linear regression.pdf

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International Conference on Methods and Models in Computer Science, 2009

A LINEAR Regression-Based Frequent Itemset

Forecast Algorithm for Stream DATA

Sonali Shukla , Sushil Kumar , Bhupendra Verma

3

TIT, Bhopal,

e-mail:}[email protected]

[email protected].

b k _ v e r m a @ r e d i f f m a i l c o m

Abstract-

Data mining deals with extracting or mining

knowledge from large and infinite amount of stream data.

It also handles the data quality with limited volume of disk

or memory. In such traditional transaction environment it

is impossible to perform frequent items mining because it

requires analyzing which item is a frequent one to

continuously incoming stream data and which is probable

to become a frequent item. This paper proposes a way to

predict frequent items using regression model to the

continuously incoming real time stream data. By

establishing the regression model from the stream data, it

may be used for prediction of uncertain items.

After gathering real-time stream data through sliding

window, algorithm FIM-2DS computes support for

appointed sequence and describes linear equation to

forecast sequence trends in the future.

Keywords: Frequent items; stream data; linear

regression; sliding window.

I. INTRODUCTION

S

ream data is generated continuously in a dynamic

environment, with huge volume, infmite flow, and

fast changing behavior.

In recent years, many time-series mining problems

have been explored for a data stream environment.

Because sequence forecast is an import subject

of

those,

some methods were designed to develop sequence trend

analysis in a dynamic environment. Yixin Chen etc. [9]

investigated methods for multi-dimensional regression

analysis of

time-series stream data; they built up a

partially materialized data cube model and took an

exception-guided regression approach to analysis stream

data. Wei-Guang Teng etc. [10] devised a FTP-DS

algorithm to mine frequent temporal patterns of data

stream. The FTP-DS algorithm uses linear regression to

perform trend detection, it s an effective method, but it

always omits some exceptions, which are too pivotal to

lead to failure.

In this paper, we present a FIM-2DS algorithm that

use plan regression approach to ameliorate FTP-DS

algorithm, so the sequence trends can cover those key

exceptions. Our experiment on comparing between the

FTP-DS algorithm and the FIM-2DS algorithm shows

that coverage ofFIM-2DS algorithm ismuch wider.

The rest

of

the paper is organized as follows. In next

Section, we introduce the basic concepts of sequence

forecast and concerned problem, Section 1 describes

FIPM algorithm with example, and Section 2 describes

the FTP-DS algorithm.

In

Section 3, we present the

algorithm

of

FIM-2DS. Section 4 shows our

experiments and performance analysis and our study

and future research are concluded in Section 5 and 6

respectively.

II .

RELATED CONCEPTS

In this section, we introduce the basic concepts

of

sequence forecast in data stream and give a brief look at

FIPM algorithm and FTP-DS algorithm.

Sequence in data stream is essentially a sequence of

sets of events, which conform to the given timing

constraints [11]. As an example, the sequential pattern

(A)(C, B)(D), encodes an interesting fact that event D

occurs after an event-set(C, B), which in tum occurs

after event A. If the support

of

sequence is no less than

the threshold, this sequence is called frequent sequence.

Sequence forecast plays an important role in gene

analysis, fmance forecast, network security, web

information extraction, communication statistic, and so

on.

1.FREQUENT ITEMS PREDICTION METHOD

We explain the frequent items prediction method [8],

called

FIPM. The method uses a regression analysis model

in one dimensional stream data and predicts frequent

items by using the estimated regression model. First,

this method preprocesses one dimensional stream data

and transforms it to a form of sampling value for further

regression. When a sampling value is generated, a

regression model is found using the method of least

squares, a way to estimate regression model.

A. Data Preprocessing

The purpose

of

regression analysis is to fmd an

estimator in the future from observed values as samples.

In other words,

if

n number

of

sample values were

obtained, an estimator, yn+1 would be predicted based

on the input, xn+1 upon the analysis of the samples.


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Therefore, it is necessary to transform the incoming

stream data into a data pair, such as (xi, yi). Stream data

has properties of time series data. As seen in the Figure

1, stream data comes in continuously as inputs with time,

t.

The stream data preprocessing is as follows: first,

each inputted value in stream data is reorganized into

stream data at the incoming time of each inputted value.

We first reorganize times of each value to

perform

preprocessing operation.

From the reorganized stream data we can find the

difference in time for each item. For example in the

value A, the value, A is entered in the stream data at t

IS, t-13, t-IO, t-S, t-4 , and t respectively. From the

example of stream data in the Figure I , it is unknown

when the value, A entered before the time

oft-IS

, but it

is possible to see the differences in time for the input

of

A from the time oft-IS to the present time, t: {2, 3, 2 , 4,

4}. Such differences in time can be sequentially paired

as follows : (2, 3), (3, 2), (2, 4), (4, 4). These pairs

indicate the differences in time before and after the

value , A is entered in the stream data . ( As given in

Table 2).

U A

B

A r

E c

A

E D

r

D E

A

I I I I

I

I I I I

I

ri

1

16

1ll

I J 11) Ig

>1

1-6 ,

l-l I)

r.[

r

time. In other words, previously appeared time intervals

can be set as an independent variable and the time

appeared intervals later as a dependent variable, we may

be able to estimate the linear regression model that we

want.

Putting the values of Dependent and Independent

variable in linear regression model, we will get the

regression fit line.

2. A BRIEF LOOK AT FPT-DS ALGORITHM

Algorithm FTP-DS [10] was presented by Wei-Guang

Teng on 29

th

VLDB conferences at 2003. There were

two key defmitions for FTP-DS algorithm. One is the

support of frequent sequence; the other is the pattern

representation, which called a compact ATF. We will

give a brieflook at those in below.

The support of frequent sequence X at a specific time

t is denoted by the ratio

of

the number

of

events having

sequence

X

in the current sliding window to total

number of events. Supposing the sliding window size is

3, there are 3 sliding windows in Figurel , i.e., [0,3],

[1,4], [2,5], the support of sequence is computed

as: in [0,3], the is in event {ID:2, ID:5}, so its

support is 2/5=0.4; in [1,4], the is in event {ID:I ,

ID:4}, so its support is 2/5=0.4; in [2,5], the is in

event {ID:I}, so its support is 1/5=0.2.

TO

St r{ am Sequence

J

1

(b)

(d ) rJ 1

2

(u , b. c (C. dl (d, f

1

3

(b)

(f.')

J

4

a

(b . eJ Cd)

I

5

(b) c . tI)

CI )

.t

aap

l 2 J

,I

Fig. 1. Exampleof onedimensionstreamdata

Calculate the values

of

Dependent variable and

Independent variable depend on the following model

using pairs of Data Sets:

TABLE I. EXAMPLEOFTHEORDERED PAIR,(X,V),

FORTHEVALUE, A

t

i mcs

input time

1 2 3 4 5

6

7 8 9

sequence

independent

2

3

2

4 4 3

5 7

6

variable(x)

dependent

3 2 4 4 3 5 7 6 5

variable(y)

TABLE2. PROCESS OFESTIMATINGREGRESSION

FORMULA BETWEEN ANINDEPENDENTVARIABLE

Fig. 2.Anexampleof supportcomputation

The ATP

form

of time series was defmed as

(ts, Df, f,

It2

and FPT-DS algorithm extracted a regression fit line:

f = a ~ t

Whereo, has to be calculated using some formulae.

Seq.

V....>


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A

b

o

= j b

l

i

A

Ix

,r-

.1\ I (x -

i f

V

- \ .)

l;

= t J I .,-- = I

J .

,

-- (

-) '

L ;; - X z: .\ - x -

Step5: Fit the regression model ofFlM-2DS:

y =b

[

Step6: Calculate the error

- -

erroron

FTPDS

e r ro ron

FIPM2D

345678

Fig. 4. Graph to show the mean residual comparison

o

0.3

0.2

0.1

5. CONCLUSION

In this method , the least square method is used to

estimate a regression line based on the linear regression

analysis. The regression in this method is a simple linear

regression model estimating a regression model with

changes in two different variables . Since stream data has

a characteristic

of being continuously transmitted in

time, they defme the changes in time with two variables.

These two variables indicate an independent variable

and a dependent variable respectively.

Here, in this method I have presented an overview

of

some vulnerabilities of algorithm FIPM and designed

linear regression based algorithm FIM-2DS to predict

frequent sequence for real time stream data, in which I

reviewed the concept of preprocessing from the

algorithm FTP-DS. Our experimental result shows the

merit of our algorithm in terms

of

errors.

6. FUTURE ENHANCEMENT

REFERENCES

[I] B. Babcock, S. Babu, M. Datar, R. Motwani, and 1. Widom,

Models and Issues in Data Stream Systems, In Proc. of PODS,

March 2002.

[2] N. Davey, S. P. Hunt, and R. 1. Frank, Time Series Prediction

and Neural Networks, In Journal of Intelligent and Robotic

Systems, 200

I.

[3] L. Golab, M. Tamer Ozsu, Issues in Data StreamManagement,

In SIGMODRecord, Volume 32, Number 2,2003.

[4] X. Hao, D. Xu, Time Series Prediction based on Non

Parametric, In SIGMODRecord, Volume 32, Number 2,2003 .

[5] D. F. Specht, A General Regression Neural Network, IEEE

Trans. on Neural Networks, Vol.2, No.6, pp.568-576, Nov. 1991.

[6] D. Wacherly, W. Mendenhall,

R.

L. Scheaffer, Mathematical

Statistics with Applications , 5th edition, 2005.

[7] O. B. Yaik, C. H. Yong, and F. Haron, Time Series Prediction

using Adaptive Association Rules, In Proc. Of DFMA05,

pp.3IO-3I4,2005.

[8] Duck Jin Chai, Eun Hee Kin, Long Jin, Frequent Items

Prediction Method to one dimensional stream data , in Fifth

International Conference on Computational Science And

Applications, IEEE -2007.

Let us analyze a few open problems of FIM-2DS

algorithm from data stream background. Stream data is

so huge , infinite, and fast changing that it always

contains lots of noisy, overflowing, incomplete data

items. As my work is concerned, it is not dealing with

this problem that too at the cost of execution time, my

future work is to resolve this problem.

--- - e rro r o n FTPDS

____ e rro r o n F IPM2D

- 1

.- L . r

Tl r-J

Error

comparison o n F TP DS a nd

FIPM2D

Fig. 3. Graph to show the residual comparison

II .J>

II

I I


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[9] Y.Chen, G.Dong, J.Han et, al, Multi-Dimensional Regression

Analysis of Time-Series Data Stream , Proceedings of the 28

th

International Conference on Very Large Data Base, Berlin, pp.

323-334,August 2002.

[10] Wei-Guang Teng, Ming-Syan Chen, Philip S.Yu, A

Regression-Based Temporal Pattern Mining Scheme for Data

Stream , Proceedings of the 29th International Conference on

Very Large Data Base, Berlin, pp.607-617, August 2003.

[11] Joshi M, Karypis G, A universal formulation of sequential

patterns , Research report No.99-021, Department of Computer

Science, University

of

Minnesota, Minnesota, 1999.

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