基于支持向量机的电信话务量预测

Table 2 Sample data of GSM net 2002 2003 900465 900003 757783 807501 832037 809786 729362 594212 872679 906576 884235 848686 874490 908827 757782 791038 798755 819426 730811 593034 892611 889142 885993 848686

A Prediction of Speech Volume Based on Support Vector Machine
Han Huimin
Automation School, Beijing University of Posts and Telecommunications, Beijing (100876)
T = {( x1 , y1 ),..., ( xl , yl )} ∈ ( X × Y )l ,
where xi ∈ X = ℜ , yi ∈ Y = ℜ , i = 1,..., l ;
n
(2) (3)
α ∈ℜ
Choose the proper positive number ε and C ; choose the proper kernel Construct the optimization function and resolve the optimization problem
l l 1 l * * * α − α α − α K x y + ε α + α − yi (α i* − α i ) , ( )( ) ( , ) ( ) ∑ i i j j i j ∑ ∑ i i 2 i , j =1 i =1 i =1
function K ( x, x ') ;
min (*) 2l
2004 175773 198257 141410 149183 155233 159401 159942 157134 166258 181022 151375 142838
2005 175843 198217 141311 147502 155279 159385 160054 157103 166208 180914 150878 142838
2001 January February March April May June July August September October November December 175685 198138 141212 147414 155093 159274 159846 156993 166092 180769 150772 142667
We use the actual data of speech volume offered by some telecommunication office to do the emulation to prove the feasibility of the method of SVR. Model Selection Firstly we choose the SVM model. Let some speech volume data of consecutive three years be the input vector, and the output vector is the speech volume data of the next year.
2. Methodologies
ε -Support Vector Regression ( ε -SVR)
Given a set of data points
T = {( x1 , y1 ),..., ( xl , yl )} ∈ ( X × Y )l
the standard form of support vector regression(Vapnik,1998) is:
2004 873624 891180 756282 789469 792416 806572 590678 591856 867046 880425 885114 848686
2005 871027 889414 757782 790254 797170 806572 730810 594212 875279 875195 879400 847845
2001 January February March April May June July August September October November December 865832 882356 750280 783982 792416 803359 724292 588912 866613 871708 878961 841116
E-mail： hanhmbupt@
Abstract Support Vector Machine (SVM) is a new tool in virtue of optimization to resolve machine learning problems, and a new technique in DataMining area. Support Vector Machine (SVM) is a new common learning approach developed by Vapnik and others on basis of statistical learning theory in recent years. It is based on the structural risk minimization criteria. This paper presents the principle and algorithm of SVR (Support Vector Regression). The application of SVR to the analysis and prediction of speech volume increases efficiency. The satisfied result of emulation shows that the method of SVR is advanced and with high accuracy and good generalization. Keywords: Support Vector Regression, Speech Volume, prediction.
1. Introduction
SVM (Support Vector Machines) are a new tool in virtue of optimization to resolve machine learning problems, and a new technique in DataMining area1. It was brought up by Vapnik based on the statistical learning theory. SVM can be used to deal with the classification and regression problems. It has been gradually extending in the area of predicting and evaluating2. With the development of communications business, it is very important for operations merchants to analyze and predict the operations reasonably so as to make decision effectively. We will introduce a new method based on SVR (Support Vector Regression) to predict the speech volume in this paper.
T
Where Qij = K ( xi , x j ) ≡ φ ( xi )
φ ( x j ).
-1-

The approximate function is:
∑ (−α
i =1
l
i
+ α i* )K ( xi , x) + b.
Algorithm The main steps of ε -SVR is to choose the parameters ε and C , to resolve optimization problems, and to construct the optimum decision making function. Below is the ε -SVR algorithm3. (1) Suppose the training set
The dual is:
l l 1 * T * * min ( ) ( ) ( ) α − α Q α − α + ε α + α + yi (α i − α i* ) ∑ ∑ i i * α ,α 2 i =1 i =1
Subject To:
∑ (α
i =1
l
i
− α i* ) = 0, 0 ≤ α i , α i* ≤ C , i = 1,..., l ,
l l 1 min * wT w + C ∑ ξi + C ∑ ξi* w ,b ,ξ ,ξ 2 i =1 i =1
Subject To: w
T
φ ( xi ) + b − yi ≤ ε + ξi ，
yi − wT φ ( xi ) − b ≤ ε + ξi* ，
ξi , ξi* ≥ 0, i = 1,..., l.
Subject To:
∑ (α
i =1
l
i
− α i* ) = 0 ，
0 ≤ α i ， α i* ≤
பைடு நூலகம்
C ， i = 1, 2,..., l ， l
* * Τ
Get the optimum α = (α 1 , α 1 ,..., α l , α l ) ; (4) Construct the decision making function
*
C ) has been l
b = y j − ∑ (α i − α i )( xi ⋅ x j ) + ε ;
*
l
i =1
If α has been chosen, then
* k
b = yk − ∑ (α i − α i )( xi ⋅ xk ) − ε .
*
l
i =1
3. The emulation prediction of speech volume
Table 1 Sample data of CDMA net 2002 2003 176563 198316 141636 147709 155248 159417 160006 156994 166192 180914 150847 142724 175755 198316 141353 147532 155171 159385 159974 157150 167089 182938 152883 143951
-2-

Below is the speech volume data called from other areas. The data of CDMA net is in Table1 and the data of GSM net is in Table2.
l
*
f ( x) = ∑ (α i − α i )K ( xi , x) + b ,
i =1
Where b is calculated according to whether α j or α k in the open interval (0, chosen. If α j has been chosen, then