Subsidy food is government program for social protection to poor households. The aims  of  this  program  are  to  effort  households  from  starve  and  to  decrease  poverty.  Less precisely  target  of  this  program  has  negative  impact.  So  that  to  successful  program,  it’s important  to  know  accuracy  classification  of  admission  subsidy  food.  The  variables classification  are  number  of  household  members,  number  of  household  member  in  work, average expenditure capita, weighted household, and floor area. Discriminant analysis is a multivariate  statistical  technique  which  can  be  used  to  classify  the  new  observation  into  a specific  group.  Kernel  discriminant  analysis  is  a  non-parametric  method  which  is  flexible because  it  does  not  have  to  concern  about  assumption  from  certain  distribution  and  equal variance matrices as in parametric discriminant analysis. The classification using the kernel discriminant  analysis  with  the  normal  kernel  function  with  optimum  bandwidth  0.6  gives accurate classification 75.35%

Mukid, Moch. Abdul

Prahutama, Alan

English

Diponegoro University Institutional Repository

Proceeding of 5th International Seminar on ISSN: 978-602-71169-7-9 New Paradigm and Innovation on Natural Sciences and Its Application (5th ISNPINSA) Alan Prahutama, et. al. P a g e  | 177 This Proceeding © Faculty of Sciences and Mathematics Diponegoro University, 2015 Analyze of Classification Accaptence Subsidy Food Using Kernel Discriminant Alan Prahutama1,a, Moch. Abdul Mukid1,b 1Statistics Department, Faculty of Sains and Mathematics, Diponegoro University aalanprahutama@undip.ac.id, bmamukid@yahoo.com Abstract. Subsidy food is government program for social protection to poor households. The aims of this program are to effort households from starve and to decrease poverty. Less precisely target of this program has negative impact. So that to successful program, it’s important to know accuracy classification of admission subsidy food. The variables classification are number of household members, number of household member in work, average expenditure capita, weighted household, and floor area. Discriminant analysis is a multivariate statistical technique which can be used to classify the new observation into a specific group. Kernel discriminant analysis is a non-parametric method which is flexible because it does not have to concern about assumption from certain distribution and equal variance matrices as in parametric discriminant analysis. The classification using the kernel discriminant analysis with the normal kernel function with optimum bandwidth 0.6 gives accurate classification 75.35%.  Keywords: Discriminant kernel, Bandwidth, Subsidy Food Introduction Economic imbalances in Indonesia resulted in increasing poverty. Furthermore Poverty is an issue that can not be solved for developing countries. Poverty reduction has also become one of the main goals Millenium Development Goals (MDGs) in 2000-2015 years. In 2013 Indonesia has been implemented several programs in an effort to overcome the problems of poverty which was impacted by fuel subsidy reduction. The programs has been implemented are Acceleration and Expansion program for Social Protection which consist of subsidy food, subsidy for poor student and family expectaion program. In addition, the government has also implemented special programs such as direct subsidy while for people and Infrastructure Development Acceleration and Expansion program. Subsidy Food is a program of social protection for poor households and in an effort to protect household from the threat of malnutrition.  Discriminant analysis is a method to determine the linier combination of features that best separates two or more groups of objects [2]. It seeks to find the projection directions along which the gropus are best separated [12]. Discriminant analysis usefull to classify object into groups based on variables. Discriminant analysis procedure is to establish a discriminant function which is used for classification. Discriminant analysis is very tight with the assumption, such as multivariate normal distribution of data and variance covariance matrix is homogeneous [8]. If the assumption is not met, then the model is not accurate for classifying new observations [14]. Another opinion expressed that althought discriminant analysis is conceptually simple and has been used in many application areas, its normality assumption limits its performance. Furthermore, as a linier method, it does not capture nonlinierity clustered structures [11]. Predictions and classifications with nonparametric techniques is one of the statistical analysis that is quite popular and widely used in various studies. Nonparametric discriminant analysis is a method that is flexible because it does not have to fulfill certain assumptions as to the parametric discriminant analysis. One nonparametric discriminant analysis developed at this time is the kernel discriminant analysis. Some studies have linked the kernel discriminant analysis has been done such as [10] regarding the selection of kernel parameters at the kernel discriminant analysis. [7] Conduct research kernel discriminant analysis using fuzzy membership functions. [9] Use kernel discriminant analysis for fault diagnosis. [5] ISSN: 978-602-71169-7-9 Proceeding of 5th International Seminar on  New Paradigm and Innovation on Natural Science  and Its Application (5th ISNPINSA) 178 | P a g e  Alan Prahutama, et. al.  This Proceeding © Faculty of Sciences and Mathematics  Diponegoro University, 2015 Use kernel discriminant embedding in face recognition. [2] Use kernel discriminant for classification data. Based on the exposure to be observed regarding the accuracy of the classification of subsidy food distribution using kernel discriminant and determine variables that influence of subsidy food distribution. Varibles to be observed regarding the subsidy food distribution such number of household members (X1), number of household members who work (X2), Average Expenditure Per Capita (X3), Weighing Household (X4) and Floor Area (X5) Materials and Methods Discriminant Kernel Kernel Discriminant Analysis is discriminant analysis method which extracts nonlinier discriminant features by generalizing discriminant function to a high dimension kernel space [1]. If density function of ( )if xunknown or in other words, distribution model of 𝑋 unknown which ( )if x  assumsed that in smooth function, then nonparametric approch should be use for estimation ( )if x  [4]. The principle of kernel discriminant analysis is that, after the data are nonlinierly mapped to high dimension kernel space, then the data can be analyzed by discriminant linier. In this procces, discriminant linier analysis convert linier to non linier space. Given sample data ijx  where i  groups (biner) dan j  observation with ( 1, 2; 1, 2, , )i j n  . Discriminant kernel function is: ( ) ( )f x g x h     (1) where ( )f x   can be estimated by: 11( | ) ( | , )njjg x h K x x hn     (2) where ( | , )jK x x h  is kernel density function, and h smoothers parameters (bandwidth). To estimate density function in Eq. (1) can be written by [14]:  1 11 1ˆ ( )n njh jj jx xf x K K x xnh h n         (3) Given H is a matrix bandwidth symmetric and definite positive dxd and ( ) 1K x dx  . If the kernel density function by following a multivariate normal distribution for each group   1 2/2 1/21( ) exp 0.5( ) ( ) /(2 ) | |Tj jd dK x x x x x hh    substituted into the Eq. (3) then obtained form:   1 2/2 1/211 1ˆ ( ; ) exp 0.5( ) ( ) /(2 ) | |nTj jd djf x H x x x x hn h      (4) So that Eq. (4) for K(x) normal multivariate distribution with mean 0 and variance covariance H can be written by:   1 2/2 1/211 1ˆ ( ; ) exp 0.5( ) ( ) /(2 ) | |nTj jd djf x H x x H x x hn h     (5) Determine H is important because it can determine function of f̂ .  Kernel Function Kernel function is one approach that can be used to estimate the probability density function of an observation. Kernel function is a nonparametric density function for estimation method that developed from the histogram estimator [6]. Kernel method is a nonparametric approach to classify the data that have nonlinear patterns [13]. Some of kernel function such as:    Proceeding of 5th International Seminar on ISSN: 978-602-71169-7-9 New Paradigm and Innovation on Natural Sciences and Its Application (5th ISNPINSA) Alan Prahutama, et. al. P a g e  | 179 This Proceeding © Faculty of Sciences and Mathematics Diponegoro University, 2015 Table 1. Kernel function density Kernel K(x) Uniform /2 2/21 21| |( ) ( ) ( )120 ;ddTj jhdK x jika x x H x x hlainnya           Normal   1 20( )1( ) exp 0.5( ) ( ) /Tj jtK x x x H x x hc      Epanechnikov  1 2 1 21( ) 1 ( ) ( ) / , ( ) ( )( )0 ;T Tt j j j jc x x H x x h if x x H x x hK xothers         Biweight  21 2 1 21( ) 1 ( ) ( ) / , ( ) ( )( )0 ;T Tt j j j jc x x H x x h if x x H x x hK xothers         Triweight  31 2 1 21( ) 1 ( ) ( ) / , ( ) ( )( )0 ;T Tt j j j jc x x H x x h if x x H x x hK xothers         where /2 1/20( ) (2 ) | |d dtc h  ; 1( ) 0( )12t tdc c    ; 2( ) 1( )14t tdc c    ; 3( ) 2( )16t tdc c      APER (Apparent Error Rate) APER is stating the proportion of samples incorrectly classified. It uses confusion matric to calculate the number of classify [8]. Confusion matrix is the form of an observation classification results. Can be shown in Table 2, 1n number of classification in group 1 and 2n number of classification in group 2  then it can be conduct as well as: Table 2. Confusion Matric  Groups prediction 1  2 Groups 1  11n 12n 2  21n 22n 11n  is number of members in group 1  that exactly classify into 1 , while 22n is number of member in group 2  that exactly classify into 2 . While 12n  is umber of member group 1  that unexactly classify into 2 , then 21n  is number of member 2 that unexctly classify into 1 . Therefore, statistic test for APER can be shown: 12 211 2100%n nAPERn n     (6) Results and Discussion The data used in this research is subsidy food data Kendal Regency in 2013. Based on the data can be shown:  ISSN: 978-602-71169-7-9 Proceeding of 5th International Seminar on  New Paradigm and Innovation on Natural Science  and Its Application (5th ISNPINSA) 180 | P a g e  Alan Prahutama, et. al.  This Proceeding © Faculty of Sciences and Mathematics  Diponegoro University, 2015 Table 3. Descriptive of Subsudy Food in Kendal Regency  Status Total Precentage Receiver subsidy food 566 71.60% Unreceiver subsidy food 225 28.40% Total 791 100%  Based on Table 3. From the data we know that, 71.6% is receiver subsidy food, then 28.4% unreceiver subsidy food. It show that, almost receiver data as a describe in this research for classification than unreceiver. Table 4. Statistics Descriptive for Variables Variable Minimum Maximum Average Std. deviation number of household members (X1) 1 14 3.5209 1.50754 number of household members who work (X2) 0 6 1.8633 0.97823 Average Expenditure Per Capita (X3) 149407 3709412.1 660898.2 1351406 Weighing Household (X4) 2.76 723.32 317.3316 121.397 Floor Area (X5) 6 728 85.2832 53.60187  Table 4 show that the variables for classifying subsidy food. the average number of household members ranges 3 until 4 person. Whereas in a houshold, the number of who work ranges 1 until 2 person. While Average Expenditure Per Capita is Rp 660. 898,- for a month. Average of Weighing household is 317.3316. Average of floor area is 85.28 m2.  Table 5. Proportion of Training Data and Testing Data Proportion Training Testing Total 90/10 712 79 791 80/20 633 158 791  Based on Table 5, it show that allocation of training data and testing tested three times. It aims to look at the level of accuracy. Tabel 6. Allocation the details of the training data and testing data Proportion 90/10 80/20 Groups Total Train. Test. Train. Test. 1 566 509 57 453 113 2 225 203 23 180 45 Total  712 79 633 158  Table 8 show that the allocation amount for each training data and testing is in proportion to the amount of data. Table 7 show that classification with discriminant kernel method using normal kernel function. The optimum bandwidth is 1 with error 0.26685 for allocation 90: 10. While allocation 80: 20, the optimum bandwidth is 0.6 with error 0.24645. Based on Table 8 with Epachenikov Kernel Function we can describe about the number of bandwidth . It is so different with normal kernel function   Proceeding of 5th International Seminar on ISSN: 978-602-71169-7-9 New Paradigm and Innovation on Natural Sciences and Its Application (5th ISNPINSA) Alan Prahutama, et. al. P a g e  | 181 This Proceeding © Faculty of Sciences and Mathematics Diponegoro University, 2015 Table 7. Classification Use Discriminant Kernel with Normal Kernel Function 90: 10 80:20 Bandwidth Error Bandwidth Error Bandwidth Error Bandwidth Error 0.1 0.375 1 0.26685 0.1 0.372828 0.5 0.252765 0.01 0.394663 1.2 0.272472 0.01 0.375987 0.6 0.24645 0.9 0.269663 1.5 0.273876 0.05 0.374408 0.7 0.249605 0.5 0.269663 1.7 0.271067 0.25 0.338073 0.8 0.248025 0.3 0.289326 2 0.275281 0.4 0.259084 0.9 0.255924  The range optimum bandwidth of normal kernel function ranges 0.01 until 1. Whereas Epachenikov kernel function, the optimum bandwidth is started by 3 until 15. It optimum bandwidth is 7 with error 0.27949. The optimum bandiwdth for allocated 80: 20 is 3 with error 0.26066. Table 8. Classification Use Discriminant Kernel with Epachenikov Kernel Function 90:10:00 1/3/1900 8:20 Bandwidth Error Bandwidth Error Bandwidth Error Bandwidth Error 7 0.27949 8 0.2809 5 0.27646 7 0.2812 7.2 0.27949 8.5 0.2809 4 0.27014 7.5 0.27962 7.5 0.2809 9 0.2823 3 0.26066 10 0.27804 7.7 0.27949 9.5 0.28371 6 0.27804 15 0.28436  Based on Table 9, it show that discriminant kernel use triweight kernel function. The optimum bandwidth for allocated 90: 10 is 7 with error 0.27528. And for 80:20, the optimum bandwidth 3 with error 0.25434. The characteristic optimum bandwidth of Epachenikov and triweight kernel function is similar. Table 9. Classification Use Discriminant Kernel with Triweight Kernel Function 90:10 80:20 Bandwidth APER Bandwidth APER Bandwidth APER  Bandwidth APER  7 0.27528 7.8 0.27809 3 0.25434 6 0.27804 7.2 0.27669 8 0.27669 4 0.2654 7 0.27646 7.3 0.27669 8.2 0.27949 5 0.27014 8 0.27646 7.5 0.27809 8.5 0.2809 5.5 0.27804 8.5 0.2812  Based on Table 7, Table 8 and Table 9, it can be concluded the optimum bandwidth is 0.6 with error 0.24645, that in allocated training and testing is 80:20 with Normal kernel function.  Then we conduct significance variables which influence of subsidy food. The method that used is binary logistic regression. The results of this method can be shown in Table 9. Based on Table 10, it show that the variables have influence for subsidy food with significant level 1% are Average Expenditure Per Capita (X3), Weighing Household (X4) and Floor Area (X5). ISSN: 978-602-71169-7-9 Proceeding of 5th International Seminar on  New Paradigm and Innovation on Natural Science  and Its Application (5th ISNPINSA) 182 | P a g e  Alan Prahutama, et. al.  This Proceeding © Faculty of Sciences and Mathematics  Diponegoro University, 2015 Table 10. Significant of Parameter use Logistic Biner Regression Variable Coefecient Standard error Wald Test df Sig. Conclusion X1 -,021 ,083 ,064 1 ,800 Not Significant X2 -,114 ,121 ,899 1 ,343 Not Significant X3 ,000 ,000 16,389 1 ,000 Significant X4 ,000 ,000 3,715 1 ,054 Significant X5 ,026 ,004 34,985 1 ,000 Significant Conclusion Bandwidth ranges for different kernel functions that produce a range of different bandwidth values. The bandwidth optimum is 0.6 with APER 0.24645 for allocate training and testing is 80:20 with normal function kernel. The accuration of subsidy food is 75.35%. The variables have influence for subsidy food with significant level 1% are Average Expenditure Per Capita (X3), Weighing Household (X4) and Floor Area (X5). References [1] Baudat, G., Anouar, F., 2000. Generalized discriminant analysis using a kernel approach. Neural Comput. 12 (10), 2385–2404. [2] Bishop C.M., Pattern Recognition and Machine Learning, Springer, Singapore, 2007. [3] Duong, T., 2007, Kernel Density estimation and kernel discriminant analysis for Multivariate Data in R, Journal of Statistical Software, Vol.21, Issue. 7 [4] Hair, J.F.Jr., et. al., 2010, Multivariate Analysis Methods and Applications. Pearson Education. Inc, New Jersey. [5] Han, P.Y., Jin, A.T.B., and Ann, T.K., 2011, Kernel discriminant Embedding in Face Recognition, J. Vis. Commun. Image R., Vol. 22, pp: 634-642. [6] Hardle, W., 1990, Applied Nonparametric Regression, Cambridge University Press, U.K. [7] Heo, G., and Gader, P., 2011, Robust kernel discriminant analysis using fuzzy memberships, International Jornal of Pattern Recognition Letters, Vol. 44, pp: 716-713 [8] Johnson, R.A., and Wichern, D.W., 2007, Applied Multivariate Statistical Analysis 6th Edition, Pearson International Edition, New Jersey. [9] Li, J. and Cui, P., 2009, Improved Kernel Fisher Discriminant Analysis for Fault Diagnosis, Expert System with Applications, Vol. 36, pp: 1423-1432. [10] Liu, J., Zhao, F., and Liu, Y., 2013, Learning kernel parameters for kernel Fisher discriminant analysis, International Journal of Pattern Recognition Letters, Vol. 34, pp: 1026-1031. [11] Park, C., Park, H., 2005. Nonlinear discriminant analysis using kernel functions and the generalized singular value decomposition. SIAM J. Matrix Anal. Appl. 27 (1), 87–102. [12] Scott, D.W., 1992, Multivariate Density estimation: Theory, Practice and Visualitation, John Wiley and Sons, New York. [13] Silverman, B.W., 1986, Density estimation for Statistics and data Analysis, Chapman and Hall, London. [14] Worth, A.P., and Cronin, M.T.D., 2003, The Use of discriminant analysis logistic regression and classification tree analysis in development of classification models for human health effects, Theochem, Vol. 622, pp:97-111.  

Analyze of Classification Accaptence Subsidy Food Using Kernel Discriminant

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Analyze of Classification Accaptence Subsidy Food Using Kernel Discriminant

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