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Note Clustering Based on 2-D Source-Filter Modeling for Underdetermined Blind Source Separation

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For blind source separation, the non-negative matrix factorization extracts single notes out of a mixture. These notes can be clustered to form the melodies played by a single instrument. A current approach for clustering utilizes a source filter model to describe the envelope over the first dimension of the spectrogram: the frequency-axis. The novelty of this paper is to extend this approach by a second source-filter model, characterizing the second dimension of a spectrogram: the time-axis. The latter one models the temporal evolution of the energy of one note: an instrument specific envelope is convolved with an activation vector, corresponding to tempo, rhythm, and amplitudes of single note instances. We introduce an unsupervised clustering framework for both models and a simple, yet effective combination strategy. Finally, we show the advantages of our separation algorithm compared with two other state-of-the-art separation frameworks: the separation quality is comparable, but our algorithm needs much less computational load, is independent from other BSS-algorithm as initialization, and works with a unique set of parameters for a wide range of audio data.

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