A Correspondence Analysis Framework for Author-Conference Recommendations
Table 1: Two-way contingency table classifying 5387 children in Caithness, Scotland, according to hair colour and eye colour [beh2004simple]
['[BOLD] Eye Colour', '[BOLD] Hair Colour Fair', '[BOLD] Hair Colour Red', '[BOLD] Hair Colour Medium', '[BOLD] Hair Colour Dark', '[BOLD] Hair Colour Black']
A contingency table is a type of table in a matrix format that displays the frequency distribution of the variables. A contingency table is usually associated with a grand total, the total number of entities represented in the table, and marginal totals, which are the row sums and column sums. The most basic concept in CA is that of a profile, which is a set of frequencies divided by their total. For a given contingency table, we can have row and column profiles. Since the objective of finding low-dimensional best-fitting subspaces coincides with the objective of finding low-rank matrix approximations by least-squares, the SVD forms the backbone of CA. On a side note, CA is symmetrical in nature i.e. column analysis and row analysis yield the same results. where M∗=minI,J−1 is the maximum number of dimensions required to graphically depict the association between the row and column responses. However, for a simple interpretation of this association, generally only the first two dimensions are used to construct such a graphical summary. that \sfracχ2n=0.2302. So, the first axis explains \sfrac0.19920.2302=0.8656 of the total variation that exists in the table, while the second axis explains \sfrac0.03010.2302=0.1307 of this variation. So, we can safely ignore the 3rd component, i.e. corresponding to λ3 without much loss. This way, we are reducing the dimensions.