# Semi-supervised Vertex Hunting, with Applications in Network and Text Analysis

arXiv: https://arxiv.org/abs/2510.22526 · HTML: https://mlsanity.com/paper/2510.22526/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 39 references that are in the map.
- First posted on arXiv 26 Oct 2025.

## Builds on (most cited first, 11 of 11)

- [A statistical interpretation of spectral embedding: the generalised random dot product graph](https://mlsanity.com/paper/1709.05506/) (2017)
- [Coauthorship and Citation Networks for Statisticians](https://mlsanity.com/paper/1410.2840/) (2014)
- [Detecting Overlapping Communities in Networks Using Spectral Methods](https://mlsanity.com/paper/1412.3432/) (2014)
- [Mixed Membership Estimation for Social Networks](https://mlsanity.com/paper/1708.07852/) (2017)
- [Anchor-Free Correlated Topic Modeling: Identifiability and Algorithm](https://mlsanity.com/paper/1611.05010/) (2016)
- [Using SVD for Topic Modeling](https://mlsanity.com/paper/1704.07016/) (2017)
- [Keyword Assisted Topic Models](https://mlsanity.com/paper/2004.05964/) (2020)
- [Non-negative Matrix Factorization via Archetypal Analysis](https://mlsanity.com/paper/1705.02994/) (2017)
- [Recent Advances in Text Analysis](https://mlsanity.com/paper/2401.00775/) (2024)
- [Improved Algorithm and Bounds for Successive Projection](https://mlsanity.com/paper/2403.11013/) (2024)
- [Semi-supervised Community Detection via Structural Similarity Metrics](https://mlsanity.com/paper/2306.01089/) (2023)

## Abstract (arXiv)

Vertex hunting (VH) is the task of estimating a simplex from noisy data points and has many applications in areas such as network and text analysis. We introduce a new variant, semi-supervised vertex hunting (SSVH), in which partial information is available in the form of barycentric coordinates for some data points, known only up to an unknown transformation. To address this problem, we develop a method that leverages properties of orthogonal projection matrices, drawing on novel insights from linear algebra. We establish theoretical error bounds for our method and demonstrate that it achieves a faster convergence rate than existing unsupervised VH algorithms. Finally, we apply SSVH to two practical settings, semi-supervised network mixed membership estimation and semi-supervised topic modeling, resulting in efficient and scalable algorithms.