  Correlation and similarity measures are widely used in all the areas of
sciences and social sciences. Often the variables are not numbers but are
instead qualitative descriptors called categorical data. We define and study
similarity matrix, as a measure of similarity, for the case of categorical
data. This is of interest due to a deluge of categorical data, such as movie
ratings, top-10 rankings and data from social media, in the public domain that
require analysis. We show that the statistical properties of the spectra of
similarity matrices, constructed from categorical data, follow those from
random matrix theory. We demonstrate this approach by applying it to the data
of Indian general elections and sea level pressures in North Atlantic ocean.
