11973783
Answering Approximate Range Aggregate Queries on OLAP Data Cubes with Probabilistic Guarantees
Approximate range aggregate queries are one of the most frequent and useful kinds of queries for Decision Support Systems (DSS). Traditionally, sampling- based techniques have been proposed to tackle this problem. However, its effectiveness will degrade when the underlying data distribution is skewed. Another approach based on the outlier management can limit the effect of data skew but fails to address other requirements of approximate range aggregate queries, such as error guarantees and query processing efficiency. In this paper, we present a technique that provide approximate answers to range aggregate queries on OLAP data cubes efficiently with theoretical error guarantees. Our basic idea is to build different data structures for outliers and the rest of the data. Experimental results verified the effectiveness of our proposed methods.
3416923
Efficient Computation of the Skyline Cube
Skyline has been proposed as an important operator for multi-criteria decision making, data mining and visualization, and user-preference queries. In this paper. we consider the problem of efficiently computing a SKYCUBE, which consists of skylines of all possible non-empty subsets of a given set of dimensions. While existing skyline computation algorithms can be immediately extended to computing each skyline query independently, such "shared-nothing" algorithms are inefficient. We develop several computation sharing strategies based on effectively identifying the computation dependencies among multiple related skyline queries. Based on these sharing strategies, two novel algorithms, Bottom-Up and Top-Down algorithms, are proposed to compute SKYCUBE efficiently. Finally, our extensive performance evaluations confirm the effectiveness of the sharing strategies. It is shown that new algorithms significantly outperform the naive ones.
2266606
Space-efficient Relative Error Order Sketch over Data Streams
We consider the problem of continuously maintaining order sketches over data streams with a relative rank error guarantee ∊. Novel space-efficient and one-scan randomised techniques are developed. Our first randomised algorithm can guarantee such a relative error precision ∊ with confidence 1 - \delta using O( 1\_ \in \frac{1} {2}2 log 1d log ∊^2N) space, where N is the number of data elements seen so far in a data stream. Then, a new one-scan space compression technique is developed. Combined with the first randomised algorithm, the one-scan space compression technique yields another one-scan randomised algorithm that guarantees the space requirement is O( 1\frac{1} { \in } log(1\frac{1}{ \in } log 1\begin{gathered} \frac{1}{\delta } \hfill \\ \hfill \\ \end{gathered} )\frac{{\log ^{2 + \alpha } \in N}} {{1 - 1/2^\alpha }} (for\alpha \gt 0) on average while the worst case space remains O( \frac{1}{{ \in ^2 }}\log \frac{1} {\delta }\log \in ^2 N). These results are immediately applicable to approximately computing quantiles over data streams with a relative error guarantee \in and significantly improve the previous best space bound O( \frac{1} {{ \in ^3 }}\log \frac{1}{\delta }\log N). Our extensive experiment results demonstrate that both techniques can support an on-line computation against high speed data streams.
15045713
Visual Specification and Optimization of XQuery Using VXQ
As the popularity of XML increases, the need for querying collections of XML data from various systems becomes imperative. Proposed by W3C, XQuery is becoming a standard for querying such systems. However, the complexity of XQuery prevents its usage by broad audience. This paper proposes a visual XQuery specification language called VXQ to address this issue. By intuitive abstractions of XML and XQuery, the proposed system can generate XQueries for users that have little knowledge about the language. We show that our visual language is more expressive than previous proposals. Finally, we extend our proposed visual XQuery to support query rewriting and optimization for multiple XQuery systems.
6564567
Stabbing the sky: efficient skyline computation over sliding windows
We consider the problem of efficiently computing the skyline against the most recent N elements in a data stream seen so far. Specifically, we study the n-of-N skyline queries; that is, computing the skyline for the most recent n (/spl forall/n/spl les/N) elements. Firstly, we developed an effective pruning technique to minimize the number of elements to be kept. It can be shown that on average storing only O(log/sup d/ N) elements from the most recent N elements is sufficient to support the precise computation of all n-of-N skyline queries in a d-dimension space if the data distribution on each dimension is independent. Then, a novel encoding scheme is proposed, together with efficient update techniques, for the stored elements, so that computing an n-of-N skyline query in a d-dimension space takes O(log N+s) time that is reduced to O(d log log N+s) if the data distribution is independent, where s is the number of skyline points. Thirdly, a novel trigger based technique is provided to process continuous n-of-N skyline queries with O(/spl delta/) time to update the current result per new data element and O(log s) time to update the trigger list per result change, where /spl delta/ is the number of element changes from the current result to the new result. Finally, we extend our techniques to computing the skyline against an arbitrary window in the most recent N element. Besides theoretical performance guarantees, our extensive experiments demonstrated that the new techniques can support on-line skyline query computation over very rapid data streams.
1993887
Locating Motifs in Time-Series Data
Finding motifs in time-series is proposed to make clustering of time-series subsequences meaningful, because most existing algorithms of clustering time-series subsequences are reported meaningless in recent studies. The existing motif finding algorithms emphasize the efficiency at the expense of quality, in terms of the number of time-series subsequences in a motif and the total number of motifs found. In this paper, we formalize the problem as a continuous top-k motif balls problem in an m-dimensional space, and propose heuristic approaches that can significantly improve the quality of motifs with reasonable overhead, as shown in our experimental studies.
7654975
Using low-discrepancy sequences and the Crofton formula to compute surface areas of geometric models
The surface area of a geometric model, like its volume, is an important integral property that needs to be evaluated frequently and accurately in practice. In this paper, we present a new quasi-Monte Carlo method using low-discrepancy sequences for computing the surface area of a 3D object. We show that the new method is more efficient than a Monte Carlo method using pseudo-random numbers. This method is based on the Cauchy ‐ Crofton formula from integral geometry, and it computes the surface area of a 3D body B by counting the number of intersection points between the boundary surface of B and a set of straight lines in E 3 . Low discrepancy sequences are used to generate the set of lines in E 3 to reduce the estimation errors that would be caused by using statistically uniformly distributed lines. We study and compare two different methods for generating 3D random lines, and demonstrate their validity theoretically and experimentally. Experiments suggest that the new quasi-Monte Carlo method is also more efficient than the conventional approach based on surface tessellation. q 2002 Elsevier Science Ltd. All rights reserved.
1459613
PK-tree: A Spatial Index Structure for High Dimensional Point Data
In this chapter we present the PK-tree which is an index structure for high dimensional point data. The proposed indexing structure can be viewed as combining aspects of the PR-quad or K-D tree but where unnecessary nodes are eliminated. The unnecessary nodes are typically the result of skew in the point distribution and we show that by eliminating these nodes the performance of the resulting index is robust to skewed data distributions. The index structure is formally defined, efficiently updateable and bounds on the number of nodes and the mean height of the tree can be proved. Bounds on the expected height of the tree can be given under certain mild constraints on the spatial distribution of points. Empirical evidence both on real data sets and generated data sets shows that the PK-tree outperforms the recently proposed spatial indexes based on the R-tree and X-tree by a wide margin. It is also significant that the relative performance advantage of the PK-tree grows with the dimensionality of the data set.
17166482
Benchmarking the effectiveness of sequential pattern mining methods
Recently, there is an increasing interest in new intelligent mining methods to find more meaningful and compact results. In intelligent data mining research, accessing the quality and usefulness of the results from different mining methods is essential. However, there is no general benchmarking criteria to evaluate whether these new methods are indeed more effective compared to the traditional methods. Here we propose a novel benchmarking criteria that can systematically evaluate the effectiveness of any sequential pattern mining method under a variety of situations. The benchmark evaluates how well a mining method finds known common patterns in synthetic data. Such an evaluation provides a comprehensive understanding of the resulting patterns generated from any mining method empirically. In this paper, the criteria are applied to conduct a detailed comparison study of the support-based sequential pattern model with an approximate pattern model based on sequence alignment. The study suggests that the alignment model will give a good summary of the sequential data in the form of a set of common patterns in the data. In contrast, the support model generates massive amounts of frequent patterns with much redundancy. This suggests that the results of the support model require more post processing before it can be of actual use in real applications.
28890
Extension of Lower Probabilities and Coherence of Belief Measures
Coherence is an important concept which is introduced and discussed in a new mathematics branch, Imprecise Probability Theory. By using the Choquet integral, belief measures can be extended to be coherent lower previsions on the linear space consisting of all bounded functions. As a special case, we establish that all belief measures are coherent imprecise probabilities.
1884379
Penalty Function Approach for Constrained Convolutive Blind Source Separation
A new approach for convolutive blind source separation(BSS) using penalty functions is proposed in this paper. Motivated by nonlinear programming techniques for the constrained optimization problem, it converts the convolutive BSS into a joint diagonalization problem with unconstrained optimization. Theoretical analyses together with numerical evaluations reveal that the proposed method not only improves the separation performance by significantly reducing the effect of large errors within the elements of covariance matrices at low frequency bins and removes the degenerate solution induced by a null unmixing matrix, but also provides an unified framework to constrained BSS.