A large margin algorithm for speech-to-phoneme and music-to-score alignment

We describe and analyze a discriminative algorithm for learning to align an audio signal with a given sequence of events that tag the signal. We demonstrate the applicability of our method for the tasks of speech-to-phoneme alignment ("forced alignment") and music-to-score alignment. In the first alignment task, the events that tag the speech signal are phonemes while in the music alignment task, the events are musical notes. Our goal is to learn an alignment function whose input is an audio signal along with its accompanying event sequence and its output is a timing sequence representing the actual start time of each event in the audio signal. Generalizing the notion of separation with a margin used in support vector machines for binary classification, we cast the learning task as the problem of finding a vector in an abstract inner-product space. To do so, we devise a mapping of the input signal and the event sequence along with any possible timing sequence into an abstract vector space. Each possible timing sequence therefore corresponds to an instance vector and the predicted timing sequence is the one whose projection onto the learned prediction vector is maximal. We set the prediction vector to be the solution of a minimization problem with a large set of constraints. Each constraint enforces a gap between the projection of the correct target timing sequence and the projection of an alternative, incorrect, timing sequence onto the vector. Though the number of constraints is very large, we describe a simple iterative algorithm for efficiently learning the vector and analyze the formal properties of the resulting learning algorithm. We report experimental results comparing the proposed algorithm to previous studies on speech-to-phoneme and music-to-score alignment, which use hidden Markov models. The results obtained in our experiments using the discriminative alignment algorithm are comparable to results of state-of-the-art systems.