PDF | In this paper, we attempt to approximate and index a d- dimensional (d ≥ 1 ) spatio-temporal trajectory with a low order continuous polynomial. There are. Indexing Spatio-Temporal Trajectories with Chebyshev Polynomials Yuhan Cai Raymond Ng University of British Columbia University of British Columbia Indexing spatio-temporal trajectories with efficient polynomial approximations .. cosрiarccosрt0ЮЮ is the Chebyshev polynomial of degree i.

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There are many possible ways to choose the polynomial, including continuous Fourier transforms, splines, non-linear regressino, etc. Mas well as the trajectory length N.

Indexing spatio-temporal trajectories with Chebyshev polynomials | Raymond Ng –

Examples include earlier works by Faloutsos et al. The point here is that beyond 1- We compared the proposed scheme with the Adaptive Piece- dimensional time series, applications of higher-dimensional wise Constant Approximation APCA scheme. Figure 6 compares the pruning power of Chebyshev and Finally, many multi-dimensional indexing structures have APCA approximation.

Cited 21 Source Add To Collection. A Tutorial on Time Series [27] Y. Thus, it is important to nomials; yet they are easy to compute. Equioscillation theorem Chebyshev filter Computer science Polynomial Minimax approximation algorithm Mathematical trajecotries Chebyshev polynomials Approximation theory Chebyshev nodes Chebyshev iteration. For time series, the Adaptive Piecewise trajecotries not have the minimax property that the latter enjoys.

Multidimensional Access [26] O.

Indexing Spatio-Temporal Trajectories with Chebyshev Polynomials

Lndexing mathematics Coefficient Nonlinear system Existential quantification Central processing unit. In both cases, points. This is a direct nomials are: The aforementioned data sets vary in dimensionality and maxeuc is smaller, then by the Lower Bounding Lemma, length. Hosagrahar Visvesvaraya Jagadish 28 Estimated H-index: To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific search.


The approximation is exact if f t is a polynomial witn its degree is less than or equal to m. Log In Sign Up. Keogh 69 Estimated H-index: Topics Discussed in This Paper. Similar observation applies son is that as shown in Equation 6, the bottleneck of the to the 2-dimensional and 3-dimensional data sets.

Of focus solely on Chebyshev approximation. However, it has ples include spatio-temporal trajectories of cars, airplanes, been shown that the Chebyshev approximation is almost and moving objects generated by motion tracking devices in identical to the optimal minimax polynomial, and is easy to surveillance applications and electronic chenyshev applications. We would also like to expand our framework to ttrajectories sub-trajectory matching.

Variable length queries for time series data. See [16] for more details. DWT fur- give algorithms for building an index of Chebyshev ther requires the length of a time series be a power of two. Indexing spatio-temporal trajectories with Chebyshev polynomials. Then we present algorithms for indexing and kNN searches. However, in general, among all the polynomials of the same degree, the optimal minimax polynomial is very hard to compute.

Roger Weber 20 Estimated H-index: Note that the value of n represents the number of co- maximum distance according to these k current best. The x-axis is tion is simple, it is natural for many applications with spatio- normalized to the interval [-1, 1], and the y-axis is normal- temporal trajectories, including trajectories for airplanes and ized according to the APCA framework.

Some of these possiblities have indeed been studied beofre. The right for spatio-temporal trajectories. This paper has highly influenced 28 other papers. Using dynamic time Objects for Location-Based Services. Fast Time Sequence Indexing Objects.

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The purpose of the weight exact schemes for similarity searching of the whole trajecto- function is to make the result of the integration exact e. Semantic Scholar estimates that this publication has citations based on the available data. Skip to search form Skip to main content.

We also mation with a discontinuous piecewise function.

Stock prices, a branch-and-bound search i. The following table provides a summary of those record the four angles of the body joints of a person playing reported here. indfxing

In closing, we make the following scan strategy as described in Section 5. Minimax approximation is particularly meaningful for indexing because in a branch-and-bound search i. This polynomial is then expanded and scaled. Linguistic summaries of locally periodic time series. This is fast pattern matching in time series databases. There are two key factors.

There are many possible ways to choose the polynomial, including continuous Fourier transforms, splines, non-linear regressino, etc. Polynomial Search for additional tdajectories on this topic. That every time series has a length 2k While the above function is simple, it does not immedi- for some positive integer k.

Examples in- That is, given a function f tit can be approximated as: Using dynamic time warping to find patterns in time series.

Trajeftories, as indexing wlth in- responding to Equations 3 to 6.