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Transcript of A New Temporal Pattern Identification Method for Characterization and Prediction of Complex Time...
A New Temporal Pattern Identification Method for
Characterization and Prediction of Complex Time Series Events
Advisor : Dr. HsuGraduate : You-Cheng ChenAuthor : Richard J Povinelli Xin Feng
Motivation Objective Introduction Fundamental Concepts Framework of The Method Application Conclusions Personal Opinion
Outline
Motivation
Many of the significant temporal patternsare unobvious, contaminated with noise,hence ,are difficult to identify usingtraditional time series analysis methods.
Objective
To propose a method for identification of temporal patterns that characterize the events of interest in the time series.
Introduction
Fig 1. Synthetic seismic time series with events
Introduction
Outline of the Proposed Method
},...,1,{ NtxX t
Using time-delayed embedding unfold time series X into IRQ
- a reconstructed phase space.
A set of Q time series observations taken from X map to
Step A
},,,{ ,2)1( tTtTtTQt xxxx
TtTtTtTQtt xxxx ),,,(x ,2)1(
Introduction
Step B
Event characterization function g(xt) is associated witheach phase space point xt
g(xt) represents the value of future “eventness” for thephase space point xt
Temporal pattern cluster P is defined as a ball consisting ofall points within a certain distance Ď of a temporal patternp in the IRQ
Construct a heterogeneous collection of temporal patternclusters C*, such that C* is the optimizer of the objectivefunction f.
Introduction
Step C
Fundamental Concepts
Because of noise, the temporal pattern does not perfectly match the time series observations that precede events. To overcome this limitation, a temporal pattern cluster is employed to capture the variability of a temporal pattern.
Temporal Pattern Cluster
Fundamental Concepts
},,,{ ,2)1( tTtTtTQt xxxx The observationscan be compared to a temporal pattern.
Temporal patterns and events are placed into three categories: past, present, and future.
Temporal Pattern & Event
Fundamental Concepts
Time-Delay Embedding
Fundamental Concepts
Event Characterization FunctionIn order to correlate a temporal pattern with an event,the event characterization function g(xt) is introduced.
1t )(x txg
3t )(x txg
The augmented phase space is a Q+1 dimensionalspace formed by extending the phase space with g(*)as the extra dimension. ex < xt,g(xt) >
Fundamental Concepts
Augmented Phase Space
Fundamental Concepts
Object Function
The object function represents the efficacy of a collection of temporal pattern clusters to characterize events.
Three example object function
Fundamental Concepts
The first object function is the t-test for the differencebetween two independent means and is useful foridentifying a single temporal pattern.
)()(
)(22
QcPc
uuPf
qp
qp
Fundamental Concepts
The second objective function is useful for finding a single temporal pattern cluster that minimizes the incorrect positive predictions.
fptp
tpPf
)(
Fundamental Concepts
The third objective function is useful for maximize Characterization/Prediction accuracy.
fnfptntp
tntpCf
)(
Framework of The Method
Diagram of Algorithm
Framework of The Method
An Example for training Stages
Framework of The Method
Step 1-Model the Goal
The event characterization function is g(Xt)=Xt+1
The objective function is
)()(
)(22
QcPc
uuPf
qp
qp
Step 2-Determize Temporal Pattern Length
The value of Q, i.e., the length of the temporal pattern
and the dimension of the phase space.Here we set Q=2, which allows a graphical presentationof the phase space.
Framework of The Method
Step 3-Unfold the Training Time Series into thePhase Space.
The Manhattan distanceGiven two points y and z in IRQ, the distance between the two points is
Q
iii zyzyd
1
),(
Step 3-Unfold the Training Time Series into thePhase Space.
Framework of The Method
Framework of The Method
Step 4-Form Augmented Phase Space.
Augmenting the phase space with the extra dimension g(*)
Framework of The Method
Step 6-Search for Optimal Temporal Pattern Cluster.
Application-Welding Droplet Releases
Application-Welding Droplet ReleasesSamples of these time series
Application-Welding Droplet Releases
The stickout time series is preprocessed to remove thelarge-scale artifact.
Application-Welding Droplet Releases
The event characterization function is g(Xt)=Xt+1
The objective function for the collection of temporalpattern clusters is
fnfptntp
tntpCf
)(
The range of phase space dimensions Q is [1,20]
Application-Welding Droplet Releases
Recalibrated stickout time series (testing)
Application-Welding Droplet Releases
Conclusions
The paper has presented the new frameworkincluding the key concept of event characterizationfunction, temporal pattern clusters, time-delay embedding,augmented phase space, and objective function.
Personal OpinionThe event function that characterizes one to fivetime steps ahead instead of in just one time step ahead may can be employed to improve accuracyand performance.