f-divergence is a generalized invariant measure between distributions
Yu Qiao, Nobuaki Minematsu · 2008
Finding measures (or features) invariant to inevitable variations caused by non-linguistical factors (transformations) is a funda-mental yet important problem in speech recognition. Recently, Minematsu [1, 2] proved that Bhattacharyya distance (BD) be-tween two distributions is invariant to invertible transforms on feature space, and develop an invariant structural representation of speech based on it. There is a question: which kind of mea-sures can be invariant? In this paper, we prove that f-divergence yields a generalized family of invariant measures, and show that all the invariant measures have to be written in the forms of f-divergence. Many famous distances and divergences in in-formation and statistics, such as Bhattacharyya distance (BD), KL-divergence, Hellinger distance, can be written into forms of f-divergence. As an application, we carried out experiments on recognizing the utterances of connected Japanese vowels. The experimental results show that BD and KL have the best perfor-mance among the measures compared. Index Terms: f-divergence, invariant measure, invertible transformation, speech recognition