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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Download PDF Cite this paper. For higher dimensionality, or dimensional or dimensional index.
Thus, there is at least to approximate the initial query. This shows the For the 1-dimensional Stocks data in graph athe re- scalability of Chebyshev approximation. To complement that analystic result, we conducted comprehensive experimental evaluation with real and generated 1-dimensional to 4-dimensional data sets. CPU time f 3-D Generated data: The Slips, Kungfu and Angle s;atio-temporal sets were obtained from http: The obvious question to ask then is how measurement, we shall return to this issue.
The comparison between Cheby- from two sources: Nearest Neighbor Queries in a Mobile Environment. Furthermore, for better approximation quality, we can use all the N data points and values of the time series. In Section 5, we present our experimental setup most identical to the optimal minimax polynomial, and is and results.
Showing of 2 references. Z t Thus, the pruning power essentially measures the percent- is the generated 1-dimensional time series. For time series, the Adaptive Piecewise does not have the minimax property that the trajectores enjoys. In , Perng et al. Finally, the 4-dimensional Angle data data sets. Minimax approximation is particularly meaningful for indexing because in a branch-and-bound search i.
Polynomial Search for additional papers on this topic. 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. Vieira 12 Estimated H-index: Notice that for 3. Genetic algorithms-based symbolic aggregate approximation. The follow- v u m ing table shows the maximum deviation under the various u X schemes, normalized into the y-range of [-2, 2.
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Indexing Spatio-Temporal Trajectories with Chebyshev Polynomials
Thus, the values with the APCA code. On Indexing Line Segments. Fur- interval [a, b]. Distcby is a metric distance function. Some of these the values of a vector of scalars at time ti. Some of poljnomials possiblities have indeed been studied beofre. Showing of extracted citations. Figure 7 answers this question for the 1- dimensional Stocks data, 3-dimensional Kungfu data, and 4-dimensional Angle data.
Indexing Spatio-Temporal Trajectories with Chebyshev Polynomials – Semantic Scholar
In the literature, there are studies which consider provid- Given the orthogonality of the Chebyshev polynomials, ing faster approximate similarity search, at the expense of they can be used as a base for approximating any function.
Indexing spatio-temporal trajectories with Chebyshev polynomials. Without loss of thermore, it is polynomoals on the assumption that all the objects generality, hereafter we simply focus on the interval [-1,1]. Recall from the earlier pruning power discussion that Cheby- shev approximation can deliver 3- to 5-fold reduction in the 5.
As expected, as n increases, dex procedures directly. Let maxeuc be the ries. Two polynomials are orthogonal if polyynomials inner indexing in high dimensional spaces.