# Robust Non-Linear Matrix Factorization for Dictionary Learning, Denoising, and Clustering

arXiv: https://arxiv.org/abs/2005.01317 · HTML: https://mlsanity.com/paper/2005.01317/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2020.

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

- [Constructing Indoor Region-based Radio Map without Location Labels](https://mlsanity.com/paper/2308.16759/) (2023)
- [Coarse to Fine Two-Stage Approach to Robust Tensor Completion of Visual Data](https://mlsanity.com/paper/2106.10422/) (2021)
- [Low-Rank Matrix Approximation for Neural Network Compression](https://mlsanity.com/paper/2504.20078/) (2025)
- [Nonlinear matrix recovery using optimization on the Grassmann manifold](https://mlsanity.com/paper/2109.06095/) (2021)
- [Deep Dictionary Learning with An Intra-class Constraint](https://mlsanity.com/paper/2207.06841/) (2022)

## Abstract (arXiv)

Low dimensional nonlinear structure abounds in datasets across computer vision and machine learning. Kernelized matrix factorization techniques have recently been proposed to learn these nonlinear structures for denoising, classification, dictionary learning, and missing data imputation, by observing that the image of the matrix in a sufficiently large feature space is low-rank. However, these nonlinear methods fail in the presence of sparse noise or outliers. In this work, we propose a new robust nonlinear factorization method called Robust Non-Linear Matrix Factorization (RNLMF). RNLMF constructs a dictionary for the data space by factoring a kernelized feature space; a noisy matrix can then be decomposed as the sum of a sparse noise matrix and a clean data matrix that lies in a low dimensional nonlinear manifold. RNLMF is robust to sparse noise and outliers and scales to matrices with thousands of rows and columns. Empirically, RNLMF achieves noticeable improvements over baseline methods in denoising and clustering.