International Conference on Mechatronics, Electronic, Industrial and Control Engineering (MEIC 2014) Application of fuzzy clustering analysis on the consumption level of residents by region in Hainan Chen Yijuan Zhang Chengyi* School of Mathematics and Statistics School of Mathematics and Statistics Hainan Normal University Hainan Normal University Haikou,China Haikou,China E-mail:[email protected] E-mail:[email protected] He Lifang School of Mathematics and Statistics Hainan Normal University Haikou,China E-mail:[email protected] Abstract—The previous literatures generally study miscellaneous goods,and services as indicators in consumption level of the single urban or rural residents in modeling the consumption structure, but few takes the Hainan.But there are few documents about the residents' social development degree into account. consumption level in Hainan province. According to the the We think that statistics analysis of overall spending data in range of year 2003-2012,this paper analyzes and behavior in both urban and rural eras would give better evaluates on consumption level of urban and rural residents understanding of the consumption structure. We therefore in Hainan from the whole perspective. We compare and employed weighted FCM algorithm to carry out the analyse the data of cities. The main conclusions are as analysis in this perspective. follows: It unveils that the urban and rural resident We categorized the factors that drive consumption consumption trend shows strong positive correlation to each behavior as essential factors, major factors and other respective local economic status. The education expense accounts for gradual increasing part of resident factors. We choose per capita GDP as the essential factor. consumption cost. In addition, the population growth, the The major factors included per capita disposable income urbanization rate, and the income differentiation between of urban, per capita net income of rural, and the income urban and rural resident play a significant role in difference between urban and rural eras. Other factor consumption behavior.The last, countermeasures and covers the number of university students the education suggestions are offered for these phenomena and their funds ,and urbanization rate and the natural population reasons. And the result from this study provides references growth rate. to the future urbanization planning. The weighted FCM algorithm was carried out to classify Hainan residents' consumption expenses. The Keywords-Hainan;Consumption Level;FCM Algorithm; classification results were subsequently discussed towards Fuzzy Cluster Analysis;Residents each driver. Recommendations were thereafter proposed to policy decision in future urbanization strategies. I. INTRODUCTION II. THE IMPROVED ALGORITHM Study of the residents' consumption in terms of expense level and portion is expected to not only unveil A. brief introduction fuzzy c-means clustering analysis the actual conditions of local people's livelihood, but also in turn to yield vital significance inputs to the strategic method decisions in improving government investment, Bezdek has proved fuzzy c-means algorithm will be optimizing investment structure, and increasing domestic convergent from iterative calculation: demand.The previous related literatures[1-7] ncc )2( generally concluded the studies with respect to data Step1: select class number and take an )0( MR from individual urban or rural in Hainan.But there are few initial fuzzy classification matrix fc . Then the documents about the residents' consumption level in l ,...2,1,0 Hainan.These researches select food, clothing, housing, iteration step by step supplies, medical, transportation, entertainment, © 2014. The authors - Published by Atlantis Press 710 ()l Step2:To R and calculate matrix clustering III. DATA ACQUISITION AND PROCESSING l l l l T VVVV() (,,() (),)... () center 1 2 c .In the formula A. data acquisition and determination of the weights n n V ()()l rl q w u r()l q In order to ensure the scientific nature of the study, i ()ik k k ()ik k1 k1 data of this article from statistical yearbook of Hainan . province.According to the information entropy method ()l Step3:Modify fuzzy classification matrix R ,and take to determine the factors impact on the consumption l c )( 2 w() uk Vi level of importance weight r l)( ([ q1]) 1 ik l)( m j1 w() uk V j j ijln ij,jppkE (2) k .. n.,2,1( j 2,1;, ,...,) c (1) i1 ()l R(l 1) Step4:Compare R with .If the accuracy of dj1 E j (3) (l 1) (l ) max{rik rik } ()l ()l fixed 0 has ,so R and V are dj l l 1 w ,j requested, and stop. Otherwise, ,back to the j n (4) step2and repeated. dj B. improvement of algorithm j1 We consider the role of index weight to the level of By type(2),(3)and(4)to determine the entropy of consumption in order to more appropriate to the needs of E j d j the actual situation in application. Assume that index each attribute ,the degree of difference and w w w w w j weight vector is (,1 2,..., m ) .So general European standardized weights .Calculated separately and be m shown in the table below:(down to one over ten 2 1 2 w(){[( uk V i wj ukj vij)] } x thousand and we denote by 1 Per Capita j1 power distance is x available to say the difference between the sample GDP(yuan), 2 Per Capita Disposable Income of u V x clustering k and category i .So in (1) the distance will be Urban(yuan), 3 Per Capita Net Income of x the improved generalized. European power distance. Rural(yuan), 4 Income Difference Between Urban And x Rural (yuan), 5 Number of University x x Students(person), 6 Education(10000yuan), 7 Urbaniz x ation Rate(%),and 8 Natural Growth Rate (%)) TABLEI. SPECIFIC DATA OF ENTROPY, DIFFERENCE DEGREE AND WEIGHT x1 x2 x3 x4 x5 x6 x7 x8 E j 0.9825 0.9887 0.9912 0.9896 0.9776 0.9787 0.9925 0.9938 d j 0.0175 0.0113 0.0088 0.0104 0.0224 0.0213 0.0075 0.0062 wj 0.1657 0.1073 0.0838 0.0987 0.2130 0.2018 0.0708 0.0589 uij m j uij 1.0 (0.9 0.1) (5) Therefore, the weight of each index for: W=(0.1657, Mj m j 0.1073, 0.0838, 0.0987, 0.2130, 0.2018, 0.0708, 0.0589) i 1,2,...,144;j 1,2,.. .,10 B. data normalization and determine the initial fuzzy At the same time the corresponding initial fuzzy )0( classification matrix classification matrix R .And determine the classification q Different impact on the result of the classification number c 4 ,take 2 ,precision .0 001. because the characteristic parameters of dimension and order of magnitude is not necessarily the same.In order to C. clustering results eliminate the influence of different characteristic index The results from iterative calculation are summarized order of magnitude.So use type(5) to normalize the data as in the below TABLEII. processing. TABLEII. CLUSTER CENTERS OF VARIOUS TYPE Cluster Indicators centers x x x x x x x x 1 2 3 4 5 6 7 8 V 1 0.3985 0.6116 0.6323 0.5488 0.3320 0.2974 0.6006 0.5488 V 0.6586 0.7911 0.8066 0.3530 0.4385 0.4258 0.6739 0.5811 2 V 0.2930 0.4412 0.4389 0.7170 0.2071 0.1973 0.7100 0.5998 指标 V 4 0.2447 0.3361 0.4054 0.8748 0.1805 0.1681 0.4526 0.6836 711 We defined the classification rule as that an clustering center. Therefore, the classification results u object k would be allocated to the closest vector are shown as in TABLEIII. TABLEIII. OUTPUT OF CLUSTERING BY REGION IN HAINAN Class Region 1 Wenchang, Qionghai, Chengmai, Lingao, Danzhou, Dongfang 2 Haikou, Sanya 3 Wuzhishan, Tunchang, Qiongzhong, Baoting, Whitesands, Changjiang 4 Wanning, Ding’an, Ledong, Lingshui The data and information from Hainan statistical lowest. In addition, from the classification results and the yearbook indicate that the eight index of Haikou and data, we can know the level of consumption of class 2 is Sanya are attributed with the values greater than the ones the highest , class1 is the second and class3 is the from Wenchang, Qionghai, Chengmai, Lingao, Danzhou lowest.So the results of the classification and the and Dongfang, which are in turn greater than the rest eras. economic development of cities and counties show strong Wuzhishan, Tunchang, Qiongzhong, Baoting, White sands relationship. and Changjiang are ranked at the bottom. We brief it in the Second:Sanya, as the most developed city in term of classification language that the class 2 is ranked as the tourism industry, exhibits higher economic level than other highest level of consumption, the class 1 as higher, class 4 eras. As shown in TABLEV, Sanya's essential factors and as lower, and class 3 seating itself at the lowest. main factor are comparable better, while the number of university student, the education investment, and IV. ANALYSIS AND EVALUATION THE urbanization rate in Sanya are comparable lower than in Haikou. The classification result categorizes the two cities CLUSTERING RESULTS AND GIVING THE in the same class that induces the education expenses CORRESPONDING SUGGESTIONS contributing to a larger proportion of residents' The above argument would be submitted to following consumption. This statement as well can be proved by the phenomena. weight. First: The clusters are classified consumption level in Third:A Data from Haikou and Danzhou (see each era., Data in TABLEIV. reveal that the economic TABLEV.) are similar, but the two cities are not in the development aspects in Hainan province four aspects.For same class. The reason is that the urbanization rate in instance,economic development in Haikou and Sanya Danzhou is low and the population growth rate, in the scores the highest.