Correspondence Analysis

Notations

Matrices are denoted with uppercase letters typeset in a boldface font; for example, X is a matrix. The elements of a matrix are denoted with a lowercase italic letter matching the matrix name, with indices indicating the row and column positions of the element; for example, xi;j is the element located at the ith row and jth column of matrix X. Vectors are denoted with lowercase, boldface letters; for example, c is a vector. The elements of a vector are denoted with a lowercase italic letter matching the vector name and an index indicating the position [Page 268]of the element in the vector; for example ci is the ith element of c. The italicized superscriptT indicates that the matrix or vector is transposed.

An Example: How Writers Punctuate

This example comes from E. Brunet, who analyzed the way punctuation marks were used by six French writers: Rousseau, Chateaubriand, Hugo, Zola, Proust, and Giraudoux. In the paper, Brunet gave a table indicating the number of times each of these writers used the period, the comma, and all the other marks (i.e., question mark, exclamation point, colon, and semicolon) grouped together. These data are reproduced in Table 1.

From these data we can build the original data matrix, which is denoted X. It has I = 6 rows and J = 3 columns and is equal to

In the matrix X, the rows represent the authors and the columns represent types of punctuation marks. At the intersection of a row and a column, we find the number of a given punctuation mark (represented by the column) used by a given author (represented by the row).

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