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.