Physiological%20Data%20Modeling

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Physiological Data Modeling
ICML 2004 Banff, AL July 8, 2004 Jack Mott and
Matt Pipke SmartSignal Corporation
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SmartSignal Corporation

• Incubator of Similarity-Based Modeling technology
• Universally applicable
• Data driven, empirical
• Scalable, deployable
• Commercially proven in our eCM software
• Delta Airlines all engines, all flights
• Power Plants Entergy, Dynegy, APS
• Transportation GM-EMD, Caterpillar

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Similarity-Based Modeling

• Snapshots at instants of time
• Needs only historical data
• Removal of normal variations
• Anomaly detection and isolation
• One technology for all applications

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Physiological Data Modeling Method

• A historical H matrix of reference data is first
  chosen comprising refXi vectors
• A local D matrix is chosen comprising a small
  number of refXi vectors with the highest
  similarities to a newX vector
• Identical vectors have similarity 1
• Non-identical vectors have 0 lt similarity lt 1
• The newY model vector is given by
• newY D(DTD) 1(DT newX)
• where the similarity operation () applies only
  to independent variables

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Physiological Data

• 11 independent variables
• User characteristics (2)
• Armband sensor values (9)
• 2 dependent variables
• Gender number
• Annotation class

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Training Data Setup

• Select 2,500 3,000 records for each H matrix
• One H matrix for gender
• One H matrix for annotation 3004
• One H matrix for annotation 5102
• Each H matrix
• Includes about equal populations for each user
• Includes positive and negative examples
• Contains no vectors too similar to each other
• Contains only filtered data (99 of total)
• User 17 excluded

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Gender H Matrix
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Annotation 5102 H Matrix
8
9
Annotation 3004 H Matrix
8
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Training Data Modeling

• If any vector to be modeled was in an H matrix it
  was removed from the H matrix before the D matrix
  was formed
• Leave-one-out cross-validation of each H matrix
• Chose 10 as number of vectors for the D matrices
• Reduced the number of independent variables to 8
  - 9
• Modeled all 580,264 unfiltered training vectors
• Inferred gender with gender H matrix
• Inferred class with annotation 5102 H matrix
• Positive examples of annotation 5102 have actual
  class 1
• Negative examples of annotation 5102 have actual
  class 0
• Inferred class with annotation 3004 H matrix
• Positive examples of annotation 3004 have actual
  class 1
• Negative examples of annotation 3004 have actual
  class 0

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Gender Windows and Thresholds

• Chose gender windows to contain all vectors in a
  session
• If the inferred gender was gt T for gt ½ the
  vectors in a window then all vectors in a window
  were assigned predicted gender 1, otherwise
  predicted gender 0
• T .5 produced Sensitivity 1 and Specificity
  1

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Annotation 5102 Windows and Thresholds

• Chose annotation 5102 windows to contain 80
  vectors
• If the inferred class was gt T for gt ½ the vectors
  in a window then only vectors in a window from
  the first to last instances where the inferred
  class was gt T were assigned predicted class 1,
  otherwise predicted class 0
• Sensitivity and Specificity varied as T varied to
  produce an ROC curve
• T .58 where the slope 1 on the ROC curve

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Window Sizes for Annotation 5102
8
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ROC curve for Annotation 5102
8
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Annotation 3004 Windows and Thresholds

• Chose annotation 3004 windows to contain 30
  vectors
• If the inferred class was gt T for gt ½ the vectors
  in a window then only vectors in a window from
  the first to last instances where the inferred
  class was gt T were assigned predicted class 1,
  otherwise predicted class 0
• Sensitivity and Specificity varied as T varied to
  produce an ROC curve
• T .48 where the slope 1 on the ROC curve

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Window Sizes for Annotation 3004
8
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ROC curve for Annotation 3004
8
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Training Data Overall Results

• Gender Predictions
• 23929 (4) gender 1
• Sensitivity 23929 / 23929 1
• 556335 (96) gender 0
• Specificity 556335 / 556335 1
• Annotation 5102 Predictions
• 173759 (30) class 1
• Sensitivity 96288 / 98172.98
• 406505 (70) class 0
• Specificity 72251 / 73668 .98
• Annotation 3004 Predictions
• 80511 (14) class 1
• Sensitivity 4129 / 4413 .94
• 499753 (86) class 0
• Specificity 157993 / 167368 .94

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Test Data Modeling

• Modeled all 720,792 unfiltered test vectors
• Assumed that characteristic 2 was an extremely
  important independent variable in modeling gender
• Used the appropriate H matrices, D matrix size,
  independent variables, thresholds and window
  sizes developed from the training data
• Predicted gender
• Predicted class for annotation 5102
• Predicted class for annotation 3004

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Test Data Overall Results

• Gender predictions
• 84426 (12) gender 1
• 4 for training data
• 636366 (88) gender 0
• 97 for training data
• Annotation 5102 predictions
• 232823 (32) class 1
• 30 for training data
• 487969 (68) class 0
• 70 for training data
• Annotation 3004 predictions
• 80511 (11) class 1
• 14 for training data
• 640281 (89) class 0
• 86 for training data

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Conclusions

• SBM is easy to apply to real people with real
  armbands
• Modeling choices, the size of D matrix and
  independent variables, are determined by only a
  small fraction of training records, the H matrix
• SBM accommodates anomalies in new data
• Can be applied to raw, unfiltered data
• SBM is automatically user-specific
• Presence or absence of a user in new data can be
  detected
• SBM might be made user-general
• Transform data into t-scores with zero mean and
  unit standard deviation for each activity