Many classes of data are composed as purely additive combinations of latent parts that do not result in subtraction or diminishment of the parts. Compositional models such as non-negative matrix factorization can effectively learn these latent structures of the data. Even though such models most naturally applies to non-signal data such as counts of populations, they can be employed to explain other forms of data as well. On signal processing, these models can be used to give more interpretable representations than what is obtained with many established signal processing methods. Therefore, during the last few years such models have provided new paradigms to solve old standing signal processing problems, e.g. source separation and robust pattern recognition. For example in the field of audio processing where we often deal with mixtures of sounds, the models have been used as parts of processing systems to advance the state of the art on many problems, for example on the analysis of polyphonic music and recognition of noisy speech. In this presentation we show how compositional models can be powerful tools for signal processing, providing highly interpretable representations, and enabling diverse applications such as signal analysis, recognition, manipulation, and enhancement. We will use several examples from the field of audio processing to demonstrate the effectiveness of the models.
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