Grouping Multivariate Time Series Variables: Applications to Chemical Process and Visual Field Data

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Grouping Multivariate Time Series Variables
Applications to Chemical Process and Visual Field
Data

• Allan Tucker - Birkbeck College
• Stephen Swift - Brunel University
• Nigel Martin - Birkbeck College
• Xiaohui Liu - Brunel University

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Introduction

• Present a methodology to group Multivariate Time
  Series (MTS) variables
• MTS is a series of observations recorded over
  time
• Test on two real-world applications
• Grouping - partitioning a set of objects into a
  number of mutually exclusive subsets
• Many, if not all, are NP-Hard

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MTS Example
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Grouping MTS - Introduction

• Desirable to model MTS as a group of several
  smaller dimensional MTS
• Decompose MTS into several smaller dimensional
  MTS based on dependencies in data
• Large number of dependencies because one variable
  may affect another after a certain time lag

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Grouping MTS - Methodology
One High Dimensional MTS (X)
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Correlation Search

• Spearmans Rank Correlation used
• Entire Search Space is too large
• Invalid Triples
• Autocorrelations
• duplicates irrespective of direction where lag
  0 e.g. (xi ,xj ,0) and (xj ,xi ,0)
• Evolutionary Programming approach found to be the
  most efficient

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Grouping Genetic Algorithm- Representation and
Operators

• Previously compared and contrasted different GA
  representations and operators
• Falkenauers Crossover Mutation ensure Schema
  Theory holds for grouping problems

Chromosome 0 1 1 0 0 2 1 2 0 1 2
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Grouping- The Grouping Metric Properties

• If Q is empty, then fitness maximised when each
  variable is in a separate group
• If Q contains all pairings of variables (the
  entire search space), then fitness maximised
  when all variables in the same group
• If data is from mixed set of MTS, fitness
  maximised when variables in the same group have
  as many correlations as possible in Q and
  variables in different groups have as few
  correlations as possible in Q

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Oil Refinery Data

• Oil Refinery Process in Scotland
• Data recorded every minute
• Hundreds of variables
• Years of data available on repository
• Selected 50 interrelated variables over 10000
  time points
• Large Time Lags (up to 120 minutes between some
  variables)

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Visual Field Data
The interval between tests is about 6 months
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Typically, 76 points are measured
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Values Range Between 60 very good, 0 blind
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B
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13
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B
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The number of tests can range between 10 and 44
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Nerve Fibre Bundle (Right Eye)
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X
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Usual Position of Blind Spot (Right Eye)
B
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Oil Refinery Data - Results (1)

• Very rapid generation of Groups (seconds)
• 3 major groups discovered, 2 relating to the
  upper and lower trays of the column
• Most of the single variables appear noisy
• Used as a method for pre-processing data before
  model building where time is short

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Oil Refinery Data - Results (2)
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Visual Field Data - Results (1)- Patient Group
Comparison

• Patients are ordered on Average Sensitivity
• Patient 1 - lowest and Patient 82 - the highest
• Graph goes from light (BRHC) to dark (TLHC)

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Visual Field Data - Results (2)

• High Sensitivity implies similar groups
• Small groups in general
• Points in the eye will be associated with similar
  nerve fibre bundles
• Low Sensitivity implies dissimilar groups
• Large groups in general
• Different areas of the visual field may be
  deteriorating

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Conclusions

• Decomposing Large, High-Dimensional MTS is a
  challenging one
• Proposed methodology very encouraging
• Oil Refinery Data 3 relatively independent
  sub-systems rapidly identified
• Visual Field Data Discovered groups offer ideal
  starting point for modelling as a VAR process

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Future Work

• Experimenting with new datasets
• Gene Expression Data
• EEG Data
• Determining the ideal Parameters
• e.g. Qlen is very influential on final groupings
• Combining the two stages - correlation search
  and grouping into one incremental process

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Acknowledgements

• Engineering and Physical Sciences Research
  Council, UK
• Moorfields Eye Hospital, UK
• Honeywell Technology Centre, USA
• Honeywell Hi-Spec Solutions, UK
• BP-Amoco, UK