# Acoustic Space Learning for Sound Source Separation and Localization on Binaural Manifolds

arXiv: https://arxiv.org/abs/1402.2683 · HTML: https://mlsanity.com/paper/1402.2683/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2014.

## Built on by (most cited first, 5 of 5)

- [PILOT: Introducing Transformers for Probabilistic Sound Event Localization](https://mlsanity.com/paper/2106.03903/) (2021)
- [SofaMyRoom: a fast and multiplatform "shoebox" room simulator for binaural room impulse response dataset generation](https://mlsanity.com/paper/2106.12992/) (2021)
- [A Review on Sound Source Localization in Robotics: Focusing on Deep Learning Methods](https://mlsanity.com/paper/2507.01143/) (2025)
- [Unsupervised Acoustic Scene Mapping Based on Acoustic Features and Dimensionality Reduction](https://mlsanity.com/paper/2301.00448/) (2023)
- [Gaussian Process Regression of Steering Vectors With Physics-Aware Deep Composite Kernels for Augmented Listening](https://mlsanity.com/paper/2509.02571/) (2025)

## Abstract (arXiv)

In this paper we address the problems of modeling the acoustic space generated by a full-spectrum sound source and of using the learned model for the localization and separation of multiple sources that simultaneously emit sparse-spectrum sounds. We lay theoretical and methodological grounds in order to introduce the binaural manifold paradigm. We perform an in-depth study of the latent low-dimensional structure of the high-dimensional interaural spectral data, based on a corpus recorded with a human-like audiomotor robot head. A non-linear dimensionality reduction technique is used to show that these data lie on a two-dimensional (2D) smooth manifold parameterized by the motor states of the listener, or equivalently, the sound source directions. We propose a probabilistic piecewise affine mapping model (PPAM) specifically designed to deal with high-dimensional data exhibiting an intrinsic piecewise linear structure. We derive a closed-form expectation-maximization (EM) procedure for estimating the model parameters, followed by Bayes inversion for obtaining the full posterior density function of a sound source direction. We extend this solution to deal with missing data and redundancy in real world spectrograms, and hence for 2D localization of natural sound sources such as speech. We further generalize the model to the challenging case of multiple sound sources and we propose a variational EM framework. The associated algorithm, referred to as variational EM for source separation and localization (VESSL) yields a Bayesian estimation of the 2D locations and time-frequency masks of all the sources. Comparisons of the proposed approach with several existing methods reveal that the combination of acoustic-space learning with Bayesian inference enables our method to outperform state-of-the-art methods.