Traditional Blind Source Separation Evaluation (BSS-Eval) metrics were originally designed to evaluate linear audio source separation models based on methods such as time-frequency masking. However, recent generative models may introduce nonlinear relationships between the separated and reference signals, limiting the reliability of these metrics for objective evaluation. To address this issue, we conduct a Degradation Category Rating listening test and analyze correlations between the obtained degradation mean opinion scores (DMOS) and a set of objective audio quality metrics for the task of singing voice separation. We evaluate three state-of-the-art discriminative models and two new competitive generative models. For both discriminative and generative models, intrusive embedding-based metrics show higher correlations with DMOS than conventional intrusive metrics such as BSS-Eval. For discriminative models, the highest correlation is achieved by the MSE computed on Music2Latent embeddings. When it comes to the evaluation of generative models, the strongest correlations are evident for the multi-resolution STFT loss and the MSE calculated on MERT-L12 embeddings, with the latter also providing the most balanced correlation across both model types. Our results highlight the limitations of BSS-Eval metrics for evaluating generative singing voice separation models and emphasize the need for careful selection and validation of alternative evaluation metrics for the task of singing voice separation.
Biosignals can be viewed as mixtures measuring particular physiological events, and blind source separation (BSS) aims to extract underlying source signals from mixtures. This paper proposes a self-supervised multi-encoder autoencoder (MEAE) to separate heartbeat-related source signals from photoplethysmogram (PPG), enhancing heart rate (HR) detection in noisy PPG data. The MEAE is trained on PPG signals from a large open polysomnography database without any pre-processing or data selection. The trained network is then applied to a noisy PPG dataset collected during the daily activities of nine subjects. The extracted heartbeat-related source signal significantly improves HR detection as compared to the original PPG. The absence of pre-processing and the self-supervised nature of the proposed method, combined with its strong performance, highlight the potential of MEAE for BSS in biosignal analysis.
Objective: Identifying the activity of motor neurons (MNs) non-invasively is possible by decomposing signals from muscles, e.g., surface electromyography (EMG) or ultrasound. The theoretical background of MN identification is convolutive blind source separation (cBSS), and different algorithms have been developed and validated. Yet, the existence and identifiability of inverse solutions and the corresponding estimation errors are not fully understood. Further, the guidelines for selecting appropriate parameters are often built on empirical observations, limiting the translation to clinical applications and other modalities. Approach: We revisited the cBSS model for MN identification, augmented it with new theoretical insights and derived a framework that can predict the existence of inverse solutions. This framework allows the quantification of estimation errors due to the imperfect inversion of the motor unit action potentials (MUAP), noise sources, and the ill-conditioning of the inverse problem. To bridge the gap between theory and practice, we used computer simulations. Main results: (1) Increasing the similarity of MUAPs or correlation between spike trains increases the bias for detecting high amplitude MUs. (2) The optimal objective function depends on the expected spike amplitude, spike amplitude statistics and the amplitude of background spikes. (3) There is some wiggle room for MN detection given non-stationary MUAPs. (4) There is no connection between MUAP duration and extension factor, in contrast to previous guidelines. (5) Source quality metrics like the silhouette score (SIL) or the pulse-to-noise ratio (PNR) are highly correlated with a source's objective function output. (6) SIL is superior to PNR. Significance: These findings will guide cBSS algorithm developments tailored to MN identification and clinical application translation.
Current generative models are able to generate high-quality artefacts but have been shown to struggle with compositional reasoning, which can be defined as the ability to generate complex structures from simpler elements. In this paper, we focus on the problem of compositional representation learning for music data, specifically targeting the fully-unsupervised setting. We propose a simple and extensible framework that leverages an explicit compositional inductive bias, defined by a flexible auto-encoding objective that can leverage any of the current state-of-art generative models. We demonstrate that our framework, used with diffusion models, naturally addresses the task of unsupervised audio source separation, showing that our model is able to perform high-quality separation. Our findings reveal that our proposal achieves comparable or superior performance with respect to other blind source separation methods and, furthermore, it even surpasses current state-of-art supervised baselines on signal-to-interference ratio metrics. Additionally, by learning an a-posteriori masking diffusion model in the space of composable representations, we achieve a system capable of seamlessly performing unsupervised source separation, unconditional generation, and variation generation. Finally, as our proposal works in the latent space of pre-trained neural audio codecs, it also provides a lower computational cost with respect to other neural baselines.
Topic models are useful tools for discovering latent semantic structures in large textual corpora. Recent efforts have been oriented at incorporating contextual representations in topic modeling and have been shown to outperform classical topic models. These approaches are typically slow, volatile, and require heavy preprocessing for optimal results. We present Semantic Signal Separation ($S^3$), a theory-driven topic modeling approach in neural embedding spaces. $S^3$ conceptualizes topics as independent axes of semantic space and uncovers these by decomposing contextualized document embeddings using Independent Component Analysis. Our approach provides diverse and highly coherent topics, requires no preprocessing, and is demonstrated to be the fastest contextual topic model, being, on average, 4.5x faster than the runner-up BERTopic. We offer an implementation of $S^3$, and all contextual baselines, in the Turftopic Python package.
The task of blind source separation (BSS) involves separating sources from a mixture without prior knowledge of the sources or the mixing system. Single-channel mixtures and non-linear mixtures are a particularly challenging problem in BSS. In this paper, we propose a novel method for addressing BSS with single-channel non-linear mixtures by leveraging the natural feature subspace specialization ability of multi-encoder autoencoders. During the training phase, our method unmixes the input into the separate encoding spaces of the multi-encoder network and then remixes these representations within the decoder for a reconstruction of the input. Then to perform source inference, we introduce a novel encoding masking technique whereby masking out all but one of the encodings enables the decoder to estimate a source signal. To this end, we also introduce a sparse mixing loss that encourages sparse remixing of source encodings throughout the decoder and a so-called zero reconstruction loss on the decoder for coherent source estimations. To analyze and evaluate our method, we conduct experiments on a toy dataset, designed to demonstrate this property of feature subspace specialization, and with real-world biosignal recordings from a polysomnography sleep study for extracting respiration from electrocardiogram and photoplethysmography signals.
The burgeoning growth of public domain data and the increasing complexity of deep learning model architectures have underscored the need for more efficient data representation and analysis techniques. This paper is motivated by the work of (Helal, 2023) and aims to present a comprehensive overview of tensorization. This transformative approach bridges the gap between the inherently multidimensional nature of data and the simplified 2-dimensional matrices commonly used in linear algebra-based machine learning algorithms. This paper explores the steps involved in tensorization, multidimensional data sources, various multiway analysis methods employed, and the benefits of these approaches. A small example of Blind Source Separation (BSS) is presented comparing 2-dimensional algorithms and a multiway algorithm in Python. Results indicate that multiway analysis is more expressive. Contrary to the intuition of the dimensionality curse, utilising multidimensional datasets in their native form and applying multiway analysis methods grounded in multilinear algebra reveal a profound capacity to capture intricate interrelationships among various dimensions while, surprisingly, reducing the number of model parameters and accelerating processing. A survey of the multi-away analysis methods and integration with various Deep Neural Networks models is presented using case studies in different application domains.
The dynamics of a power system with large penetration of renewable energy resources are becoming more nonlinear due to the intermittence of these resources and the switching of their power electronic devices. Therefore, it is crucial to accurately identify the dynamical modes of oscillation of such a power system when it is subject to disturbances to initiate appropriate preventive or corrective control actions. In this paper, we propose a high-order blind source identification (HOBI) algorithm based on the copula statistic to address these non-linear dynamics in modal analysis. The method combined with Hilbert transform (HOBI-HT) and iteration procedure (HOBMI) can identify all the modes as well as the model order from the observation signals obtained from the number of channels as low as one. We access the performance of the proposed method on numerical simulation signals and recorded data from a simulation of time domain analysis on the classical 11-Bus 4-Machine test system. Our simulation results outperform the state-of-the-art method in accuracy and effectiveness.
Guided source separation (GSS) is a type of target-speaker extraction method that relies on pre-computed speaker activities and blind source separation to perform front-end enhancement of overlapped speech signals. It was first proposed during the CHiME-5 challenge and provided significant improvements over the delay-and-sum beamforming baseline. Despite its strengths, however, the method has seen limited adoption for meeting transcription benchmarks primarily due to its high computation time. In this paper, we describe our improved implementation of GSS that leverages the power of modern GPU-based pipelines, including batched processing of frequencies and segments, to provide 300x speed-up over CPU-based inference. The improved inference time allows us to perform detailed ablation studies over several parameters of the GSS algorithm -- such as context duration, number of channels, and noise class, to name a few. We provide end-to-end reproducible pipelines for speaker-attributed transcription of popular meeting benchmarks: LibriCSS, AMI, and AliMeeting. Our code and recipes are publicly available: https://github.com/desh2608/gss.
Designing efficient and labor-saving prosthetic hands requires powerful hand gesture recognition algorithms that can achieve high accuracy with limited complexity and latency. In this context, the paper proposes a compact deep learning framework referred to as the CT-HGR, which employs a vision transformer network to conduct hand gesture recognition using highdensity sEMG (HD-sEMG) signals. The attention mechanism in the proposed model identifies similarities among different data segments with a greater capacity for parallel computations and addresses the memory limitation problems while dealing with inputs of large sequence lengths. CT-HGR can be trained from scratch without any need for transfer learning and can simultaneously extract both temporal and spatial features of HD-sEMG data. Additionally, the CT-HGR framework can perform instantaneous recognition using sEMG image spatially composed from HD-sEMG signals. A variant of the CT-HGR is also designed to incorporate microscopic neural drive information in the form of Motor Unit Spike Trains (MUSTs) extracted from HD-sEMG signals using Blind Source Separation (BSS). This variant is combined with its baseline version via a hybrid architecture to evaluate potentials of fusing macroscopic and microscopic neural drive information. The utilized HD-sEMG dataset involves 128 electrodes that collect the signals related to 65 isometric hand gestures of 20 subjects. The proposed CT-HGR framework is applied to 31.25, 62.5, 125, 250 ms window sizes of the above-mentioned dataset utilizing 32, 64, 128 electrode channels. The average accuracy over all the participants using 32 electrodes and a window size of 31.25 ms is 86.23%, which gradually increases till reaching 91.98% for 128 electrodes and a window size of 250 ms. The CT-HGR achieves accuracy of 89.13% for instantaneous recognition based on a single frame of HD-sEMG image.
Independent component analysis (ICA), is a blind source separation method that is becoming increasingly used to separate brain and non-brain related activities in electroencephalographic (EEG) and other electrophysiological recordings. It can be used to extract effective brain source activities and estimate their cortical source areas, and is commonly used in machine learning applications to classify EEG artifacts. Previously, we compared results of decomposing 13 71-channel scalp EEG datasets using 22 ICA and other blind source separation (BSS) algorithms. We are now making this framework available to the scientific community and, in the process of its release are testing a recent ICA algorithm (Picard) not included in the previous assay. Our test framework uses three main metrics to assess BSS performance: Pairwise Mutual Information (PMI) between scalp channel pairs; PMI remaining between component pairs after decomposition; and, the complete (not pairwise) Mutual Information Reduction (MIR) produced by each algorithm. We also measure the "dipolarity" of the scalp projection maps for the decomposed component, defined by the number of components whose scalp projection maps nearly match the projection of a single equivalent dipole. Within this framework, Picard performed similarly to Infomax ICA. This is not surprising since Picard is a type of Infomax algorithm that uses the L-BFGS method for faster convergence, in contrast to Infomax and Extended Infomax (runica) which use gradient descent. Our results show that Picard performs similarly to Infomax and, likewise, better than other BSS algorithms, excepting the more computationally complex AMICA. We have released the source code of our framework and the test data through GitHub.
Blind source separation (BSS) algorithms are unsupervised methods, which are the cornerstone of hyperspectral data analysis by allowing for physically meaningful data decompositions. BSS problems being ill-posed, the resolution requires efficient regularization schemes to better distinguish between the sources and yield interpretable solutions. For that purpose, we investigate a semi-supervised source separation approach in which we combine a projected alternating least-square algorithm with a learning-based regularization scheme. In this article, we focus on constraining the mixing matrix to belong to a learned manifold by making use of generative models. Altogether, we show that this allows for an innovative BSS algorithm, with improved accuracy, which provides physically interpretable solutions. The proposed method, coined sGMCA, is tested on realistic hyperspectral astrophysical data in challenging scenarios involving strong noise, highly correlated spectra and unbalanced sources. The results highlight the significant benefit of the learned prior to reduce the leakages between the sources, which allows an overall better disentanglement.
Extraction of latent sources of complex stimuli is critical for making sense of the world. While the brain solves this blind source separation (BSS) problem continuously, its algorithms remain unknown. Previous work on biologically-plausible BSS algorithms assumed that observed signals are linear mixtures of statistically independent or uncorrelated sources, limiting the domain of applicability of these algorithms. To overcome this limitation, we propose novel biologically-plausible neural networks for the blind separation of potentially dependent/correlated sources. Differing from previous work, we assume some general geometric, not statistical, conditions on the source vectors allowing separation of potentially dependent/correlated sources. Concretely, we assume that the source vectors are sufficiently scattered in their domains which can be described by certain polytopes. Then, we consider recovery of these sources by the Det-Max criterion, which maximizes the determinant of the output correlation matrix to enforce a similar spread for the source estimates. Starting from this normative principle, and using a weighted similarity matching approach that enables arbitrary linear transformations adaptable by local learning rules, we derive two-layer biologically-plausible neural network algorithms that can separate mixtures into sources coming from a variety of source domains. We demonstrate that our algorithms outperform other biologically-plausible BSS algorithms on correlated source separation problems.
The recently proposed semi-blind source separation (SBSS) method for nonlinear acoustic echo cancellation (NAEC) outperforms adaptive NAEC in attenuating the nonlinear acoustic echo. However, the multiplicative transfer function (MTF) approximation makes it unsuitable for real-time applications especially in highly reverberant environments, and the natural gradient makes it hard to balance well between fast convergence speed and stability. In this paper, we propose two more effective SBSS methods based on auxiliary-function-based independent vector analysis (AuxIVA) and independent low-rank matrix analysis (ILRMA). The convolutive transfer function (CTF) approximation is used instead of MTF so that a long impulse response can be modeled with a short latency. The optimization schemes used in AuxIVA and ILRMA are carefully regularized according to the constrained demixing matrix of NAEC. Experimental results validate significantly better echo cancellation performance of the proposed methods.
In natural auditory environments, acoustic signals originate from the temporal superimposition of different sound sources. The problem of inferring individual sources from ambiguous mixtures of sounds is known as blind source decomposition. Experiments on humans have demonstrated that the auditory system can identify sound sources as repeating patterns embedded in the acoustic input. Source repetition produces temporal regularities that can be detected and used for segregation. Specifically, listeners can identify sounds occurring more than once across different mixtures, but not sounds heard only in a single mixture. However, whether such a behaviour can be computationally modelled has not yet been explored. Here, we propose a biologically inspired computational model to perform blind source separation on sequences of mixtures of acoustic stimuli. Our method relies on a somatodendritic neuron model trained with a Hebbian-like learning rule which can detect spatio-temporal patterns recurring in synaptic inputs. We show that the segregation capabilities of our model are reminiscent of the features of human performance in a variety of experimental settings involving synthesized sounds with naturalistic properties. Furthermore, we extend the study to investigate the properties of segregation on task settings not yet explored with human subjects, namely natural sounds and images. Overall, our work suggests that somatodendritic neuron models offer a promising neuro-inspired learning strategy to account for the characteristics of the brain segregation capabilities as well as to make predictions on yet untested experimental settings.
Sparse Blind Source Separation (BSS) has become a well established tool for a wide range of applications - for instance, in astrophysics and remote sensing. Classical sparse BSS methods, such as the Proximal Alternating Linearized Minimization (PALM) algorithm, nevertheless often suffer from a difficult hyperparameter choice, which undermines their results. To bypass this pitfall, we propose in this work to build on the thriving field of algorithm unfolding/unrolling. Unrolling PALM enables to leverage the data-driven knowledge stemming from realistic simulations or ground-truth data by learning both PALM hyperparameters and variables. In contrast to most existing unrolled algorithms, which assume a fixed known dictionary during the training and testing phases, this article further emphasizes on the ability to deal with variable mixing matrices (a.k.a. dictionaries). The proposed Learned PALM (LPALM) algorithm thus enables to perform semi-blind source separation, which is key to increase the generalization of the learnt model in real-world applications. We illustrate the relevance of LPALM in astrophysical multispectral imaging: the algorithm not only needs up to $10^4-10^5$ times fewer iterations than PALM, but also improves the separation quality, while avoiding the cumbersome hyperparameter and initialization choice of PALM. We further show that LPALM outperforms other unrolled source separation methods in the semi-blind setting.
Single image reflection separation (SIRS), as a representative blind source separation task, aims to recover two layers, $\textit{i.e.}$, transmission and reflection, from one mixed observation, which is challenging due to the highly ill-posed nature. Existing deep learning based solutions typically restore the target layers individually, or with some concerns at the end of the output, barely taking into account the interaction across the two streams/branches. In order to utilize information more efficiently, this work presents a general yet simple interactive strategy, namely $\textit{your trash is my treasure}$ (YTMT), for constructing dual-stream decomposition networks. To be specific, we explicitly enforce the two streams to communicate with each other block-wisely. Inspired by the additive property between the two components, the interactive path can be easily built via transferring, instead of discarding, deactivated information by the ReLU rectifier from one stream to the other. Both ablation studies and experimental results on widely-used SIRS datasets are conducted to demonstrate the efficacy of YTMT, and reveal its superiority over other state-of-the-art alternatives. The implementation is quite simple and our code is publicly available at $\href{https://github.com/mingcv/YTMT-Strategy}{\textit{https://github.com/mingcv/YTMT-Strategy}}$.
This paper presents a novel system architecture that integrates blind source separation with joint beat and downbeat tracking in musical audio signals. The source separation module segregates the percussive and non-percussive components of the input signal, over which beat and downbeat tracking are performed separately and then the results are aggregated with a learnable fusion mechanism. This way, the system can adaptively determine how much the tracking result for an input signal should depend on the input's percussive or non-percussive components. Evaluation on four testing sets that feature different levels of presence of drum sounds shows that the new architecture consistently outperforms the widely-adopted baseline architecture that does not employ source separation.
Independent component analysis provides a principled framework for unsupervised representation learning, with solid theory on the identifiability of the latent code that generated the data, given only observations of mixtures thereof. Unfortunately, when the mixing is nonlinear, the model is provably nonidentifiable, since statistical independence alone does not sufficiently constrain the problem. Identifiability can be recovered in settings where additional, typically observed variables are included in the generative process. We investigate an alternative path and consider instead including assumptions reflecting the principle of independent causal mechanisms exploited in the field of causality. Specifically, our approach is motivated by thinking of each source as independently influencing the mixing process. This gives rise to a framework which we term independent mechanism analysis. We provide theoretical and empirical evidence that our approach circumvents a number of nonidentifiability issues arising in nonlinear blind source separation.
Time-domain audio separation network (TasNet) has achieved remarkable performance in blind source separation (BSS). Classic multi-channel speech processing framework employs signal estimation and beamforming. For example, Beam-TasNet links multi-channel convolutional TasNet (MC-Conv-TasNet) with minimum variance distortionless response (MVDR) beamforming, which leverages the strong modeling ability of data-driven network and boosts the performance of beamforming with an accurate estimation of speech statistics. Such integration can be viewed as a directed acyclic graph by accepting multi-channel input and generating multi-source output. In this paper, we design a "multi-channel input, multi-channel multi-source output" (MIMMO) speech separation system entitled "Beam-Guided TasNet", where MC-Conv-TasNet and MVDR can interact and promote each other more compactly under a directed cyclic flow. Specifically, the first stage uses Beam-TasNet to generate estimated single-speaker signals, which favors the separation in the second stage. The proposed framework facilitates iterative signal refinement with the guide of beamforming and seeks to reach the upper bound of the MVDR-based methods. Experimental results on the spatialized WSJ0-2MIX demonstrate that the Beam-Guided TasNet has achieved an SDR of 21.5 dB, exceeding the baseline Beam-TasNet by 4.1 dB under the same model size and narrowing the gap with the oracle signal-based MVDR to 2 dB.