# BASiS: Batch Aligned Spectral Embedding Space

arXiv: https://arxiv.org/abs/2211.16960 · HTML: https://mlsanity.com/paper/2211.16960/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 34 references that are in the map.
- First posted on arXiv 30 Nov 2022.

## Builds on (most cited first, 10 of 10)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [SpectralNet: Spectral Clustering using Deep Neural Networks](https://mlsanity.com/paper/1801.01587/) (2018)
- [Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning](https://mlsanity.com/paper/2008.13333/) (2020)
- [Diffusion Nets](https://mlsanity.com/paper/1506.07840/) (2015)
- [Multiclass Data Segmentation using Diffuse Interface Methods on Graphs](https://mlsanity.com/paper/1302.3913/) (2013)
- [Multiclass Total Variation Clustering](https://mlsanity.com/paper/1306.1185/) (2013)
- [GraphXCOVID: Explainable Deep Graph Diffusion Pseudo-Labelling for Identifying COVID-19 on Chest X-rays](https://mlsanity.com/paper/2010.00378/) (2020)
- [SpecNet2: Orthogonalization-free spectral embedding by neural networks](https://mlsanity.com/paper/2206.06644/) (2022)
- [Solving the functional Eigen-Problem using Neural Networks](https://mlsanity.com/paper/2007.10205/) (2020)

## Built on by (most cited first, 4 of 4)

- [Graph Laplacian for Semi-Supervised Learning](https://mlsanity.com/paper/2301.04956/) (2023)
- [Neural Normalized Cut: A Differential and Generalizable Approach for Spectral Clustering](https://mlsanity.com/paper/2503.09260/) (2025)
- [Routing Channel-Patch Dependencies in Time Series Forecasting with Graph Spectral Decomposition](https://mlsanity.com/paper/2603.13702/) (2026)
- [Generalizable Spectral Embedding with an Application to UMAP](https://mlsanity.com/paper/2501.11305/) (2025)

## Abstract (arXiv)

Graph is a highly generic and diverse representation, suitable for almost any data processing problem. Spectral graph theory has been shown to provide powerful algorithms, backed by solid linear algebra theory. It thus can be extremely instrumental to design deep network building blocks with spectral graph characteristics. For instance, such a network allows the design of optimal graphs for certain tasks or obtaining a canonical orthogonal low-dimensional embedding of the data. Recent attempts to solve this problem were based on minimizing Rayleigh-quotient type losses. We propose a different approach of directly learning the eigensapce. A severe problem of the direct approach, applied in batch-learning, is the inconsistent mapping of features to eigenspace coordinates in different batches. We analyze the degrees of freedom of learning this task using batches and propose a stable alignment mechanism that can work both with batch changes and with graph-metric changes. We show that our learnt spectral embedding is better in terms of NMI, ACC, Grassman distance, orthogonality and classification accuracy, compared to SOTA. In addition, the learning is more stable.