A Study on the Classification of Islands by PCA(II)

PCA에 의한 도서분류에 관한 연구(II)

  • Published : 1984.06.01

Abstract

The classification of islands is prerequisite for establishing a development policy to vitalize many-sided function of islands. We try to classify the 440 inhabited islands which exist in Jeon-Nam area and Kyong-Nam area by means of PCA. PCA begins with making correlation matrix of orignal variables. From this matrix we can comprehend the rough relationships between two variables. Next, we look for the eigenvalues which are roots of characteristic equation of correlation matrix. The number of eigenvalues is equal to that of original variables. We choose the largest eigenvalue λ$_1$among them and then look for the eigenvector of correlation matrix corresponding to the largest eigenvalue. Linear combination of eigenvector obtained above and original variables is namely first Principal Component (PC). Using an eigenvalue criterion(λ$\geq$ 1), we choose 3 PCs in Jeon-Nam area and 2 PCs in Kyong-Nam area. But we decide to consider only two PCs in both areas to faciliate a comparative analysis. Now, loss of information is 31.7% in Jeon-Nam area and 26.64% in Kyong-Nam area. PCs extracted by preceding procedure have characteristics as follows. The first PC relates to aggregate size of islands in case of both areas. The second PC relates to income per household, factors of agricultural production and factors of fisheries production in Jeon-Nam area, but in Kyong-Nam area it means distance from island and income per household. A classification of islands can be attained by plotting component scores of each island in graph used two PCs as axes and grouping similiar islands. 6 groups are formed in Jeon-Nam area and 5 groups in Kyong-Nam area. The result of this study in kyong-Nam area accords with prior result of study.

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