Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measuring Congruence on High Dimensional Time Series   A time series is a sequence of data items; typical examples are videos, stock
ticker data, or streams of temperature measurements. Quite some research has
been devoted to comparing and indexing simple time series, i.e., time series
where the data items are real numbers or integers. However, for many
application scenarios, the data items of a time series are not simple, but
high-dimensional data points. Motivated by an application scenario dealing with
motion gesture recognition, we develop a distance measure (which we call
congruence distance) that serves as a model for the approximate congruency of
two multi-dimensional time series. This distance measure generalizes the
classical notion of congruence from point sets to multi-dimensional time
series. We show that, given two input time series $S$ and $T$, computing the
congruence distance of $S$ and $T$ is NP-hard. Afterwards, we present two
algorithms that compute an approximation of the congruence distance. We provide
theoretical bounds that relate these approximations with the exact congruence
distance.

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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc