# Non-Gaussian Component Analysis with Log-Density Gradient Estimation

arXiv: https://arxiv.org/abs/1601.07665 · HTML: https://mlsanity.com/paper/1601.07665/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2016.

## Built on by (most cited first, 3 of 3)

- [Sum-of-squares lower bounds for Non-Gaussian Component Analysis](https://mlsanity.com/paper/2410.21426/) (2024)
- [Overparametrized linear dimensionality reductions: From projection pursuit to two-layer neural networks](https://mlsanity.com/paper/2206.06526/) (2022)
- [PTF Testing Lower Bounds for Non-Gaussian Component Analysis](https://mlsanity.com/paper/2511.19398/) (2025)

## Abstract (arXiv)

Non-Gaussian component analysis (NGCA) is aimed at identifying a linear subspace such that the projected data follows a non-Gaussian distribution. In this paper, we propose a novel NGCA algorithm based on log-density gradient estimation. Unlike existing methods, the proposed NGCA algorithm identifies the linear subspace by using the eigenvalue decomposition without any iterative procedures, and thus is computationally reasonable. Furthermore, through theoretical analysis, we prove that the identified subspace converges to the true subspace at the optimal parametric rate. Finally, the practical performance of the proposed algorithm is demonstrated on both artificial and benchmark datasets.