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Toward a General Framework for Polyphonic Comparison

Allali J., Ferraro P., Hanna P., Iliopoulos C.

Fundamenta Informaticae

2009

Vol. 97, nr 3

331-346

Existing symbolic music comparison systems generally consider monophonic music or monophonic reduction of polyphonic music. Adaptation of alignment algorithms to music leads to accurate systems, but their extensions to polyphonic music raise new problems. Indeed, a chord may match several consecutive notes, or the difference between two similar motifs may be a few swapped notes. Moreover, the substitution scores between chords are difficult to set up. In this paper, we propose a general framework for polyphonic music using the substitution score scheme set for monophonic music, which allows new operations by extending the operations proposed by Mongeau and Sankoff [15]. From a practical point of view, the limitation of chord sizes and the number of notes that can be merged consecutively lead to a complexity that remains quadratic.

On adaptive estimation based on ranks in ARMA processes

Allali J., Kaaouachi A., Melhaoui S.

Probability and Mathematical Statistics

2002

Vol. 22, Fasc. 2

293--302

This paper describes the adaptive estimation problem based on ranks for the parameter of an ARMA process. The local asymptotic normality property with a ranked based central sequence allows for the construction of estimators which are locally asymptotically minimax (LAM). By using a consistent estimate of the score function, we obtain the adaptive estimators which are LAM and which do not depend on the innovation density.