# Connections Between Nuclear Norm and Frobenius Norm Based Representations

arXiv: https://arxiv.org/abs/1502.07423 · HTML: https://mlsanity.com/paper/1502.07423/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2015.

## Built on by (most cited first, 7 of 7)

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- [MAPLE: Self-Supervised Learning-Enhanced Nonlinear Dimensionality Reduction for Visual Analysis](https://mlsanity.com/paper/2601.20173/) (2026)
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## Abstract (arXiv)

A lot of works have shown that frobenius-norm based representation (FNR) is competitive to sparse representation and nuclear-norm based representation (NNR) in numerous tasks such as subspace clustering. Despite the success of FNR in experimental studies, less theoretical analysis is provided to understand its working mechanism. In this paper, we fill this gap by building the theoretical connections between FNR and NNR. More specially, we prove that: 1) when the dictionary can provide enough representative capacity, FNR is exactly NNR even though the data set contains the Gaussian noise, Laplacian noise, or sample-specified corruption, 2) otherwise, FNR and NNR are two solutions on the column space of the dictionary.