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Signal 1Mscale1(7,‘db1’)
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7Wavelet Tree
0 2 4 6 8100
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0 2 4 6 8-10
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Signal 1 Division Plots
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Signal 2 Mscale1(7,‘db1’)
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0 2 4 6 8120
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0 2 4 6 8-60
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Signal 2 Division Plots
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Test Pattern
0 5 10 15 20 25 30 35 40-1
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Results (Mscale1(2,‘cs1’)) - Different Templates Discovered?
5 10 15 20 25 30 350
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1
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2Wavelet Tree
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1Approximation
0 5 10 15 20-1.5
-1
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0 10 20 30 40-2
-1
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2Segmentation
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Other Patterns Mscale1(6,‘cs1’)
0 200 400 6001
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6Wavelet Tree
0 2 4 6 8 1030
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55Approximation
0 2 4 6 8 10-30
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-10
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10Detail
0 200 400 600 80030
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60Segmentation
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Other patterns contd. Mscale1(9,‘cs1’)
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Timing - Two plots of Mscale time with increasing values of scale (m)
1 2 3 4 5 6 70.05
0.1
0.15
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0.5Plot of Time (in seconds) as a function of scale (m)
Scale (m)
Time (s)
1 2 3 4 5 6 7 80
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1.4
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Different Wavelets - Mscale2(7,cs2)
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7Wavelet Tree
0 200 400 600 800 100012
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30Segmentation
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Different Wavelets - Mscale2(7,D-2)
0 200 400 600 800 10001
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7Wavelet Tree
0 200 400 600 800 100010
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0 200 400 600 800 1000-1.5
-1
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30Segmentation
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Different Wavelets - Mscale2(7,D-5)
0 200 400 600 800 10001
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7Wavelet Tree
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0 200 400 600 800 1000-4
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2Detail
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30Segmentation
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Different Wavelets - Mscale2(7,D-8)
0 200 400 600 800 10001
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3
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6Wavelet Tree
0 200 400 600 800 100010
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0 200 400 600 800 1000-2
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30Segmentation
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Different Wavelets - Mscale2(7,BO1)
0 200 400 600 800 10000
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4
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8Wavelet Tree
0 200 400 600 800 100010
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0 200 400 600 800 1000-0.5
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30Segmentation
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Different Wavelets - Mscale2(7,BO3)
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8Wavelet Tree
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30Segmentation
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Different Wavelets - Mscale2(6,cs2)
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6Wavelet Tree
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0 200 400 600 800-6
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60Segmentation
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Different Wavelets - Mscale2(6,D-2)
0 200 400 600 8001
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3
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6Wavelet Tree
0 200 400 600 80040
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0 200 400 600 800-2
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60Segmentation
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Different Wavelets - Mscale2(6,D-5)
0 200 400 600 8001
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6Wavelet Tree
0 200 400 600 80035
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0 200 400 600 800-3
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60Segmentation
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Different Wavelets - Mscale2(6,D-8)
0 200 400 600 8001
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6Wavelet Tree
0 200 400 600 80040
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0 200 400 600 800-6
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-2
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4Detail
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60Segmentation
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Different Wavelets - Mscale2(6,BO1)
0 200 400 600 8001
2
3
4
5
6Wavelet Tree
0 200 400 600 80040
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55Approximation
0 200 400 600 800-6
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-2
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4Detail
0 200 400 600 80030
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60Segmentation
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Different Wavelets - Mscale2(6,BO3)
0 200 400 600 8001
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6Wavelet Tree
0 200 400 600 80040
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0 200 400 600 800-6
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2Detail
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60Segmentation
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Wavelet Comparison
• Performance depended very much on original signal
• For example Debauchies was best for tag1s but not so good for others
• Best overall wavelet for patterns on tag1s, tag3 and tag5 = Cubic Spline 2.
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The Primitives
1 2 3
4 5 6
7
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Primitives discovered using sum of mean sq error and Mscale2(s2,7,’cs2’)
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1 3 3 6 44 1
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Primitives discovered MScale2(s1,8,’ cs2’)
5 7 6 1 12
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Problems to still address: 1) Improve Tree Path Heuristic
10 20 30 401
1.2
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2Wavelet Tree
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Tree Heuristic
• Crossover should not be allowed
• Some improvement to take into account the magnitude (as well as position) of extrema on the detail signal.This should help determine the corresponding point on the next level.
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Problems to still address:2) Determining further refinement (e.g. segmenting at extrema)
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0 5 10 15 20 257
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Signal 1 Division(599:684)
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Further segment refinement
• Should detect if pattern within segment is an extrema or not
• If it is then split the segment again at the extrema
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Problems to still be addressed:3) The distortion of the approximation and detail signals at lower levels
related to tree path heuristic
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0 200 400 600 800 1000 120010
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Problems to still be addressed:4) Confusion between primitives
• Primitives 1 & 3 & 5 are confused
• Primitives 2 & 4 & 6 are confused
• An association amongst these could be made in determining the complete pattern
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Work since Return
• Coded up a representation of a Dynamic Bayesian Network
• Updated the GA to work with a Bayesian Network metric rather than Pearson’s Correlation Coefficient
• Now looking at different discretizations to learn the best structure from the data
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Typical model learnt from the data
A
D
C
B
0-1-2-3-16