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...es an observation vector by finding an unmixing matrix , so that the estimated variables, i.e., the elements of vector are statistically independent from each other. The convolutive extension of ICA (=-=[15]-=-, pp. 361–370) suits well for multichannel sound source separation, where the elements of the observation vector are the signals recorded with different microphones. In ICA the number of sources has t...

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...s to be entry-wise nonnegative. Moreover, the components can be restricted to be purely additive, meaning that the gains are restricted to be nonnegative. The NMF algorithms proposed by Lee and Seung =-=[21]-=- do the decomposition by minimizing the reconstruction error between the observation matrix and the model while constraining the matrices to be entry-wise nonnegative. The algorithms have been used in...

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...y Hoyer [24] combines NMF and sparse coding. He estimated the matrices by combining the multiplicative update rule proposed by Lee and Seung [21] with projected gradient descent [discussed, e.g., in (=-=[25]-=-, pp. 203–224)]. The algorithm was used with a temporal continuity criterion for sound separation by Virtanen [10]. No large-scale evaluation has been carried out to investigate whether the use of a s...

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...better approximation of human auditory perception. 3) Sparse Coding: An unsupervised learning technique called sparse coding has been successfully used for example to model the early stages of vision =-=[22]-=-. The term sparse refers to a signal model, where the data is represented in terms of a small number of active elements chosen out of a larger set. In the signal model (1), this means that the probabi...

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...y Abdallah and Plumbley [9], [11], Benaroya, McDonagh, Bimbot, and Gribonval [23], and Blumensath and Davies [12], to mention a few examples. The nonnegative sparse coding algorithm proposed by Hoyer =-=[24]-=- combines NMF and sparse coding. He estimated the matrices by combining the multiplicative update rule proposed by Lee and Seung [21] with projected gradient descent [discussed, e.g., in ([25], pp. 20...

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...t 9.6 for an ISA algorithm, in which the time-domain signals of the sources were trained before mixing [4]. The term Source to Distortion Ratio has also been used to refer to this performance measure =-=[38]-=-. The SNR (in decibels) was averaged over all the sources and mixtures to get the total measure of the separation performance. If no components were assigned to a source, the source was defined to be ...

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...n where the sources are statistically independent or nonredundant. Algorithms have been proposed that are based on independent component analysis (ICA) [5]–[7], nonnegative matrix factorization (NMF) =-=[8]-=-, and sparse coding [9]–[11]. This paper proposes an unsupervised sound source separation algorithm which combines NMF with temporal continuity and sparseness objectives. The proposed algorithm is sho...

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...frequency line as a phase-invariant feature calculated in each frame. The factorization of the spectrogram can be seen as separation of phase-independent features into (2) invariant feature subspaces =-=[16]-=-. Letting the magnitude or power spectrum in frame to be the observation, the separation can be done using basic ICA, as explained above. With this procedure the estimated gains of different component...

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...nt within frames is calculated as . To get complex spectra, the phases of the original spectrogram can be used for the separated components, or the phase generation method proposed by Griffin and Lim =-=[31]-=- with the improvements proposed by Slaney, Naar, and Lyon [32] can be used. In most cases where the separation is successful, the use of the original phases produces good results. It also allows the s...

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...get signals has to be restricted. The most successful algorithms have been those which try to extract only the most prominent source [1], [2], or which utilize prior information of the source signals =-=[3]-=-, [4]. Recently, unsupervised machine learning algorithms have been successfully used in one-channel source separation. These are typically based on a simple linear model, and instead of using prior k...

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...ited separation quality, and usually the complexity of the target signals has to be restricted. The most successful algorithms have been those which try to extract only the most prominent source [1], =-=[2]-=-, or which utilize prior information of the source signals [3], [4]. Recently, unsupervised machine learning algorithms have been successfully used in one-channel source separation. These are typicall...

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...the separation is done by finding a decomposition where the sources are statistically independent or nonredundant. Algorithms have been proposed that are based on independent component analysis (ICA) =-=[5]-=-–[7], nonnegative matrix factorization (NMF) [8], and sparse coding [9]–[11]. This paper proposes an unsupervised sound source separation algorithm which combines NMF with temporal continuity and spar...

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... proposed by Lee and Seung [21] with projected gradient descent [discussed, e.g., in ([25], pp. 203–224)]. The algorithm was used with a temporal continuity criterion for sound separation by Virtanen =-=[10]-=-. No large-scale evaluation has been carried out to investigate whether the use of a sparse prior increases the separation quality in the case of audio signals. The spectra which typically constitute ...

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...lustering methods have been proposed [5], [6], but in our simulations their performance was not sufficient. Supervised clustering based on pattern recognition techniques produces better results [27], =-=[28]-=-, but these require that the sources are known and their models trained beforehand. In this paper, we do not consider the clustering problem but circumvent this step by using the original signals as a...

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...tistically independent or nonredundant. Algorithms have been proposed that are based on independent component analysis (ICA) [5]–[7], nonnegative matrix factorization (NMF) [8], and sparse coding [9]–=-=[11]-=-. This paper proposes an unsupervised sound source separation algorithm which combines NMF with temporal continuity and sparseness objectives. The proposed algorithm is shown to provide a better separ...

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...FitzGerald, Coyle, and Lawlor [18], Uhle, Dittmar, and Sporer [19], and Brown and Smaragdis [7]. Also, a sound recognition system based on ISA has been adopted in the MPEG-7 standardization framework =-=[20]-=-. 2) Nonnegative Matrix Factorization: In addition to statistical independence, some other estimation principles have also been found useful in finding the decomposition . Each component is modeled us...

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...independent from each other. ISA has been used in one-channel sound source separation, for example, by Casey and Westner [5], Orife [17], FitzGerald, Coyle, and Lawlor [18], Uhle, Dittmar, and Sporer =-=[19]-=-, and Brown and Smaragdis [7]. Also, a sound recognition system based on ISA has been adopted in the MPEG-7 standardization framework [20]. 2) Nonnegative Matrix Factorization: In addition to statisti...

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...ignals has to be restricted. The most successful algorithms have been those which try to extract only the most prominent source [1], [2], or which utilize prior information of the source signals [3], =-=[4]-=-. Recently, unsupervised machine learning algorithms have been successfully used in one-channel source separation. These are typically based on a simple linear model, and instead of using prior knowle...

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... following sections, we briefly review some commonly used separation principles. The model (1) can be extended to allow time-varying components; some proposals have been made by Blumensath and Davies =-=[12]-=-, Smaragdis [13], and Virtanen [14]. More complex models can potentially enable better separation quality, but in this paper we compare only methods which are based on the linear model (1). 1) Indepen...

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...iew some commonly used separation principles. The model (1) can be extended to allow time-varying components; some proposals have been made by Blumensath and Davies [12], Smaragdis [13], and Virtanen =-=[14]-=-. More complex models can potentially enable better separation quality, but in this paper we compare only methods which are based on the linear model (1). 1) Independent Subspace Analysis (ICA): ICA h...

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...onstruction error term and a term which penalizes nonzero gains . Sparse coding has been used for audio signal separation by Abdallah and Plumbley [9], [11], Benaroya, McDonagh, Bimbot, and Gribonval =-=[23]-=-, and Blumensath and Davies [12], to mention a few examples. The nonnegative sparse coding algorithm proposed by Hoyer [24] combines NMF and sparse coding. He estimated the matrices by combining the m...

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...e phases of the original spectrogram can be used for the separated components, or the phase generation method proposed by Griffin and Lim [31] with the improvements proposed by Slaney, Naar, and Lyon =-=[32]-=- can be used. In most cases where the separation is successful, the use of the original phases produces good results. It also allows the synthesis of sharp attacks with an accuracy which would otherwi...

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...nt components are statistically independent from each other. ISA has been used in one-channel sound source separation, for example, by Casey and Westner [5], Orife [17], FitzGerald, Coyle, and Lawlor =-=[18]-=-, Uhle, Dittmar, and Sporer [19], and Brown and Smaragdis [7]. Also, a sound recognition system based on ISA has been adopted in the MPEG-7 standardization framework [20]. 2) Nonnegative Matrix Factor...

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...ons, we briefly review some commonly used separation principles. The model (1) can be extended to allow time-varying components; some proposals have been made by Blumensath and Davies [12], Smaragdis =-=[13]-=-, and Virtanen [14]. More complex models can potentially enable better separation quality, but in this paper we compare only methods which are based on the linear model (1). 1) Independent Subspace An...

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...ised clustering methods have been proposed [5], [6], but in our simulations their performance was not sufficient. Supervised clustering based on pattern recognition techniques produces better results =-=[27]-=-, [28], but these require that the sources are known and their models trained beforehand. In this paper, we do not consider the clustering problem but circumvent this step by using the original signal...

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...the separation can be directed towards the spectrograms A and B. Temporal continuity was addressed in a system proposed Vincent and Rodet who modeled the activity of a source by a hidden Markov model =-=[30]-=-. In this paper, we apply a simple temporal continuity criterion which does not require training beforehand. Temporal continuity of the components is measured by assigning a cost to large changes betw...

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...age SNR. D. Results The average SNRs and detection error rates are shown in Table II. The averages are shown for all sources, and separately for pitched and drum sounds. The 95% confidence intervals (=-=[39]-=-, pp. 212–219) for the average detection error rate and the SNR were smaller than 1% and 1 dB, respectively, for all the algorithms, which means that the differences between the algorithms are statist...

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...separation is done by finding a decomposition where the sources are statistically independent or nonredundant. Algorithms have been proposed that are based on independent component analysis (ICA) [5]–=-=[7]-=-, nonnegative matrix factorization (NMF) [8], and sparse coding [9]–[11]. This paper proposes an unsupervised sound source separation algorithm which combines NMF with temporal continuity and sparsene...

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... statistically independent or nonredundant. Algorithms have been proposed that are based on independent component analysis (ICA) [5]–[7], nonnegative matrix factorization (NMF) [8], and sparse coding =-=[9]-=-–[11]. This paper proposes an unsupervised sound source separation algorithm which combines NMF with temporal continuity and sparseness objectives. The proposed algorithm is shown to provide a better ...

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...terms, respectively. A. Reconstruction Error Term The human auditory system has a wide dynamic range: the difference between the threshold of hearing and the threshold of pain is approximately 100 dB =-=[29]-=-. Unsupervised learning algorithms tend to be more sensitive to high-energy observations, and some methods fail to separate low-energy sources even though these are perceptually and musically meaningf...

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...edure the estimated gains of different components are statistically independent from each other. ISA has been used in one-channel sound source separation, for example, by Casey and Westner [5], Orife =-=[17]-=-, FitzGerald, Coyle, and Lawlor [18], Uhle, Dittmar, and Sporer [19], and Brown and Smaragdis [7]. Also, a sound recognition system based on ISA has been adopted in the MPEG-7 standardization framewor...

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...mponents are used which are then clustered to sound sources. Automatic clustering of the components has turned out to be a difficult task. Some unsupervised clustering methods have been proposed [5], =-=[6]-=-, but in our simulations their performance was not sufficient. Supervised clustering based on pattern recognition techniques produces better results [27], [28], but these require that the sources are ...

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...a limited separation quality, and usually the complexity of the target signals has to be restricted. The most successful algorithms have been those which try to extract only the most prominent source =-=[1]-=-, [2], or which utilize prior information of the source signals [3], [4]. Recently, unsupervised machine learning algorithms have been successfully used in one-channel source separation. These are typ...