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Data Analysis Machine Learning and Applications Episode 1 Part 9

Tham khảo tài liệu 'data analysis machine learning and applications episode 1 part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Factorial Analysis of a Set of Contingency Tables 221 As a result SA proceeds by performing a principal component analysis PCA of the matrix X X ỰÕĨX1 . V X . ỰÕTXT The PCA results are also obtained using the SVD of X giving singular values sfks on the s-th dimension and corresponding left and right singular vectors us and Vs. We calculate projections on the s-th axis of the columns as principal coordinates gs gs hsD-1 2 vs where Dc J X J is a diagonal matrix of all the column masses that is all the Dzc. One of the aims of the joint analysis of several data tables is to compare them through the points corresponding to the same row in the different tables. These points will be called partial rows and denoted by Ĩ. The projection on the s-th axis of each partial row is denoted by ft and the vector of projections of all the partial rows for table t is denoted by fs f Dr -1 2 0 . yffiX . 0 Vs Especially when the number of tables is large comparison of partial rows is complicated. Therefore each partial row will be compared with the overall row projected as fs Dw -1 ựõĩX1 . y ãỊX . ựõỹX7 vs Dw -1 X vs where Dw is the diagonal matrix whose general term is 52t eT a P . The choice of this matrix Dw allows us to expand the projections of the overall rows to keep them inside the corresponding set of projections of partial rows and is appropriate when the partial rows have different weights in the tables. With this weighting the projections of the overall and partial rows are related as follows fis teT V fts XteTV pi. So the projection of a row is a weighted average of the projections of partial rows. It is closer to those partial rows that are more similar to the overall row in terms of the relation expressed by the axis and have a greater weight than the rest of the partial rows. The dispersal of the projections of the partial rows with regard to the projection of their overall row indicates discrepancies between the same row in the different tables. Notice that if pt is .