Time Series Bitmap Experiments

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Time Series Bitmap Experiments

• This file contains full color, large scale
  versions of the experiments shown in the paper,
  and additional experiments which were omitted
  because of space constraints
• Note that in every case, all the data is freely
  available

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Dataset 1 Heterogeneous Data, Part 1
The clustering achieved on 15 pairs of samples
from 15 diverse datasets. The red lines in the
dendrogram draw attention to objectively
incorrect subtrees Parameters Level 3 N 100 n
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Data Key
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1 MotorCurrent 2
MotorCurrent 3 Video
Surveillance Ann, gun 4 Video
Surveillance Ann, no gun 5 Video
Surveillance Eamonn, gun 6 Video
Surveillance Eamonn, no gun 7 Power
Demand Jan-March (Italian) 8 Power
Demand April-June (Italian) 9 Great Lakes
(Erie) 10 Great Lakes
(Ontario) 11 Buoy Sensor
North Salinity 12 Buoy Sensor East
Salinity 13 Koski ECG slow 1
14 Koski ECG slow 2
15 Koski ECG fast 1
16 Koski ECG fast 2 17
Exchange Rate Swiss Franc 18
Exchange Rate German Mark 19
Furnace heating input 20
Furnace cooling input 21 Reel
2 angular speed 22 Reel 2
tension 23 Balloon1
24 Balloon2 (lagged)
25 Evaporator feed flow
26 Evaporator vapor flow
27 Shuttle Inertia Sensor X
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29 Shuttle Inertia Sensor Z 30 Shuttle
Inertia Sensor Z
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Data is in ASCII file time_series_bitmap_1
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Dataset 1 Heterogeneous Data, Part 2
If we do the clustering with only level 2
information, the clustering is very slightly
worse, but still quite robust considering that we
are only using 1.6 of the information available
in the time series Parameters Level 2 N 100 n
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Data Key
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1 MotorCurrent 2
MotorCurrent 3 Video
Surveillance Ann, gun 4 Video
Surveillance Ann, no gun 5 Video
Surveillance Eamonn, gun 6 Video
Surveillance Eamonn, no gun 7 Power
Demand Jan-March (Italian) 8 Power
Demand April-June (Italian) 9 Great Lakes
(Erie) 10 Great Lakes
(Ontario) 11 Buoy Sensor
North Salinity 12 Buoy Sensor East
Salinity 13 Koski ECG slow 1
14 Koski ECG slow 2
15 Koski ECG fast 1
16 Koski ECG fast 2 17
Exchange Rate Swiss Franc 18
Exchange Rate German Mark 19
Furnace heating input 20
Furnace cooling input 21 Reel
2 angular speed 22 Reel 2
tension 23 Balloon1
24 Balloon2 (lagged)
25 Evaporator feed flow
26 Evaporator vapor flow
27 Shuttle Inertia Sensor X
28 Shuttle Inertia Sensor X
29 Shuttle Inertia Sensor Z 30 Shuttle
Inertia Sensor Z
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Dataset 1 Heterogeneous Data, Part 3
Changing the parameters by up to 50 either way
has little effect on the quality of the
clustering. Here are some random examples
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Data Key
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1 MotorCurrent 2
MotorCurrent 3 Video
Surveillance Ann, gun 4 Video
Surveillance Ann, no gun 5 Video
Surveillance Eamonn, gun 6 Video
Surveillance Eamonn, no gun 7 Power
Demand Jan-March (Italian) 8 Power
Demand April-June (Italian) 9 Great Lakes
(Erie) 10 Great Lakes
(Ontario) 11 Buoy Sensor
North Salinity 12 Buoy Sensor East
Salinity 13 Koski ECG slow 1
14 Koski ECG slow 2
15 Koski ECG fast 1
16 Koski ECG fast 2 17
Exchange Rate Swiss Franc 18
Exchange Rate German Mark 19
Furnace heating input 20
Furnace cooling input 21 Reel
2 angular speed 22 Reel 2
tension 23 Balloon1
24 Balloon2 (lagged)
25 Evaporator feed flow
26 Evaporator vapor flow
27 Shuttle Inertia Sensor X
28 Shuttle Inertia Sensor X
29 Shuttle Inertia Sensor Z 30 Shuttle
Inertia Sensor Z
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Parameters Level 3 N 64 n 8
Parameters Level 3 N 77 n 11
Parameters Level 3 N 54 n 9
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Dataset 1 Heterogeneous Data, Part 4
We compared our approach to a Markov model based
approach and a ARIMA based approach. For both
competitors we spent one hour of human time
trying to find the best parameters
Segmental Markov model 1
Mixtures of ARMA models 2
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Data Key
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1 MotorCurrent 2
MotorCurrent 3 Video
Surveillance Ann, gun 4 Video
Surveillance Ann, no gun 5 Video
Surveillance Eamonn, gun 6 Video
Surveillance Eamonn, no gun 7 Power
Demand Jan-March (Italian) 8 Power
Demand April-June (Italian) 9 Great Lakes
(Erie) 10 Great Lakes
(Ontario) 11 Buoy Sensor
North Salinity 12 Buoy Sensor East
Salinity 13 Koski ECG slow 1
14 Koski ECG slow 2
15 Koski ECG fast 1
16 Koski ECG fast 2 17
Exchange Rate Swiss Franc 18
Exchange Rate German Mark 19
Furnace heating input 20
Furnace cooling input 21 Reel
2 angular speed 22 Reel 2
tension 23 Balloon1
24 Balloon2 (lagged)
25 Evaporator feed flow
26 Evaporator vapor flow
27 Shuttle Inertia Sensor X
28 Shuttle Inertia Sensor X
29 Shuttle Inertia Sensor Z 30 Shuttle
Inertia Sensor Z
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Parameters Level 3 N 100 n 10
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Dataset 2 Homogenous Data, Part 1
Here we cluster 5 randomly chosen subsections
from 4 different ECG datasets
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Data Key
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Cluster 1 (datasets 1 5) BIDMC Congestive
Heart Failure Database (chfdb) record chf02
Start times at 0, 82, 150, 200, 250,
respectively Cluster 2 (datasets 6 10) BIDMC
Congestive Heart Failure Database (chfdb) record
chf15 Start times at 0, 82, 150, 200, 250,
respectively Cluster 3 (datasets 11 15) Long
Term ST Database (ltstdb) record 20021 Start
times at 0, 50, 100, 150, 200, respectively Cluste
r 4 (datasets 16 20) MIT-BIH Noise Stress
Test Database (nstdb) record 118e6 Start times
at 0, 50, 100, 150, 200, respectively
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Parameters Level 3 N 50 n 10
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Dataset 2 Homogenous Data, Part 2
The bitmap approach is defined (and very robust)
when the time series are of different lengths
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Dataset 3 MIT ECG Arrhythmia Data Part 1
Segmental Markov model 1
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In Ge and Smyth 2000, this dataset was explored
with segmental hidden Markov models. After they
careful adjusted the parameters they reported 98
classification accuracy. Using time series
bitmap with virtually any parameter settings, we
get perfect classifications and clustering. We
can get perfect classifications using one nearest
neighbor classification, or we can project the
data into 2 dimensional space (see next slide)
and get perfect accuracy using a simple linear
classifier, a decision tree or SVD. (Dataset
donated by Padhraic Smyth and Seyoung Kim)
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Parameters Level 1 N 60 n 12
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Dataset 3 MIT ECG Arrhythmia Data Part 2
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Parameters Level 1 N 60 n 12
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Dataset 4 MotorCurrent Part 1
Euclidean Distance
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The Bitmap approach is completely phase
independent, which may be useful for certain
datasets. Consider the Motorcurrent dataset
(Donated by Richard J. Povinelli). Here the
problem is to distinguish between normal motor
operations and broken connectors. If we attempt
to cluster this dataset with Euclidean distance
or DTW, the fact that the sample are out of phase
confuses the algorithm (far left), however the
bitmap approach can easily produce objectively
correct clusterings. In this problem the time
series bitmaps are very very similar between
classes, and humans will find it hard to
distinguish them. Nevertheless, there is enough
information to achieve correct clusterings
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More information about the Kalpakis_ECG
demonstration
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A clustering of a subset of the Kalpakis_ECG
dataset. Note that while ECGs have incredible
variability, the 5 non-ECGs clearly stand out in
the bitmap representation.
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This drawing shows the correlation of muscle
depolarization and ECG tracings at corresponding
times. Phase 0 denotes ventricular
depolarization. This is seen on the ECG as the
beginning of the QRS complex. Phase 1 denotes
the initial rapid repolarization due to closing
of fast sodium channels. This is seen as the
large drop in mV on the ECG. Phase 2 represents
the plateau stage during which inflow and outflow
currents are balanced. The ECG returns to
baseline.Phase 3 is repolarization. Potassium
channels open and calcium closes. The ECG shows
the repolarizing T wave.Phase 4 is the recover
phase. Both the muscle tracing and ECG return to
baseline levels
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Anomaly detection
http//www.physionet.org/cgi-bin/chart?databasemi
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