  Each time-series has its own linear trend, the directionality of a
timeseries, and removing the linear trend is crucial to get the more intuitive
matching results. Supporting the linear detrending in subsequence matching is a
challenging problem due to a huge number of possible subsequences. In this
paper we define this problem the linear detrending subsequence matching and
propose its efficient index-based solution. To this end, we first present a
notion of LD-windows (LD means linear detrending), which is obtained as
follows: we eliminate the linear trend from a subsequence rather than each
window itself and obtain LD-windows by dividing the subsequence into windows.
Using the LD-windows we then present a lower bounding theorem for the
index-based matching solution and formally prove its correctness. Based on the
lower bounding theorem, we next propose the index building and subsequence
matching algorithms for linear detrending subsequence matching.We finally show
the superiority of our index-based solution through extensive experiments.

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