# Persistent Laplacian-enhanced Algorithm for Scarcely Labeled Data Classification

arXiv: https://arxiv.org/abs/2305.16239 · HTML: https://mlsanity.com/paper/2305.16239/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 116 references that are in the map.
- First posted on arXiv 25 May 2023.

## Builds on (most cited first, 28 of 28)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [GaAN: Gated Attention Networks for Learning on Large and Spatiotemporal Graphs](https://mlsanity.com/paper/1803.07294/) (2018)
- [On Deep Multi-View Representation Learning: Objectives and Optimization](https://mlsanity.com/paper/1602.01024/) (2016)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [Graph-based Semi-supervised Learning: A Comprehensive Review](https://mlsanity.com/paper/2102.13303/) (2021)
- [AET vs. AED: Unsupervised Representation Learning by Auto-Encoding Transformations rather than Data](https://mlsanity.com/paper/1901.04596/) (2019)
- [HARP: Hierarchical Representation Learning for Networks](https://mlsanity.com/paper/1706.07845/) (2017)
- [Graph Convolutional Networks using Heat Kernel for Semi-supervised Learning](https://mlsanity.com/paper/2007.16002/) (2020)
- [Poisson Learning: Graph Based Semi-Supervised Learning At Very Low Label Rates](https://mlsanity.com/paper/2006.11184/) (2020)
- [Persistent Laplacians: properties, algorithms and implications](https://mlsanity.com/paper/2012.02808/) (2020)
- [Multiclass Data Segmentation using Diffuse Interface Methods on Graphs](https://mlsanity.com/paper/1302.3913/) (2013)
- [Analysis and algorithms for ℓp-based semi-supervised learning on graphs](https://mlsanity.com/paper/1901.05031/) (2019)
- [A random matrix analysis and improvement of semi-supervised learning for large dimensional data](https://mlsanity.com/paper/1711.03404/) (2017)
- [Uniform Convergence Rates for Lipschitz Learning on Graphs](https://mlsanity.com/paper/2111.12370/) (2021)
- [Hamilton-Jacobi equations on graphs with applications to semi-supervised learning and data depth](https://mlsanity.com/paper/2202.08789/) (2022)
- [Convex and Scalable Weakly Labeled SVMs](https://mlsanity.com/paper/1303.1271/) (2013)
- [Multiscale Laplacian Learning](https://mlsanity.com/paper/2109.03718/) (2021)
- [Simplified Energy Landscape for Modularity Using Total Variation](https://mlsanity.com/paper/1707.09285/) (2017)
- [Graph Laplacian Regularized Graph Convolutional Networks for Semi-supervised Learning](https://mlsanity.com/paper/1809.09839/) (2018)
- [Semi-supervised Deep Representation Learning for Multi-View Problems](https://mlsanity.com/paper/1811.04480/) (2018)
- [Integrating Transformer and Autoencoder Techniques with Spectral Graph Algorithms for the Prediction of Scarcely Labeled Molecular Data](https://mlsanity.com/paper/2211.06759/) (2022)
- [Fully Linear Graph Convolutional Networks for Semi-Supervised Learning and Clustering](https://mlsanity.com/paper/2111.07942/) (2021)

## Built on by (most cited first, 2 of 2)

- [MALADY: Multiclass Active Learning with Auction Dynamics on Graphs](https://mlsanity.com/paper/2409.09475/) (2024)
- [Lipschitz Bounds for Persistent Laplacian Eigenvalues under One-Simplex Insertions](https://mlsanity.com/paper/2506.21352/) (2025)

## Abstract (arXiv)

The success of many machine learning (ML) methods depends crucially on having large amounts of labeled data. However, obtaining enough labeled data can be expensive, time-consuming, and subject to ethical constraints for many applications. One approach that has shown tremendous value in addressing this challenge is semi-supervised learning (SSL); this technique utilizes both labeled and unlabeled data during training, often with much less labeled data than unlabeled data, which is often relatively easy and inexpensive to obtain. In fact, SSL methods are particularly useful in applications where the cost of labeling data is especially expensive, such as medical analysis, natural language processing (NLP), or speech recognition. A subset of SSL methods that have achieved great success in various domains involves algorithms that integrate graph-based techniques. These procedures are popular due to the vast amount of information provided by the graphical framework and the versatility of their applications. In this work, we propose an algebraic topology-based semi-supervised method called persistent Laplacian-enhanced graph MBO (PL-MBO) by integrating persistent spectral graph theory with the classical Merriman-Bence- Osher (MBO) scheme. Specifically, we use a filtration procedure to generate a sequence of chain complexes and associated families of simplicial complexes, from which we construct a family of persistent Laplacians. Overall, it is a very efficient procedure that requires much less labeled data to perform well compared to many ML techniques, and it can be adapted for both small and large datasets. We evaluate the performance of the proposed method on data classification, and the results indicate that the proposed technique outperforms other existing semi-supervised algorithms.