利用部分已知的重心坐标信息，提升网络与文本分析中的顶点估计效率。
Semi-supervised Vertex Hunting, with Applications in Network and Text Analysis
- 基于正交投影矩阵特性，结合部分重心坐标信息进行顶点推断。
- 理论证明收敛速度优于传统无监督方法，实际应用中更高效。
- 适用于半监督网络社团识别与主题建模，计算可扩展性强。
顶点探测（Vertex Hunting, VH）是从噪声数据点中估计单纯形的任务，在网络与文本分析中有广泛应用。本文提出一种新变体——半监督顶点探测（SSVH），其中部分数据点的重心坐标已知，但仅以未知变换形式给出。为此，我们发展了一种方法，利用正交投影矩阵的性质，并引入线性代数的新洞察。理论上建立了误差界，证明该方法的收敛速度优于现有无监督VH算法。最后，将SSVH应用于两个实际场景：半监督网络混合成员估计与半监督主题建模，实现了高效且可扩展的算法。
原文摘要 · Abstract (English)
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.
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