## Sound Source Separation using Shifted Non-negative Tensor Factorisation (2006)

Venue: | Proceedings on the IEE Conference on Audio and Speech Signal Processing (ICASSP |

Citations: | 14 - 0 self |

### BibTeX

@INPROCEEDINGS{Fitzgerald06soundsource,

author = {Derry Fitzgerald and Matt Cranitch},

title = {Sound Source Separation using Shifted Non-negative Tensor Factorisation},

booktitle = {Proceedings on the IEE Conference on Audio and Speech Signal Processing (ICASSP},

year = {2006}

}

### OpenURL

### Abstract

Recently, shifted Non-negative Matrix Factorisation was developed as a means of separating harmonic instruments from single channel mixtures. However, in many cases two or more channels are available, in which case it would be advantageous to have a multichannel version of the algorithm. To this end, a shifted Non-negative Tensor Factorisation algorithm is derived, which extends shifted Non-negative Matrix Factorisation to the multi-channel case. The use of this algorithm for multi-channel sound source separation of harmonic instruments is demonstrated. Further, it is shown that the algorithm can be used to perform Non-negative Tensor Deconvolution, a multi-channel version of Non-negative Matrix Deconvolution, to separate sound sources which have time evolving spectra from multi-channel signals. 1.

### Citations

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(Show Context)
Citation Context ...2} where S is a size k x r x m tensor containing the time envelopes associated with each translation of each source. For the decomposition described above, the cost function proposed by Lee and Seung =-=[11]-=-, called the generalised Kullback-Liebler divergence, was used: D(X� ˆX) = � ij � X(i, j) X(i, j)log ˆX(i, j) − X(i, j) + � ˆX(i, j) From this, update equations for A and S were derived, and the algor... |

164 | Non-negative matrix factorization for polyphonic music transcription
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(Show Context)
Citation Context ...ed as means of attempting single channel sound source separation. These methods include the use of Independent Subspace Analysis (ISA), Sparse Coding (SC), and Non megative Matrix Factorisation (NMF) =-=[1, 2, 3]-=-. These techniques attempt to factorise a magnitude spectrogram X into matrix factors A and S such that X ≈ AS, where X is an n x m spectrogram, where n is the number of frequency bins, and m is the n... |

121 |
Calculation of a constant Q spectral transform
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- 1991
(Show Context)
Citation Context ...m of any note played on the instrument in question. Using this assumption requires that the chosen time-frequency representation has logarithmic frequency resolution, such as the Constant Q transform =-=[8]-=-. If the center frequencies in the representation are set so that fi = fi−12 1/12 , where fi is the center frequency of band i, then the spacing between center frequencies will match that of the even-... |

103 |
Separation of Mixed Audio Sources By Independent Subspace Analysis
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(Show Context)
Citation Context ...ed as means of attempting single channel sound source separation. These methods include the use of Independent Subspace Analysis (ISA), Sparse Coding (SC), and Non megative Matrix Factorisation (NMF) =-=[1, 2, 3]-=-. These techniques attempt to factorise a magnitude spectrogram X into matrix factors A and S such that X ≈ AS, where X is an n x m spectrogram, where n is the number of frequency bins, and m is the n... |

48 |
Sound source separation using sparse coding with temporal continuity objective
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(Show Context)
Citation Context ...ed as means of attempting single channel sound source separation. These methods include the use of Independent Subspace Analysis (ISA), Sparse Coding (SC), and Non megative Matrix Factorisation (NMF) =-=[1, 2, 3]-=-. These techniques attempt to factorise a magnitude spectrogram X into matrix factors A and S such that X ≈ AS, where X is an n x m spectrogram, where n is the number of frequency bins, and m is the n... |

37 | Separation of sound sources by convolutive sparse coding
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(Show Context)
Citation Context ...trol Engineering Dublin Institute of Technology Kevin Street, Dublin, Ireland eugene.coyle@dit.ie over time. In an attempt to overcome this problem, convolutive forms of SC and NMF have been proposed =-=[4, 5]-=-. Both of these methods attempt to describe a source as a sequence of successive spectra and a corresponding amplitude envelope across time. Another shortcoming in the standard factorisation technique... |

30 | Matlab tensor classes for fast algorithm prototyping
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- 2006
(Show Context)
Citation Context .... . . , iN, k1, . . . , kP ) Using this notation, the modes to be multiplied are specified in the subscripts that follow the angle brackets, in line with the conventions adapted by Bader and Kolda in =-=[10]-=-. Outer product multiplication is denoted by ◦, ./ denotes elementwise division and .∗ denotes elementwise multiplication. Translation is carried out by means of a translation matrix. For an n x 1 vec... |

26 | Discovering auditory objects through nonnegativity constraints
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(Show Context)
Citation Context ...trol Engineering Dublin Institute of Technology Kevin Street, Dublin, Ireland eugene.coyle@dit.ie over time. In an attempt to overcome this problem, convolutive forms of SC and NMF have been proposed =-=[4, 5]-=-. Both of these methods attempt to describe a source as a sequence of successive spectra and a corresponding amplitude envelope across time. Another shortcoming in the standard factorisation technique... |

19 |
Automatic Drum Transcription and Source Separation”, Ph.D Thesis presented to the Dublin Institute of Technology
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(Show Context)
Citation Context ...is required. Methods for clustering basis function have been proposed by Casey and Virtanen [1, 2]. However, it is difficult to obtain a correct clustering in many situations for reasons discussed in =-=[6]-=-. As a result of this, shifted Non-Negative Matrix Factorisation has recently been proposed to deal with the situation where different notes from the same instrument occur over the course of a spectro... |

8 |
Shifted Non-negative Matrix Factorisation for Sound Source Separation
- FitzGerald, Cranitch, et al.
- 2005
(Show Context)
Citation Context ...a result of this, shifted Non-Negative Matrix Factorisation has recently been proposed to deal with the situation where different notes from the same instrument occur over the course of a spectrogram =-=[7]-=-. Shifted Non-Negative Matrix Factorisation assumes that the notes belonging to a single source consist of translated versions of a single frequency basis function which represents the typical frequen... |

3 |
Essential Psychology
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(Show Context)
Citation Context ...cies in the representation are set so that fi = fi−12 1/12 , where fi is the center frequency of band i, then the spacing between center frequencies will match that of the even-tempered tuning system =-=[9]-=-. As a result, translating a frequency basis function of a note up by one bin is equivalent to a pitch change of one semitone. For the remainder of this paper the following conventions are used. Index... |

3 |
Matlab tensor classes
- Kolda, Bader
(Show Context)
Citation Context ...used for NMF (see [11]) no longer apply, in practice it has been observed that the algorithm converges reliably. The algorithm was implemented in Matlab using the Matlab Tensor Classes available from =-=[12]-=-. Fig. 1 shows the original waveforms of flute,viola and piano respectively, while Fig 2 shows a two-channel mixture of these sources. Fig 3 shows the separated waveforms obtained with the number of i... |