Time Series Search Research Articles

A Monte Carlo Approach to Biomedical Time Series Search.

Time series subsequence matching (or signal searching) has importance in a variety of areas in health care informatics. These areas include case-based diagnosis and treatment as well as the discovery of trends and correlations between data. Much of the traditional research in signal searching has focused on high dimensional R-NN matching. However, the results of R-NN are often small and yield minimal information gain; especially with higher dimensional data. This paper proposes a randomized Monte Carlo sampling method to broaden search criteria such that the query results are an accurate sampling of the complete result set. The proposed method is shown both theoretically and empirically to improve information gain. The number of query results are increased by several orders of magnitude over approximate exact matching schemes and fall within a Gaussian distribution. The proposed method also shows excellent performance as the majority of overhead added by sampling can be mitigated through parallelization. Experiments are run on both simulated and real-world biomedical datasets.

Aggregated Indexing of Biomedical Time Series Data.

Remote and wearable medical sensing has the potential to create very large and high dimensional datasets. Medical time series databases must be able to efficiently store, index, and mine these datasets to enable medical professionals to effectively analyze data collected from their patients. Conventional high dimensional indexing methods are a two stage process. First, a superset of the true matches is efficiently extracted from the database. Second, supersets are pruned by comparing each of their objects to the query object and rejecting any objects falling outside a predetermined radius. This pruning stage heavily dominates the computational complexity of most conventional search algorithms. Therefore, indexing algorithms can be significantly improved by reducing the amount of pruning. This paper presents an online algorithm to aggregate biomedical times series data to significantly reduce the search space (index size) without compromising the quality of search results. This algorithm is built on the observation that biomedical time series signals are composed of cyclical and often similar patterns. This algorithm takes in a stream of segments and groups them to highly concentrated collections. Locality Sensitive Hashing (LSH) is used to reduce the overall complexity of the algorithm, allowing it to run online. The output of this aggregation is used to populate an index. The proposed algorithm yields logarithmic growth of the index (with respect to the total number of objects) while keeping sensitivity and specificity simultaneously above 98%. Both memory and runtime complexities of time series search are improved when using aggregated indexes. In addition, data mining tasks, such as clustering, exhibit runtimes that are orders of magnitudes faster when run on aggregated indexes.

Time Series Subsequence Retrieval Based on the Properties of Multi-index

Nowadays, the approach of window mechanism indexing for subsequence retrieval is the mostly used in one-dimensional time series subsequence algorithm. Among the existing time series subsequence retrieval algorithm, the multi-index concept has been proposed, but this method which is still a one-dimensional time series, merely divides the time series on the time dimension to establish the multi-index structure. Current high-dimensional time series retrieval research is still dominated by a single-index structure. This paper demonstrates a multi-index method for high dimensional time series search, in accordance with division based on the strength of correlation between the properties of high-dimensional time series to create the multi-index structure. Related properties are in the same index, non-relevant ones are in a different index. This paper cites human motion high time series to show the advantages of time series subsequence retrieval based on the properties of multi-index which improve the retrieval accuracy and reduce the search complexity.

Online algorithms for the multiple time series search problem

This work investigates the online multiple time series search problem. Given a storage with finite capability, a player receives one product for sale and observes a selling price as well at each period. With the knowledge that prices in all periods vary within [m,M](0<m<M), the player decides at the period whether to sell some of the products in the storage together with the one currently received at the price observed or to store the current one in the storage. Our main contributions are three online algorithms TRPP, SOEP and TS where TS is a combination of TRPP and SOEP, and their competitiveness analyses. Moreover, we prove a lower bound of the competitive ratio for the problem, and prove that TS is optimal as the ratio M/m goes to infinity. Numerical computation further shows that the gap between the upper and lower bounds first increases and then decreases as M/m rises.

A SEARCH FOR ADDITIONAL PLANETS IN FIVE OF THE EXOPLANETARY SYSTEMS STUDIED BY THE NASAEPOXIMISSION

We present time series photometry and constraints on additional planets in five of the exoplanetary systems studied by the EPOCh (Extrasolar Planet Observation and Characterization) component of the NASA EPOXI mission: HAT-P-4, TrES-3, TrES-2, WASP-3, and HAT-P-7. We conduct a search of the high-precision time series for photometric transits of additional planets. We find no candidate transits with significance higher than our detection limit. From Monte Carlo tests of the time series using putative periods from 0.5 days to 7 days, we demonstrate the sensitivity to detect Neptune-sized companions around TrES-2, sub-Saturn-sized companions in the HAT-P-4, TrES-3, and WASP-3 systems, and Saturn-sized companions around HAT-P-7. We investigate in particular our sensitivity to additional transits in the dynamically favorable 3:2 and 2:1 exterior resonances with the known exoplanets: if we assume coplanar orbits with the known planets, then companions in these resonances with HAT-P-4b, WASP-3b, and HAT-P-7b would be expected to transit, and we can set lower limits on the radii of companions in these systems. In the nearly grazing exoplanetary systems TrES-3 and TrES-2, additional coplanar planets in these resonances are not expected to transit. However, we place lower limits on the radii of companions that would transit if the orbits were misaligned by 2.0 degrees and 1.4 degrees for TrES-3 and TrES-2, respectively.

Optimal algorithms for online time series search and one-way trading with interrelated prices

The basic models of online time series search and one-way trading are introduced by El-Yaniv et al. in Algorithmica 30(1), 101---139 (2001) where it is assumed that the prices are bounded within interval [m,M] (0<m<M). In this paper, we consider another case where every two consecutive prices are interrelated, that is, the variation range of each price depends on its preceding price. We present optimal deterministic online algorithms for the two problems, respectively. According to one conclusion in Algorithmica 30(1), 101---139 (2001), we further point out that for the case we considered, an optimal deterministic algorithm for the one-way trading problem can be regarded as an optimal randomized one for the time series search problem, and randomization is useless for the one-way trading problem.

A SEARCH FOR ADDITIONAL PLANETS IN THE NASAEPOXIOBSERVATIONS OF THE EXOPLANET SYSTEM GJ 436

We present time series photometry of the M dwarf transiting exoplanet system GJ 436 obtained with the the EPOCh (Extrasolar Planet Observation and Characterization) component of the NASA EPOXI mission. We conduct a search of the high-precision time series for additional planets around GJ 436, which could be revealed either directly through their photometric transits, or indirectly through the variations these second planets induce on the transits of the previously known planet. In the case of GJ 436, the presence of a second planet is perhaps indicated by the residual orbital eccentricity of the known hot Neptune companion. We find no candidate transits with significance higher than our detection limit. From Monte Carlo tests of the time series, we rule out transiting planets larger than 1.5 R_Earth interior to GJ 436b with 95% confidence, and larger than 1.25 R_Earth with 80% confidence. Assuming coplanarity of additional planets with the orbit of GJ 436b, we cannot expect that putative planets with orbital periods longer than about 3.4 days will transit. However, if such a planet were to transit, we rule out planets larger than 2.0 R_Earth with orbital periods less than 8.5 days with 95% confidence. We also place dynamical constraints on additional bodies in the GJ 436 system. Our analysis should serve as a useful guide for similar analyses for which radial velocity measurements are not available, such as those discovered by the Kepler mission. These dynamical constraints on additional planets with periods from 0.5 to 9 days rule out coplanar secular perturbers as small as 10 M_Earth and non-coplanar secular perturbers as small as 1 M_Earth in orbits close in to GJ 436b. We present refined estimates of the system parameters for GJ 436. We also report a sinusoidal modulation in the GJ 436 light curve that we attribute to star spots. [Abridged]

Optimal algorithms for the online time series search problem

In the problem of online time series search introduced by El-Yaniv et al. (2001) [1], a player observes prices one by one over time and shall select exactly one of the prices on its arrival without the knowledge of future prices, aiming to maximize the selected price. In this paper, we extend the problem by introducing profit function. Considering two cases where the search duration is either known or unknown beforehand, we propose two optimal deterministic algorithms respectively. The models and results in this paper generalize those of El-Yaniv et al. (2001) [1].

Approach for effective fractal-based similarity search of stochastic non-stationary time series

Traditional dimension reduction methods about similarity query introduce the smoothness to data series in some degree that the important features of time series about non-linearity and fractal are destroyed.A high-precision random non-stationary time series method named FSPA was proposed based on fractal theory and R/S analysis,which retained a non-linear time series and important fractal characteristics,and realized the reduction of the dimensions.The experiments have been performed on synthetic,as well as real data sequences to evaluate the proposed method,and the results indicate that the method has higher accuracy and requires less storage space.

Similarity Search of Time Series with Moving Average Based Indexing

提出了基于移动均值的索引来解决子序列匹配中的"(-查询"问题;提出并证明了基于移动均值的缩距定理和缩距比关系定理,后者具有很好的"裁减"能力,可以在相似查询时淘汰大部分不符合条件的候选时间序列,从而达到快速相似查找的目的;引入了由Jagadish 等人提出的BATON^*-树,并在此基础上适当修改,建立了MABI索引,极大地加快了相似查询过程;最后,在一个股票交易数据集上进行了实验,证明了MABI索引的良好性能.;In this paper, a method called MABI (moving average based indexing) is proposed to effectively deal with the issue of (-search query in subsequence matching. Two important theorems, distance reduction theorem and DRR(distance reduction rate) relation theorem, are proposed here to be as the basis of MABI. DRR relation theorem has strong capability in pruning those unqualified candidate sequences so as to achieve of fast similarity search. Furthermore, by modifying BATON^* introduced by Jagadish, et al., a multi-way balanced tree structure is introduced, to construct the index from time series, which significantly speeds up the similarity search. Extensive experiments over a stock exchange dataset show that MABI can achieve desirable performance.

다중속성 시계열 데이타베이스의 효율적인 유사 검색

시계열에 대한 색인 및 검색 연구는 하나의 속성으로 구성된 시계열에 대하여 주로 수행되어 왔다. 그러나 음악, 비디오 등의 멀티미디어 데이타베이스는 다중속성 시계열 데이타베이스에서 유사 검색을 다룰 수 있어야 한다. 기존의 다중속성 시계열 데이타베이스에 대한 연구는 두 다중속성 시퀀스간의 유사도로 속성 간의 거리의 누적을 사용하고 있기에, 개별적인 속성 시퀀스에 대한 정보를 상실하게 된다. 본 연구에서는 이러한 문제를 해결하기 위해 속성 시퀀스 측면에서 다중속성 시계열 데이타베이스의 유사검색 기법을 제안한다. 제안된 기법은 검색 공간을 효율적으로 줄일 수 있으며, 착오 누락이 없음을 보장한다. 또한 실험을 통해 제안된 기법의 성능 향상을 확인하였다. Most of previous work on indexing and searching time series focused on the similarity matching and retrieval of one-attribute time series. However, multimedia databases such as music, video need to handle the similarity search in multi-attribute time series. The limitation of the current similarity models for multi-attribute sequences is that there is no consideration for attributes' sequences. The multi-attribute sequences are composed of several attributes' sequences. Since the users may want to find the similar patterns considering attributes's sequences, it is more appropriate to consider the similarity between two multi-attribute sequences in the viewpoint of attributes' sequences. In this paper, we propose the similarity search method based on attributes's sequences in multi-attribute time series databases. The proposed method can efficiently reduce the search space and guarantees no false dismissals. In addition, we give preliminary experimental results to show the effectiveness of the proposed method.

Improving Similarity Search in Time Series Using Wavelets

Sequences constitute a large portion of data stored in databases. Data mining applications require the ability to process similarity queries over a large amount of time series data. The query processing performance is an important factor that needs to be taken into consideration. This article proposes a similarity retrieval algorithm for time series. The proposed approach utilizes wavelet transformation in order to reduce the dimensionality of the time series. The transformed series are indexed using X-Trees, which is a spatial indexing technique able to efficiently index high-dimensional data. The article proves that this technique outperforms the usage of the Fourier transformation, since the wavelet transformation provides better approximation of the time series. Through the experiments, it can be concluded that the optimum performance is obtained using 16 to 20 wavelet coefficients. Furthermore, a novel mechanism for reducing the complexity of the calculation for the false alarms removal is proposed. Storing the approximation coefficients of the penultimate level of the decomposition tree, the Euclidean distance between the two sequences is calculated, thus reducing further the number of false alarms before calculating the actual Euclidean distance using the complete time series. The article concludes with a detailed performance evaluation of the proposed similarity retrieval algorithm using data from the Greek stock market and the temperature measurements from Athens. The comparison is done with techniques that use the Haar transform and the R*-Tree, and the proposed algorithm is shown to outperform them.

Quick audio retrieval using multiple feature vectors

This paper reports a new quick audio search algorithm for the contents based audio retrieval. In the previous work, the time-series audio search method with the upper bound proof was employed. However, the searching speed of a time-series search method is very poor. Therefore, we introduce the preprocessing stage to overcome this defect. In addition to the search speed, the search accuracy is improved by using multiple feature vectors of audio signal. Through the experiment, the results of retrieval performance will be presented.

A quick AND/OR search for multimedia signals based on histogram features

AbstractThe problem of finding the point in time at which a known audio or video source (reference signal) appears in a long audio or video source (input signal) is referred to as a time series search, in contrast to a text string search. In a time series search, a search can be performed quickly by combining the audio and video, and then identifying several search conditions using logical equations. Thus, in this paper the authors describe the application of the time series active search method, a method to search audio signals proposed in the authors' previous paper, to video searches. Next, the authors propose an efficient algorithm for AND searches and OR searches of reference signals. In addition, the authors propose a multimodal AND search which combines audio and video. The proposed algorithms are faster than combining the results of searches performed individually. For instance, in an OR search of a reference signal, when the mutual similarity in the reference signals is above 0.8, five reference signals can be searched in a search time that is 1.2 times faster than searching one reference signal. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(12): 54–64, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10142

Haar wavelets for efficient similarity search of time-series: with and without time warping

We address the handling of time series search based on two important distance definitions: Euclidean distance and time warping distance. The conventional method reduces the dimensionality by means of a discrete Fourier transform. We apply the Haar wavelet transform technique and propose the use of a proper normalization so that the method can guarantee no false dismissal for Euclidean distance. We found that this method has competitive performance from our experiments. Euclidean distance measurement cannot handle the time shifts of patterns. It fails to match the same rise and fall patterns of sequences with different scales. A distance measure that handles this problem is the time warping distance. However, the complexity of computing the time warping distance function is high. Also, as time warping distance is not a metric, most indexing techniques would not guarantee any false dismissal. We propose efficient strategies to mitigate the problems of time warping. We suggest a Haar wavelet-based approximation function for time warping distance, called Low Resolution Time Warping, which results in less computation by trading off a small amount of accuracy. We apply our approximation function to similarity search in time series databases, and show by experiment that it is highly effective in suppressing the number of false alarms in similarity search.

Optimal Search and One-Way Trading Online Algorithms

This paper is concerned with the time series search and one-way trading problems. In the (time series) search problem a player is searching for the maximum (or minimum) price in a sequence that unfolds sequentially, one price at a time. Once during this game the player can decide to accept the current price p in which case the game ends and the player's payoff is p . In the one-way trading problem a trader is given the task of trading dollars to yen. Each day, a new exchange rate is announced and the trader must decide how many dollars to convert to yen according to the current rate. The game ends when the trader trades his entire dollar wealth to yen and his payoff is the number of yen acquired.

Indexing time series using signatures

This paper describes a new approach to indexing time series. Indexing time series is more problematic than indexing text since in extreme we need to find all possible subsequences in the time series sequence. We propose to use signature files to index the time series and we also propose a new method to index the signature files to speed up the search of large time series. We propose a novel index structure, the signature tree, for time series indexing. We implemented the signature tree and we discuss its performance.

Time series search for trend in total ozone measurements

Time series analysis of monthly average total ozone measurements at 37 Dobson stations throughout the world shows that no ozone depletion has occurred at these stations through 1979. The trends at the 14 stations with records from 1958–1979 show an average increase of (1.5±1.0)% (95% confidence). The trends at the other 23 stations with shorter data records show an average increase of (1.0±1.7)%; the choice of stations is not critical to the conclusions. The average change is the sum of all long‐term global trends. The confidence limits are calculated from the variation among stations and include all effects that differ from station to station. A comprehensive evaluation of model adequacy indicated that variations in the statistical methodology have only small effects on the results. The uncertainty in the observed average change decreases with each year's new data. It is concluded that a downward trend from whatever cause equal to half that hypothesized by current atmospheric models as due to chlorofluorocarbons (CFC's) would be detected. These stations provide a good early warning of any depletion at the measuring stations that might be due to CFC's.