# Invertible Kernel PCA with Random Fourier Features

arXiv: https://arxiv.org/abs/2303.05043 · HTML: https://mlsanity.com/paper/2303.05043/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 25 references that are in the map.
- First posted on arXiv 9 Mar 2023.

## Builds on (most cited first, 2 of 2)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)

## Built on by (most cited first, 6 of 6)

- [Towards a Scalable Reference-Free Evaluation of Generative Models](https://mlsanity.com/paper/2407.02961/) (2024)
- [Towards an Explainable Comparison and Alignment of Feature Embeddings](https://mlsanity.com/paper/2506.06231/) (2025)
- [KODA: Contrastive Representation Comparison and Alignment for Vision-Language Foundation Models](https://mlsanity.com/paper/2606.04180/) (2026)
- [Coupled Flow Matching](https://mlsanity.com/paper/2510.23015/) (2025)
- [A Metric-based Principal Curve Approach for Learning One-dimensional Manifold](https://mlsanity.com/paper/2405.12390/) (2024)
- [Factor Decorrelation Enhanced Data Removal from Deep Predictive Models](https://mlsanity.com/paper/2509.23443/) (2025)

## Abstract (arXiv)

Kernel principal component analysis (kPCA) is a widely studied method to construct a low-dimensional data representation after a nonlinear transformation. The prevailing method to reconstruct the original input signal from kPCA -- an important task for denoising -- requires us to solve a supervised learning problem. In this paper, we present an alternative method where the reconstruction follows naturally from the compression step. We first approximate the kernel with random Fourier features. Then, we exploit the fact that the nonlinear transformation is invertible in a certain subdomain. Hence, the name invertible kernel PCA (ikPCA). We experiment with different data modalities and show that ikPCA performs similarly to kPCA with supervised reconstruction on denoising tasks, making it a strong alternative.