Similarity Measure Based on Partial Information of Time Series

Advisor ： Dr. HsuGraduate ： You-Cheng ChenAuthor ： Xiaoming Jin

Yuchang Lu Chunyi Shi

Motivation Objective Introduction Retrieval and Representation of partial Information System Setup Results and Discussion Conclusions Personal Opinion

Outline

Motivation

A “good” similarity measurement is determined by human.

Objective

To propose a model for the retrieval and representation of the partial information in time series.

Introduction

The model has three objects: Get the partial information Represent partial information in a compressed form Most similarity model could be applied

Retrieval and Representation of Partial Information

3.1 General Description

Definition 1: Use a rule F to decompose X into a set of time series

))(),...,1(( NXXX

),...,( ''1 TXXX

3.1 General Description

Definition 2: (1) Segment X into a set of sub-series

))(),...,1(( jrXrjrXX j

(2) X’jk is the k-th F-based component of sub-series Xj

Use mapping rule T to map each X’jk to a value Rk

(j)

3.1 General Description

),...,( 1 WKKK is the orders of all the representing sequences of interest.

Definition 3:

),...,( 1 Wk AAA where An is the degree of user’s interest to n-th component

is portion of partial information of interest

n KnKnXA )( '

3.1 General Description

Definition 4:

)()( /),(),( wmKK KRAmRwmMODwmMOD

is the full representing sequence(FRS) of the partialinformation

n KnKnXA )( '

Definition 5: Given two time series X,Y

3.1 General Description

))(),((),( YFRSXFRSDYXMD

Sum up, a representing model for partial informationcan be summarized by

3.1 General Description

Decomposition method F Representation method T Distance measurement

D

3.1 General Description

Example 1

3.1 General Description

Use F to decompose time series to two components

(1) Local fluctuating movement S’1 (2) Global movement S’2

nfluctuatioS

otherwise

j

jR

1'

01 )(

FRS(X)=R1 and the length of the FRS(X)=200/8

3.2 Practial Method

Let H is transform matrix of a given orthonormaldiscrete transform

So Tj=H*Xj

We denote the results of discrete transform of timeSeries Xj and Yj by DT(Xj)=XTj, DT(Yj)=YTj

3.2 Practial Method

))1/(()()( /' rrnnIBkTnX krnn

T

mrmmm HHHIB

1

,11

,11,0

The k-th component of X is

)()( kTmR mk The k-th representing sequence isThen FRS(X) can be calculated as:

)()( ),(/),( WmMODwmK KTAmRwmMOD

Here we use DCT(discrete Cosine transform) in ourexperiments

3.2 Practial Method

W

n

W

nKnKnKnKn AYAXL

1 1

''2 ),(

q

j

W

nKnnjnj AKYTKXTYXMD

1 1

22))()((),(

W

n

W

nKnKnKnKn AYAXL

1 1

''2 ),(

4. System Setup

4.1 Evaluation of Similarity Measurement Based on Partial Information

We use hierarchical agglomerative clustering(HAC) to cluster FRSs.

)/(2),( jijiji SCSCSCSim

kSCSimSCSimi

jij

/,max),(

5. Results and Discussion

We used historical stock data and only considered the time series of closing price. Step 1: use DCT to decompose time series and to represent partial information.

Step 2: E=(E1,…,Er) to represent the chosen portion.

Step 3: E was used to calculate K and together with A Then FRSs of each time series were generatedStep 4: calculating MD and clustering

5. Results and Discussion

11,15,14,10,19,10,14,17,14 3, 3, 3, 3, 2, 4, 4, 5, 5

5. Results and Discussion

Conclusions

The experimental results could help designing a more effective and more efficient similarity measurement

Personal Opinion

The similarity measurement can be improvedbetter by increasing the weight of the meaningfulcomponent.