘interesting zones’ (a large number of frequent patterns concentrated over a period of time, or ‘super-frequent’ patterns), discovering very long sequential patterns and interactive data mining (‘on-the-fly’ modification of the minimum support).

Sequential pattern mining is used to find frequent data sequences over time. When sequential patterns are generated, the newly arriving patterns may not be identified as frequent sequential patterns due to the existence of old data and sequences. Progressive sequential pattern mining aims to find the most up-to-date sequential patterns given that obsolete items will be deleted from the sequences. When sequences come with multiple data streams, it is difficult to maintain and update the current sequential patterns. Even worse, when we consider the sequences across multiple streams, previous methods cannot efficiently compute the frequent sequential patterns. In this work, we propose an efficient algorithm PSP-AMS to address this problem. PSP-AMS uses a novel data structure PSP-MS-tree to insert new items, update current items, and delete obsolete items. By maintaining a PSP-MS-tree, PSP-AMS efficiently finds the frequent sequential patterns across multiple streams. The experimental results show that PSP-AMS significantly outperforms previous algorithms for mining of progressive sequential patterns across multiple streams on synthetic data as well as real data.

SummaryAs a well‐known field of big data applications, smart city takes advantage of massive data analysis to achieve efficient management and sustainable development in the current worldwide urbanization process. An important problem in smart city is how to discover frequent trajectory sequence pattern and cluster trajectory. To solve this problem, this paper proposes a cloud‐based taxi trajectory pattern mining and trajectory clustering framework for smart city. Our work mainly includes (1) preprocessing raw Global Positioning System trace by calling the Baidu API Geocoding; (2) proposing a distributed trajectory pattern mining (DTPM) algorithm based onSpark; and (3) proposing a distributed trajectory clustering (DTC) algorithm based onSpark. The proposed DTPM algorithm and DTC algorithm can overcome the high input/output overhead and communication overhead by adopting in‐memory computation. In addition, the proposed DTPM algorithm can avoid generating redundant local trajectory patterns to significantly improve the overall performance. The proposed DTC algorithm can enhance the performance of trajectory similarity computation by transforming the trajectory similarity calculation into AND and OR operators. Experimental results indicate that DTPM algorithm and DTC algorithm can significantly improve the overall performance and scalability of trajectory pattern mining and trajectory clustering on massive taxi trace data. Copyright © 2016 John Wiley & Sons, Ltd.

Rooted Mahalanobis distance based Gustafson-Kessel fuzzy C-means

In this paper, an algorithm for mining the nonredundant closed weighted sequential patterns with flexible time intervals for the medical time series data is proposed. Initially, the sequence weight for each sequence is calculated based on the time interval between the itemsets and subsequently the candidate sequences are generated with flexible time intervals. The next step is, computation of frequent sequential patterns with the aid of proposed support measure and subsequently the frequent sequential patterns are subjected to closure checking process which leads to filter the closed sequential patterns with flexible time intervals. Finally, the proposed methodology produces a necessary sequential patterns which is proved. The proposed methodology constructs closed sequential patterns which are 23.2% lesser than the sequential patterns.

The principle component analysis(PCA) is a common feature extraction method in machine learning and pattern recognition approaches. PCA has been used in many applications, and face recognition in which specific faces are recognizing in an images database is one of the popular applications. The default distance metric which has been used with PCA based-face recognition is Euclidean distance. In this study, we have tested the Mahalanobis distance instead of Euclidean, and PCA based on Mahalanobis distance suggested a better performance on our students images database with highest recognition rate. However, we proposed weighted and normalized Mahalanobis distance based PCA-face recognition(PCA_WNMD). The proposed algorithm (PCA_WNMD) showed an improvement in faces recognition rate when tested on our students images database compared to PCA based on Mahalanobis and default Euclidean distances.

Fuzzy C-means (FCM) is a kind of classic cluster method, which has been widely used in various fields, such as image segmentation and data mining. Euclidean distance is a frequently used distance metric in FCM, but it is only suitable for data with spherical structure. As an extension of Euclidean distance, Mahalanobis distance has been used in Gustafson–Kessel FCM and its variants to tackle ellipsoidal data. For the convenience of optimizing, most existing Mahalanobis distance-based FCM algorithms only focus on squared Mahalanobis distance. However, squared Mahalanobis distance may not be the best distance metric for FCM because it is easy to enlarge the influence of outliers. In this article, we propose a novel <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{2,p}$</tex-math></inline-formula> -norm and Mahalanobis distance-based FCM model, abbreviated as LM-FCM, which can help FCM improve the ability of tackling ellipsoidal clusters and outliers. Then, in order to reduce computational complexity, we propose a more simplified model, abbreviated as SLM-FCM. Furthermore, we develop an iteratively reweighted optimization algorithm to optimize the proposed models and provide a rigorous monotonous convergence proof. Finally, compared with the existing state-of-the-art FCM algorithms, we conduct extensive experiments on both synthetic and real-world datasets to manifest the superior clustering performance and robustness of the proposed algorithms.

Randomness has stimulated mankind's attention and imagination ever since we began to observe the behavior of nature. It was by understanding the randomness and patterns that humans learned to control crops, for example, which led to the creation of the first communities. In the modern world, with the aim of mimicking the randomness of natural phenomena, computers are used to generate sequences that look as random as possible running pseudo-random number generators (PRNG). PRNGs have diverse applications in information security, digital games, simulations, modeling, gambling, arts, among others. Despite this fact, existing methods of randomness measure do not offer a definitive solution to the need of classifying PRNGs. The main methods of randomness measurement consist of statistical tests through which the sequences generated by the algorithms are analyzed. Once PRNGs are analyzed by these test suits, they are considered (un)satisfactory random. This paper explores an aspect that has been neglected in statistical tests: the spatial distribution of pseudo-random sequences. It is conjectured that this distribution is the source of undisclosed patterns in test suites. One way to study this arrangement more depth is using models that explore the relation of values and iterations. The relation of elements in space has to be the basis of the paradigm. This work applies theory of graphs and computational geometry methods to find patterns in pseudo-random sequences. The analyzed sequences are plotted in a Cartesian plan generating a set of points that are converted into graphs considering the Euclidean distance between the points within a radius. The best combination of descriptors formed by measurements of graphs and geometric properties is selected. When patterns emerge, one can point out flaws in the widely used methods for measuring PRNGs quality. It is intended to suggest a complementary approach for the evaluation of PRNGs, contributing to a better classification of the PRNGs and, consequently, to cause improvements in the studies on information security. This includes identifying patterns in sequences generated by algorithms that are considered pseudo-random by current statistical tests and thus identifying the limitations of these assessments.