Grégory Nuel

Dorian Cazau, Yuancheng Wang, Olivier Adam et al.

Many methods for automatic music transcription involves a multi-pitch estimation method that estimates an activity score for each pitch. A second processing step, called note segmentation, has to be performed for each pitch in order to identify the time intervals when the notes are played. In this study, a pitch-wise two-state on/off firstorder Hidden Markov Model (HMM) is developed for note segmentation. A complete parametrization of the HMM sigmoid function is proposed, based on its original regression formulation, including a parameter alpha of slope smoothing and beta? of thresholding contrast. A comparative evaluation of different note segmentation strategies was performed, differentiated according to whether they use a fixed threshold, called "Hard Thresholding" (HT), or a HMM-based thresholding method, called "Soft Thresholding" (ST). This evaluation was done following MIREX standards and using the MAPS dataset. Also, different transcription scenarios and recording natures were tested using three units of the Degradation toolbox. Results show that note segmentation through a HMM soft thresholding with a data-based optimization of the {alpha,beta} parameter couple significantly enhances transcription performance.

D. Cazau, G. Nuel

Hidden Markov Models (HMMs) are a ubiquitous tool to model time series data, and have been widely used in two main tasks of Automatic Music Transcription (AMT): note segmentation, i.e. identifying the played notes after a multi-pitch estimation, and sequential post-processing, i.e. correcting note segmentation using training data. In this paper, we employ the multi-pitch estimation method called Probabilistic Latent Component Analysis (PLCA), and develop AMT systems by integrating different HMM-based modules in this framework. For note segmentation, we use two different twostate on/o? HMMs, including a higher-order one for duration modeling. For sequential post-processing, we focused on a musicological modeling of polyphonic harmonic transitions, using a first- and second-order HMMs whose states are defined through candidate note mixtures. These different PLCA plus HMM systems have been evaluated comparatively on two different instrument repertoires, namely the piano (using the MAPS database) and the marovany zither. Our results show that the use of HMMs could bring noticeable improvements to transcription results, depending on the instrument repertoire.

Vittorio Perduca, Gregory Nuel

We measure the influence of individual observations on the sequence of the hidden states of the Hidden Markov Model (HMM) by means of the Kullback-Leibler distance (KLD). Namely, we consider the KLD between the conditional distribution of the hidden states' chain given the complete sequence of observations and the conditional distribution of the hidden chain given all the observations but the one under consideration. We introduce a linear complexity algorithm for computing the influence of all the observations. As an illustration, we investigate the application of our algorithm to the problem of detecting outliers in HMM data series.