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We apply the Non-negative Matrix Factorization (NMF) method to the problem of detecting industry clusters of a region. We follow the methods using Factor Analysis (FA) proposed by Bergman and others. We use the three Input-output tables of the two prefectures Yamaguchi-ken and Tottori-ken and the Chugoku area in Japan and prepare the production coefficient matrix and the linkage matrix from each of the IO tables. We apply NMF and FA to those two kinds of matrices to get clusters of the area and compare the results. We found that for the linkage matrices, NMF and FA produce very similar results and that for production coefficient matrices, they produce different results. We investigate the reasons for these similarities and differences and conclude that NMF and FA (and other methods) can complement each other and NMF can take advantage of its features if it is applied to raw data or simple coefficient matrices of IO tables.