# Learning Nonlinear Mixtures: Identifiability and Algorithm

arXiv: https://arxiv.org/abs/1901.01568 · HTML: https://mlsanity.com/paper/1901.01568/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jan 2019.

## Built on by (most cited first, 2 of 2)

- [Identifiability-Guaranteed Simplex-Structured Post-Nonlinear Mixture Learning via Autoencoder](https://mlsanity.com/paper/2106.09070/) (2021)
- [Provable Subspace Identification Under Post-Nonlinear Mixtures](https://mlsanity.com/paper/2210.07532/) (2022)

## Abstract (arXiv)

Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is well-studied, under frameworks such as independent component analysis and constrained matrix factorization. Nevertheless, when the linear mixtures are distorted by an unknown nonlinear functions -- which is well-motivated and more realistic in many cases -- the identifiability issues are much less studied. This work proposes an identification criterion for a nonlinear mixture model that is well grounded in many real-world applications, and offers identifiability guarantees. A practical implementation based on a judiciously designed neural network is proposed to realize the criterion, and an effective learning algorithm is proposed. Numerical results on synthetic and real-data corroborate effectiveness of the proposed method.