Exact%20Discovery%20of%20Time%20Series%20Motifs

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Exact Discovery of Time Series Motifs
This document was created to support our paper.
It contains additional experiments and details
which we could not fit into the paper.
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Sandeep Tata (2007). Declarative Querying For
Biological Sequences. Ph.d Thesis, The University
of Michigan. Advisor Jignesh M. Patel.
In our paper we claimed that FLAME does not give
exact motifs with respect to the raw time series.
Here we make this clearer. Suppose we have three
time series A 9.9, 50.1, 89.9, 49.9 B
0.1, 59.9, 80.1, 40.1 C 10.1, 49.9, 90.1,
50.1 Assume they are discretized using the FLAME
scheme, with each bucket covering a range of ten
(i.e 0 to 9.999, 10 to 10.999, 20 to 20.999
etc), and we thus have.. A A,F,I,E B
A,F,I,F C B,E,J,F Note that the squared
Euclidean distance between A and B is 384.16, but
the distance between A and C is only 0.16. In
this trivial dataset, A and C are the true
motifs. However, under the FLAME mapping, A and
B are identical, but A and C have a distance of
4. Note that it might be possible to fix this
with a SAX-like lower bound, however this has not
been done, and it would require significant
overhead, since many false positives would have
to be checked
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This is from DQmatixC, row 19 Note that the end
of this row is padded with some zeros, so only
the first 33,021 datapoints are used
Here is the entire dataset
This is from DQmatixD1, row 16 Note that the end
of this row is padded with some zeros, so only
the first 78,254 datapoints are used
Here is the entire dataset
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Here are the file names of the near duplicated
images discovered by our algorithm
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• In the following slides we give some more
  information about the Beet leafhopper example in
  the paper.

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Economic Importance

• Only known vector of beet curly top virus in
  North America

CDFA
UC IPM Online
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History On Sugar Beets

• First reported in Nebraska in 1888
• Outbreak in 1925 in California resulted in loss
  of one third of the sugarbeet crop throughout the
  Sacramento Valley, and in a total loss of all
  late plantings in both the San Joaquin Valley and
  southern Salinas Valley (Severin Schwing, 1926)
• Closure/part time operation of sugarbeet refinery
  factories, complete abandonment of thousands of
  acres of planted or prospective land for
  sugarbeet in Western U.S.(Bennett, 1971)
• So severe in the Salinas Valley that in 1947 a
  permanent research laboratory of plant pathology,
  entomology, and plant breeding was established by
  the USDA to work on controlling BCTV outbreaks
  (Wisler Duffus, 2000).
• Resistant varieties became available in 1933
  (Owen et al., 1938)

H.H.P. Severin, 1930
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History On Tomatoes

• San Joaquin Valley in 1948 and 1950, it was
  estimated that 80 of the tomato crop was lost or
  damaged by BCTV (Bennett, 1971)
• Today commercial and recreational growth of
  tomatoes in the western United States is still
  limited in many areas by the incidence of BCTV
• Breeding program to develop BCTV resistant tomato
  varieties was established in Utah in 1930 by the
  U.S. Department of Agriculture (Martin, 1970).
• Resistant varieties have small fruit of poor
  quality (Martin, 1970)
• Resistant lines only confer a reduction to the
  initial infection
• Once resistant varieties are infected, they react
  in the same way as susceptible varieties (Thomas
  Martin, 1971, 1972)

H.H.P. Severin, 1930
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Control Measures
Breeding Area

• Biological control
• Not effective due to migratory patterns
• Chemical Control
• Malathion treatments applied to thousands of
  acres of overwintering areas
• Insecticides on host plants
• Resistant plants
• Increasingly important

esrpweb.csustan.edu/ gis/rp/lom.html
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Resistant Plants

• Develop BCTV resistant plants with
  horticulturally favorable properties
• Determine mechanisms of resistance
• Resistance in tomatoes
• Appears to be due to change in feeding behavior
• In order to experimentally test if the mechanism
  of resistance is an effect on vector feeding
  behavior, we need to develop a methodology to
  study the feeding behavior of beet leafhopper.

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Electrical Penetration Graph(EPG)
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What EPGs Measure

• Fluctuations in voltage level
• Occur in distinct patterns called waveforms
• Each waveform is associated with a specific
  feeding behavior
• Before EPGs can be used to study feeding
  behavior, the waveforms must first be
  experimentally correlated with specific feeding
  behaviors

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Example of beet leafhopper EPG recording
Example of beet leafhopper EPG recording
Amplitude (V)
Time
5 min
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In addition to telemetry, we have a video stream
we can refer to
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Some examples of manually discovered motifs.
(Note that entomologists dont use the term
motifs)
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Here is the raw data in which we found the motif
shown below This is from DQmatixD1, row 16