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Event has a period of 20. Occurrences of the event happen between 20k+5 to 20k+10.
Time
5
18
26
29
48
50
67
79
13
62
Segment the data using length 20
Segment the data using length 16
Overlay the segments
Overlay the segments
Observations are clustered in [5,10] interval.
Observations are scattered.
Fig. 12.2 The underlying true period is 20. The black dots and cross marks correspond to “in” and
“out” events separately. When using the correct period 20 to segment and overlay the observations,
as shown in the figure on the left , the “in” observations are clustered. Figure is from [ 24 ]
on the map to form semantic regions called reference spots . Figure 12.1 shows an
example of an eagle movement data. There are three reference spots detected from
the movement. Reference spots could be fairly large but frequently visited regions
over several years, such as an area in Quebec (Spot #1 in Fig. 12.1 ) where birds
frequently stay during the summer. In the second step, the movement is transformed
into a binary in-and-out sequence , and then Fourier transform is applied on the
sequence to detect the period.
Due to the limitations of positioning technology and data collection mechanisms,
movement data collected from GPS or sensors could be highly sparse, noisy and
unsynchronized. First, the data is often sampled at an unsynchronized rate (e.g., if
the sampling rate of a tracking device is set to 1 h, data may be collected at 1:01, 2:08,
3:02, 4:15, and so on). Second, movement data collected can be scattered unevenly
over time (e.g., collected only when the tracking device is triggered, such as the
check-ins using smart phones). Third, the observations could be highly sparse .For
example, a bird can only carry a tiny device with limited battery life. There could be
only one or two reported locations in three to five days. If a sensor is not functioning
or a tracking facility is turned off, it could result in a large portion of missing data.
Traditional period detection methods, such as Fourier transform and auto-correlation,
are known to be sensitive to such nuisances. Lomb-Scargle periodogram [ 27 , 32 ]is
proposed as a variation of Fourier transform to deal with unevenly spaced data, but
it cannot handle the case when the data is also sparse and noisy.
Li et al. [ 24 ] develop a novel approach to detect periodicity for sparse, noisy
and unsynchronized data. A “ segment-and-overlay ” idea is explored to uncover the
hidden period: Even when the observations are incomplete, the limited periodic ob-
servations will be clustered together if data is overlaid with the correct period ,as
shown in Fig. 12.2 . The method tries every potential periods. For a period candidate
 
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