Providing prior knowledge about sources to guide source sep-aration is known to be useful in many audio applications. In this paper we present two tensor factorization models for mu-sical source separation where musical information is incorpo-rated by using the Generalized Coupled Tensor Factorization (GCTF) framework. The approach is an extension of Non-negative Matrix Factorization where more than one matrix or tensor object is simultaneously factorized. The first model uses a temporally aligned transcription of the mixture and in-corporates spectral knowledge via coupling. In contrast of using a temporally aligned transcription, the second model incorporates harmonic information by taking an approximate, incomplete, and not necessarily aligned transcription of the musical piece as input. We evaluate our models on piano and cello duets where the experiments show that instead of using a temporally aligned transcription, we can achieve competitive results by using only a partial and incomplete transcription.

Many kinds of non-negative data, such as power spectra and count data, have been modeled using non-negative matrix factorization. Even though this modeling paradigm has yielded successful applications, it falls short when the data have certain hierarchical and temporal structure. In this study, we propose a novel dynamical system model that can handle these kinds of complex structures that often arise in non-negative data. We show that our model can be extended to handle heterogeneous data for data-driven regularization. We present convergence-guaranteed update rules for each latent factor. In order to assess the performance, we evaluate our model on the transcription of classical piano pieces, and show that it outperforms related models. We also illustrate that the performance can be further improved by making use of symbolic data.

Scalable audio separation with light kernel additive modelling

Abstract: This survey is about Tensor Factorization methods for audio modeling, which focuses on probabilistic latent tensor factorization and generalized coupled tensor factorization by expectation maximization method while using several linear and nonlinear distance measure methods.

In this study, we derive algorithms for estimating mixed β-divergences. Such cost functions are useful for Nonnegative Matrix and Tensor Factorization models with a compound Poisson observation model. Compound Poisson is a particular Tweedie model, an important special case of exponential dispersion models characterized by the fact that the variance is proportional to a power function of the mean. There are several well known matrix and tensor factorization algorithms that minimize the β-divergence; these estimate the mean parameter. The probabilistic interpretation gives us more flexibility and robustness by providing us additional tunable parameters such as power and dispersion. Estimation of the power parameter is useful for choosing a suitable divergence and estimation of dispersion is useful for data driven regularization and weighting in collective/coupled factorization of heterogeneous datasets. We present three inference algorithms for both estimating the factors and the additional parameters of the compound Poisson distribution. The methods are evaluated on two applications: modeling symbolic representations for polyphonic music and lyric prediction from audio features. Our conclusion is that the compound poisson based factorization models can be useful for sparse positive data. Proceedings of the 30 th