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Published byErin Francis Modified over 8 years ago
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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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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 Similarity-Based Non-Parametric Empirical Model Similarity-Based Non-Parametric Empirical Model Predictions Residuals Alerts Diagnostics Engine Input
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Physiological Data Modeling Method A historical H matrix of reference data is first chosen comprising ref X i vectors A local D matrix is chosen comprising a small number of ref X i vectors with the highest similarities to a new X vector Identical vectors have similarity = 1 Non-identical vectors have 0 <= similarity < 1 The new Y model vector is given by new Y = D(D T #D) –1 (D T # new X) 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 8
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Annotation 5102 H Matrix 8
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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 > T for > 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 > T for > ½ the vectors in a window then only vectors in a window from the first to last instances where the inferred class was > 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 > T for > ½ the vectors in a window then only vectors in a window from the first to last instances where the inferred class was > 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
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