Using multiple indexes for efficient subsequence matching in time-series databases

In this paper, an algorithm is proposed for subsequence matching that supports normalization transform in time-series databases. Normalization transform enables finding sequences with similar fluctuation patterns even though they are not close to each other before the normalization transform. Simple application of existing subsequence matching algorithms to support normalization transform is not feasible since the algorithms do not have information for normalization transform of subsequences of arbitrary lengths. Application of the existing whole matching algorithm supporting normalization transform to the subsequence matching is feasible, but requires an index for every possible length of the query sequence causing serious overhead on both storage space and update time. The proposed algorithm generates indexes only for a small number of different lengths of query sequences. For subsequence matching it selects the most appropriate index among them. Better search performance can be obtained by using more indexes. In this paper, the approach is called index interpolation. It is formally proved that the proposed algorithm does not cause false dismissal. The search performance can be traded off with storage space by adjusting the number of indexes. For performance evaluation, a series of experiments is conducted using the indexes for only five different lengths out of lengths 256~512 of the query sequence. The results show that the proposed algorithm outperforms the sequential scan by up to 2.4 times on the average when the selectivity of the query is 10?2 and up to 14.6 times when it is 10?5. Since the proposed algorithm performs better with smaller selectivities, it is suitable for practical situations, where the queries with smaller selectivities are much more frequent.

Time series and multimedia data are ubiquitous; large volumes of such data are routinely created in scientific, industrial, entertainment, medical and biological domains. Examples include gene expression data, X-rays, electrocardiograms, electroencephalograms, gait analysis, stock market quotes, space telemetry etc.A decade ago, a seminal paper by Faloutsos, Ranganathan, Manolopoulos appeared in SIGMOD [1]. The paper, Fast Subsequence Matching in Time-Series Databases, has spawned at least a thousand references and extensions in the database/data mining and information retrieval communities. This tutorial will summarize the decade of progress since this influential paper appeared.

In our previous works, we have found the optimal window size for ALOS2-PALSAR2 data is $7 \times 7$ (or other window size settings including around 50 pixels). Such an optimal window size is fixed for the whole observation area. However, the optimal window size for different types of targets are actually different. In order to improve general interpretation performance, we propose a “target-wise” window size optimization algorithm. The process is like automatically zooming and finding the particular optimal window sizes for different target areas. The results show that the proposed algorithm has higher interpretation performance than fixed-type window size optimization.

Empirical investigation of optimal window size using the least squares image matching method

LiDAR is a useful technology for gathering point cloud data from its environment and has been adapted to many applications. We use a cost-efficient LiDAR system attached to a moving object to estimate the location of the moving object using referenced linear structures. In the stationary state, the accuracy of extracting linear structures is low given the low-cost LiDAR. We propose a merging scheme for the LiDAR data frames to improve the accuracy by using the movement of the moving object. The proposed scheme tries to find the optimal window size by means of an entropy analysis. The optimal window size is determined by finding the minimum point between the entropy indicator of the ideal result and the entropy indicator of the actual result of each window size. The proposed indicator can describe the accuracy of the entire path of the moving object at each window size using a simple single value. The experimental results show that the proposed scheme can improve the linear structure extraction accuracy.

Relationship between braking intensity and driver heart rate as a function of the size of the measurement window and its position

Due to the limitation from the uncertainty principle, the window size consistently affects the resolution of time–frequency distributions. Determining the optimal window size is crucial for time–frequency analysis. In this work, we propose the concept of the reliable window width range along time and frequency axes, which simplifies the process of determining the optimal window size and the search range for adaptive methods. Moreover, in existing work, adaptive time–frequency analyses apply either time- or frequency-varying windows. In this study, we utilize a multitaper technique to integrate time- and frequency-varying windows. The proposed concept of the reliable window width range can be applied to any window-based time–frequency analysis method and enhance post-processing methods in the time–frequency plane. Subsequently, together with the reliable window width range, we propose the multitaper adaptive time–frequency windowed synchroextracting transform. It can estimate the optimal window size for time and frequency axes simultaneously and achieve a more energy-concentrated time–frequency analysis result.

We investigate clustered orthogonal frequency-division multiplexing (OFDM) with adaptive antenna arrays for interference suppression. To calculate weights for interference suppression, instantaneous correlations of the received signals and channel responses corresponding to the desired signals have to be estimated. However, due to smaller size of each cluster for clustered OFDM than for classical OFDM, the discrete Fourier transform (DFT)-based estimator has large leakage and results in severe performance degradation. Therefore, a polynomial-based parameter estimator is proposed to combat the severe leakage of the DFT based estimator. We study the impact of the polynomial order and window size on the estimation error. An approximately optimal window size for the polynomial-based estimator is obtained and an adaptive algorithm for the optimal window size is developed. With the adaptive algorithm, the polynomial-based estimator has no leakage and does not require channel statistics. Simulation results show that the developed algorithm improves the performance significantly.

The phase-shifting point diffraction interferometer (PS/PDI) is so far the most accurate measurement tool in atwavelength interferometry of projection optics for extreme ultraviolet lithography (EUVL). The complicate interrelationships between configuration parameters of PS/PDI call for an optimization to achieve high accuracy of PS/PDI. In this paper, a novel system-level modeling approach is proposed to optimize the parameters of PS/PDI designed for visible light (λ=632.8nm) concept proof experiment. The optimal reference pinhole size selection is performed by modeling pinhole spatial filtering effect using Diffraction-Based Beam Propagation (BPR) module of CODE V and in house software. The result shows that various pinhole diameters ranging from 1.6um to 2.2um should be used in our PS/PDI experiment. The test window size and grating duty cycle optimization, which is based on the spatial frequency domain analysis of PS/PDI, is conducted by modeling the entire PS/PDI system using Physical Optics Propagation (POP) module of Zemax and in house software. The optimal window size is approximately 62um for a given window-pinhole separation of 63.3um. The optimal duty cycle of grating is calculated to be 83% to obtain the maximum fringe contrast of 0.879.

What is the optimal shape and size of a cortical window that least affects bone strength? A biomechanical study.

PurposeThis paper introduces a novel method, Variance Rule-based Window Size Tracking (VR-WT), for deriving a sequence of estimation window sizes. This approach not only identifies structural change points but also ascertains the optimal size of the estimation window. VR-WT is designed to achieve accurate model estimation and is versatile enough to be applied across a range of models in various disciplines.Design/methodology/approachThis paper proposes a new method named Variance Rule-based Window size Tracking (VR-WT), which derives a sequence of estimation window sizes. The concept of VR-WT is inspired by the Potential Scale Reduction Factor (PSRF), a tool used to evaluate the convergence and stationarity of MCMC.FindingsMonte Carlo simulation study demonstrates that VR-WT accurately detects structural change points and select appropriate window sizes. The VR-WT is essential in applications where accurate estimation of model parameters and inference about their value, sign, and significance are critical. The VR-WT has also helped us understand shifts in parameter-based inference, ensuring stability across periods and highlighting how the timing and impact of market shocks vary across fields and datasets.Originality/valueThe first distinction of the VR-WT lies in its purpose and methodological differences. The VR-WT focuses on precise parameter estimation. By dynamically tracking window sizes, VR-WT selects flexible window sizes and enables the visualization of structural changes. The second distinction of VR-WT lies in its broad applicability and versatility. We conducted empirical applications across three fields of study: CAPM; interdependence analysis between global stock markets; and the study of time-dependent energy prices.

본 논문에서는 시계열 데이터베이스에서 타임 워핑 하의 서브시퀀스 매칭을 효과적으로 처리하는 방안에 관하여 논의한다. 타임 워핑은 시퀀스의 길이가 서로 다른 경우에도 유사한 패턴을 갖는 시퀀스들을 찾을 수 있도록 해 준다. 먼저, 사전 실험을 통하여 기존의 기본적인 처리 방식인 Naive-Scan의 성능 병목이 CPU 처리 과정에 있음을 지적하고, Naive-Scan의 CPU 처리 과정을 최적화하는 새로운 기법을 제안한다. 제안된 기법은 질의 시퀀스와 서브시퀀스들간의 타임 워핑 거리들을 계산하는 과정에서 발생하는 중복 작업들을 사전에 제거함으로써 CPU 처리 성능을 극대화한다. 제안된 기법이 착오 기각을 발생시키지 않음과 Naive-Scan을 처리하기 위한 최적의 기법임을 이론적으로 증명한다. 또한, 제안된 기법을 기존의 타임 워핑 하의 서브시퀀스 매칭 기법인 LB-Scan과 ST-Filter의 후처리 정량적으로 검증한다. 실험 결과에 의하면, 기존의 타임 워핑 하의 서비시퀀스 매칭을 위한 모든 기법들이 제안된 최적화 기법에 의하여 성능이 개선되는 것으로 나타났다. 특히, Nsive-Scan은 최적화 기법의 적용 전에는 가장 떨어지는 성능을 보였으나, 최적화 기법의 적용 후에는 모든 경우에서 ST-Filter나 LB-Scan을 사용한 경우보다 더 좋은 성능을 보였다. 이것은 성능 병목인 CPU 처리 과정을 최적화함으로써 기존 기법들인 Naive-Scan, LB-Scan, ST-Filter 간의 처리 성능 상의 순위 역전 현상이 발생하였음을 보이는 매우 중요한 결과이다. This paper discusses an effective processing of subsequence matching under time warping in time-series databases. Time warping is a trans-formation that enables finding of sequences with similar patterns even when they are of different lengths. Through a preliminary experiment, we first point out that the performance bottleneck of Naive-Scan, a basic method for processing of subsequence matching under time warping, is on the CPU processing step. Then, we propose a novel method that optimizes the CPU processing step of Naive-Scan. The proposed method maximizes the CPU performance by eliminating all the redundant calculations occurring in computing the time warping distance between the query sequence and data subsequences. We formally prove the proposed method does not incur false dismissals and also is the optimal one for processing Naive-Scan. Also, we discuss the we discuss to apply the proposed method to the post-processing step of LB-Scan and ST-Filter, the previous methods for processing of subsequence matching under time warping. Then, we quantitatively verify the performance improvement ef-fects obtained by the proposed method via extensive experiments. The result shows that the performance of all the three previous methods im-proves by employing the proposed method. Especially, Naive-Scan, which is known to show the worst performance, performs much better than LB-Scan as well as ST-Filter in all cases when it employs the proposed method for CPU processing. This result is so meaningful in that the performance inversion among Nive- Scan, LB-Scan, and ST-Filter has occurred by optimizing the CPU processing step, which is their perform-ance bottleneck.

Quantification of the climate change-induced variations in Intensity–Duration–Frequency curves in the Canadian Prairies

The design of space-time turbo trellis codes (ST Turbo TC) for improving the bandwidth efficiency and the reliability of wireless data networks, which is based on the turbo structure, has been proposed in the literature. However, like other turbo based coding schemes, the fundamental problems with the ST Turbo TC decoder are its complexity and decoding delay. In some cases the decoding delay may be so long that the use of ST Turbo TC system is unattractive for time sensitive applications. The aim of this paper is to propose a simplified ST Turbo TC decoder using the sliding window technique in order to achieve memory savings and reduce decoding delay. In particular, we consider the performance of QPSK ST Turbo TC schemes on fast fading channels for various system parameters. Different window sizes are employed and investigated. Through computer simulation, the optimum window sizes are defined for different system parameters.

Gene tree discordance along a set of aligned genomes presents a challenge for phylogenomic methods to identify the non-recombining regions and reconstruct the phylogenetic tree for each region. To address this problem, many studies used the non-overlapping window approach, often with an arbitrary selection of fixed window sizes that potentially include intra-window recombination events. In this study, we propose an information theoretic approach to select a window size that best reflects the underlying histories of the alignment. First, we simulated chromosome alignments that reflected the key characteristics of an empirical data set and found that the Akaike information criterion (AIC) is a good predictor of window size accuracy in correctly recovering the tree topologies of the alignment. To address the issue of missing data in empirical data sets, we designed a stepwise non-overlapping window approach that compares the AIC of two window sizes at a time, retaining only genomic regions that can be analyzed using both window sizes. We then applied this method to the genomes of Heliconius butterflies and great apes. We found that the best window sizes for the butterflies’ chromosomes ranged from ≤125 to 250 bp, which are much shorter than those used in a previous study even though this difference in window size did not significantly change the most common topologies across the genome. On the other hand, the best window sizes for great apes’ chromosomes ranged from 500 bp to 1 kb with the proportion of the major topology (grouping human and chimpanzee) falling between 60% and 87%, consistent with previous findings. Additionally, we observed a notable impact of gene tree estimation error and concatenation when using small and large windows, respectively. For instance, the proportion of the major topology for great apes was 50% when using 250 bp windows, but reached almost 100% for 64 kb windows. In conclusion, our study highlights the challenges associated with selecting a fixed window size in non-overlapping window analyses and proposes the AIC as a less arbitrary way to select the optimal window size when running the non-overlapping window method on whole genome alignments.