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

Yicong Jiang, Tracy Ke

Keywords: Eigenvalue problem, successive projection, mixed membership estimation, topic modeling

TL;DR: We propose a novel semi-supervised vertex hunting (SSVH) algorithm that has a theoretical guarantee. We use SSVH to develop semi-supervised learning algorithms for network and text analysis.

Abstract: 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.

Primary Area: General machine learning (supervised, unsupervised, online, active, etc.)

Submission Number: 13861