STIFF: A Forecasting Framework for Spatio-Temporal Data

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STIFF A Forecasting Framework for
Spatio-Temporal Data

• Zhigang Li, Margaret H. Dunham
• Department of Computer Science and Engineering
• Southern Methodist University
• Dallas, Texas
• USA

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Our goal

• In this paper, we present a novel forecasting
  framework for spatio-temporal data, in which not
  only spatial but also temporal characteristics of
  the data are considered to obtain a more
  appropriate result.

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Presentation Outline

• Motivation
• Prior Research
• Our Approach STIFF
• Combining two approaches to achieve better
  results Time Series Analysis and ANNs
• Performance
• Future Work

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Why

• There are many application fields which require
  spatio-temporal forecasting
• river hydrology, biological patterns, housing
  price research, rainfall distribution, waste
  monitoring, fishery, hotel pickup rate, etc.
• In spatio-temporal forecasting, both spatial and
  temporal properties, as well as their mutual
  correlation, are taken into account.

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What work has been done

• Jothityangkoon, Sivapalan, and Viney, 2000
• Rainfall forecasting
• Hidden Markov Model
• De-aggregate high level to lower level
• Large error
• Pokrajac and Obradovic,2001
• Current event assumed to be impacted only by
  immediate temporal ancestors.

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More related research

• Cressie and Majure,1997
• Model livestock waste in a river basin
• Condensed time into a three day area of
  influence
• large variation of the predicted values.
• Deutsch etal,1986 Kelly etal,1998 Pfeifer
  etal,1990
• Extended time series analysis with a spatial
  correlation from a simple distance matrix.
• It is too arbitrary to just rely upon the pure
  distance measurement.

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Flood Forecasting (Our Motivating Application)

• Catchment
• Many different types of sensors
• Predict at one sensor location
• Water level or Flow rate
• May not be interested in actual prediction of
  value

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Our approach Problem definition

• ?a0, a1, a2, an is the research field,
  composed of n 1 spatially separated
  subcomponents, named by ai accordingly.
• WLOG, a0 is assumed the target place where
  forecasting is about to be carried out.
• For each ai in ?, there are j observations with
  equal time intervals between consecutive ones,
  denoted by ?iai1, ai2, ai3, aij.

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Problem definition (Cont.)

• Given ?a0, a1, a2, an, ??1, ?2, ?n, the
  length of observations j and the look-ahead steps
  of ?, we are expected to find an as good as
  possible forecasting relationship ƒ that is
  defined as follows.

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Our approach Algorithm sketch

• Describe the forecasting problem according the
  problem definition.
• Build a time series (ARIMA) model for each ai.
  Name the forecasting from a0 time series model as
  ƒT.
• Construct and train an ANN to capture the spatial
  correlation and influence over the target
  subcomponent a0. Name the forecasting from the
  neural network as ƒS.
• Combine ƒT and ƒS via a statistical regression
  mechanism.

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Time Series Data Transformation

• Convert non-stationary to stationary to prevent
  skewness as much as possible.
• Box and Cox proposed a transformation family,
  namely, Box-Cox transformation

• The key is to determine the right value for ? so
  as to find the appropriate transformation. For
  example, when ? 0 or .5 the transformation is
  in fact log or square root accordingly. But how?

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Data transformation (contd)

• Box and Cox proposed a large-sample
  maximum-likelihood approach.
• Wei proposed to use the ? that minimizes

• The former requires much computation while the
  latter one may incur some problems for it does
  not consider the difference compared to the real
  observation.
• We therefore propose the following way to
  determine ?.

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Time series Model

• A time series model is chosen as it has the
  proven capability of describing and capturing the
  temporal dependency and relationship.
• Our work focused on the ARIMA technique which can
  be embodied in the following formula.

• And roughly speaking, the building process can be
  divided into three main steps. They are
• Model identification
• Parameter estimation
• Diagnostic checking

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Find the spatial influence

• Normally it is much harder to find than its
  temporal counterpart in the problem.
• No precise way to convert from the spatial
  measurement to the value it may change.
• Time is only 1 dimension while space is 3 (or 2)
  dimensions.
• A simple distance measure is not enough, other
  factors are important.

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Artificial Neural Network (ANN)

• Why is ANN used for finding spatial influence?
• Itself a black-box and non-linear technology
  used to find the hidden pattern.
• Like human brain, it can self-adjust and learn
  automatically even if the problem is not defined
  very well.
• Practice proves its usefulness
• See,1997 found ANN was especially useful in
  situations where the underlying physical
  relationships are not fully understood

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ANN Construction

• Simple 3-layer back-propagation MLP
• One input node for each sensor value except a0.
• Actual input shifted by predicted time lag.
• The hidden layer has a certain number of neurons
  that have to be decided by experiment.
• The output layer has only one neuron that
  corresponds to the target subcomponent a0.
• We also employ a kind of pruning strategy to
  achieve the most simplicity of ANN structure
  without harming the efficacy much.

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Integrate the two forecasts

• We have two forecasts so far at the target
  subcomponent a0. One is ƒT, from the time series
  model, and the other is ƒS, from ANN. We may
• Either dynamically select one from the two as the
  current forecast
• Or fuse them together since they contribute to
  the overall forecasting from two different
  aspects. (Thats what we take in the paper.)
• The two forecasts are integrated via a very
  simple linear regression mechanism. Of course
  other more advanced alternatives can be used
  instead for better results.

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A case study (National River Flow Archive Great
Britain)

• Here we are going to present a practical case
  study to demonstrate how the framework works.
• We will conduct the spatio-temporal forecasting
  at the outlet gauging station 28010 regarding the
  river water flow rate (m3/s). The basin is shown
  as follows.

• The target station is 28010 while its siblings
  are lying upstream.
• Derwent Catchment
• Daily mean flow values

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Data transformation

• Checking the water flow rate data at station
  28010 tells us the data is not very stable. The
  abrupt change is obvious and present roughly
  about 25 of the whole time.
• We therefore employ the data transformation first
  according to the proposed approach discussed
  before .
• We empirically vary the value of ? from 1.0 to
  1.0 with the step of .1. It turns out ? 0.0 is
  the best (relatively). In other words, we will
  log-transform the original water flow rate data.

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Actual Flow at Derwent
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Case Study ANN

• 6 input nodes
• 1 output node
• 6 chosen as number of hidden nodes based on
  experimentation
• Number of links pruned based on river topology
• Lag time used for input based on expected flow
  lag time

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Building models

• Following the framework specification, we then
  build a time series model based upon the dataset
  collected from each gauging station.
• An ANN is constructed after that, with the
  spatially-induced pruning strategy applied to
  erase as many as possible unnecessary links while
  sacrificing little to the forecasting accuracy.
• The final overall spatio-temporal forecasting is
  generated then following this simple regression

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STIFF Model
x1 fT x2 fS C
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Performance Analysis

• Compared STIFF to pure time series (CTS) and pure
  ANN (CANN)
• Data starting at 10/01/75
• 30, 60, 120 days
• Normalized Absolute Ratio Error (NARE)

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Forecasting result

• The forecasting comparison result, measured in
  NARE, is outlined in the following table. The
  other two models, built to our best knowledge,
  are used to compare with STIFF.
• Here Over means overestimation while Under
  for underestimation.

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Result 30 Days
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Conclusion

• STIFF has a better forecast accuracy than the
  normal single time series model and ANN model,
  and more balanced (over vs. under estimation).
• Compared with other related work, it avoids the
  oversimplification.
• Does not have the large variation problem.
• STIFF requires much human intervention and
  interpretation.
• STIFF is promising for future research.

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Future work

• Extend to multivariate forecasting
• Use more sophisticated fusing techniques
• Test on more flood data
• Compare to other techniques
• Examine different ANN structures
• So far, it can only deal with univariate
  forecasting.
• Extend to other application domains
• ..

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Thank you!