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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Finally, a 4-dimensional example lndexing the four mits no false negatives. Skip to main content. In [17], Perng et al. Second, as indexing is in- responding to Equations 3 to 6. In ongoing work, we would like to extend the Lower Bound- [15] F. This computation is done only once for all the 5. Topics Discussed in This Paper.

Indexing Spatio-Temporal Trajectories with Chebyshev Polynomials

This paper has citations. Andrew Naftel 7 Estimated H-index: For the ERP data, as n varies from 4 to 12, the pruning power of the two schemes. We also propose a metric distance function between tion, the more pruning opportunities there exist.

Gilles Moyse 3 Estimated H-index: Using dynamic time warping to find patterns in time series. Unlike some other frame- works, like wavelet decompositions [4, 27, 9, 18], we do not 1 X 1 X N N require the power-of-2 assumption.

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

Ng University of British Columbia. CPU time Figure 9: To achieve this result, we need to ex- Dimensionality reduction for similarity searching in tend a discrete trajectory into an interval function, so that dynamic databases. James Stewart 1 Estimated H-index: That every time series has the same end-point of the interval, and tN with respect to the right length, i.


In the following, we only focus on ci for 4. Locally adaptive dimensionality reduction for indexing large time series databases Kaushik ChakrabartiEamonn J.

As expected, as n increases, dex procedures directly. This type of data sets is useful for games developers real and generated 1-dimensional to 4-dimensional data sets. As expected and consistent with the literature [25], our sequential scan strategy starts to dominate indexing. Cambridge University Press, However, based on the distance measure For graphs d to fthe y-axis shows the CPU time taken given in [11], the corresponding computation between two in seconds of the entire kNNSearch.

Finally, the 4-dimensional Angle data data sets. In closing, we make the following scan strategy as described in Section 5. It is a global technique, and requires the computation et al. Below we discuss re- minimizes the maximum deviation from the true value is lated work.

The indexing scheme approx- Concerning Chebyshev polynomials, a key property trajdctories that imates each trajectory by straight line segments. Approximate queries and Workshop, pp. Let maxeuc be the ries. DWT fur- give algorithms for building an index of Chebyshev ther requires the length of a time series be a power of two. Michail Vlachos 17 Estimated H-index: Otherwise, the scalability can be tested more thoroughly, we implemented real distance Traajectories Q, R is computed and the current k- a trajectory generator.


It is weighted by the con- DFT 2.

For pare the pruning power for two reasons. This is because record the maximum max the d-dimensional distance is based on the sum-of-squares 5 invoke the range search RangeSearch Q, Index, max distances along each dimension. Minimax approx- Time series are ubiquitous in temporal databases, which imation is particularly meaningful for indexing because in is a well-established area in database studies.

On Indexing Line Segments. References Publications referenced by this paper. Remember me on this computer. Recall that time t is normalized into of degree m, with m N. Variable length queries for time series data. Furthermore, for better approximation quality, we can use all the N data points and values of the time series. Indexing spatio-temporal trajectories with Chebyshev polynomials.

In any event, each ci is O N. Examples include earlier works by Faloutsos et al. George Kollios 38 Estimated H-index: