A New Temporal Pattern Identification Method for Characterization and Prediction of Complex Time Series Events Advisor ： Dr. Hsu Graduate ： You-Cheng Chen Author ： 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 patterns are unobvious, contaminated with noise, hence,are difficult to identify using traditional 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 Using time-delayed embedding unfold time series X into IR Q - a reconstructed phase space. A set of Q time series observations taken from X map to Step A

Introduction Step B Event characterization function g(x t ) is associated with each phase space point x t g(x t ) represents the value of future “eventness” for the phase space point x t

Temporal pattern cluster P is defined as a ball consisting of all points within a certain distance Ď of a temporal pattern p in the IR Q Construct a heterogeneous collection of temporal pattern clusters C*, such that C* is the optimizer of the objective function 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 The observations can 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 Function In order to correlate a temporal pattern with an event, the event characterization function g(x t ) is introduced.

The augmented phase space is a Q+1 dimensional space formed by extending the phase space with g(*) as the extra dimension. ex 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 difference between two independent means and is useful for identifying a single temporal pattern.

Fundamental Concepts The second objective function is useful for finding a single temporal pattern cluster that minimizes the incorrect positive predictions.

Fundamental Concepts The third objective function is useful for maximize Characterization/Prediction accuracy.

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(X t )=X t+1 The objective function is 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 presentation of the phase space.

Framework of The Method Step 3-Unfold the Training Time Series into the Phase Space. The Manhattan distance Given two points y and z in IR Q, the distance between the two points is

Step 3-Unfold the Training Time Series into the Phase Space. 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

Samples of these time series

Application-Welding Droplet Releases The stickout time series is preprocessed to remove the large-scale artifact.

Application-Welding Droplet Releases The event characterization function is g(X t )=X t+1 The objective function for the collection of temporal pattern clusters is 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 framework including the key concept of event characterization function, temporal pattern clusters, time-delay embedding,augmented phase space, and objective function.

Personal Opinion The event function that characterizes one to five time steps ahead instead of in just one time step ahead may can be employed to improve accuracy and performance.