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 mea
sure 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.
We find the general conditions for viable cosmological solution at the background level in bigravity models. Furthermore, we constrain the parameters by comparing to the Union 2.1 supernovae catalog and identify, in some cases analytically, the best
fit parameter or the degeneracy curve among pairs of parameters. We point out that a bimetric model with a single free parameter predicts a simple relation between the equation of state and the density parameter, fits well the supernovae data and is a valid and testable alternative to $Lambda$CDM. Additionally, we identify the conditions for a phantom behavior and show that viable bimetric cosmologies cannot cross the phantom divide.
