High-dimensional Semi-supervised Classification via the Fermat Distance
Semi-supervised classification, where unlabeled data are massive but labeled data are limited, often arises in machine learning applications. We address this challenge under high-dimensional data by leveraging the manifold and cluster assumptions. Based on the Fermat distance, a density-sensitive metric that naturally encodes the cluster assumption, we propose the weighted $k$-nearest neighbors (NN) classifier and multidimensional scaling (MDS)-induced classifiers. The use of MDS with a large target dimension allows the effective application of linear classifiers to complex manifold data. Theoretically, we derive a sharp lower bound for the expected excess risk within clusters and prove t...
| Authors | Ruoxu Tan, Yiming Zang |
|---|---|
| Primary category | stat.ML |
| Published | 26 April 2026 |
| Last updated at source | 26 April 2026 |
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