The covariance matrix formed from differences between comparable documents is the noise covariance in OPCA: we wish to minimize the latter covariance, to make the projection languageindependent.
we create the weighted documentterm matrix D m for each language: We then derive a signal covariance matrix over all languages: where µ m is the mean of each D m over its columns, and a noise covariance matrix, where D is the mean across all languages of the document-term matrix, and M is the number of languages.