# Quadric Hypersurface Intersection for Manifold Learning in Feature Space

arXiv: https://arxiv.org/abs/2102.06186 · HTML: https://mlsanity.com/paper/2102.06186/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 48 references that are in the map.
- First posted on arXiv 11 Feb 2021.

## Builds on (most cited first, 8 of 8)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [VGGFace2: A dataset for recognising faces across pose and age](https://mlsanity.com/paper/1710.08092/) (2017)
- [MS-Celeb-1M: A Dataset and Benchmark for Large-Scale Face Recognition](https://mlsanity.com/paper/1607.08221/) (2016)
- [Cross-Age LFW: A Database for Studying Cross-Age Face Recognition in Unconstrained Environments](https://mlsanity.com/paper/1708.08197/) (2017)
- [The MegaFace Benchmark: 1 Million Faces for Recognition at Scale](https://mlsanity.com/paper/1512.00596/) (2015)
- [Can We Gain More from Orthogonality Regularizations in Training Deep CNNs?](https://mlsanity.com/paper/1810.09102/) (2018)
- [Efficient Manifold and Subspace Approximations with Spherelets](https://mlsanity.com/paper/1706.08263/) (2017)

## Built on by (most cited first, 1 of 1)

- [Implicit Manifold Gaussian Process Regression](https://mlsanity.com/paper/2310.19390/) (2023)

## Abstract (arXiv)

The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier or to use the geometry to come up with a better distance metric. Manifold learning problems are often posed in a very high dimension, e.g. for spaces of images or spaces of words. Today, with deep representation learning on the rise in areas such as computer vision and natural language processing, many problems of this kind may be transformed into problems of moderately high dimension, typically of the order of hundreds. Motivated by this, we propose a manifold learning technique suitable for moderately high dimension and large datasets. The manifold is learned from the training data in the form of an intersection of quadric hypersurfaces -- simple but expressive objects. At test time, this manifold can be used to introduce a computationally efficient outlier score for arbitrary new data points and to improve a given similarity metric by incorporating the learned geometric structure into it.