Not yet reviewed by Pith; the record is open.

The centrality and diversity of the labeled data are very influential to the performance of semi-supervised learning (SSL), but most SSL models select the labeled data randomly. This study first construct a leading forest that forms a partially ordered topological space in an unsupervised way, and select a group of most representative samples to label with one shot (differs from active learning essentially) using property of homeomorphism. Then a kernelized large margin metric is efficiently learned for the selected data to classify the remaining unlabeled sample. Optimal leading forest (OLF) has been observed to have the advantage of revealing the difference evolution along a path within a subtree. Therefore, we formulate an optimization problem based on OLF to select the samples. Also with OLF, the multiple local metrics learning is facilitated to address multi-modal and mix-modal problem in SSL, especially when the number of class is large. Attribute to this novel design, stableness and accuracy of the performance is significantly improved when compared with the state-of-the-art graph SSL methods. The extensive experimental studies have shown that the proposed method achieved encouraging accuracy and efficiency. Code has been made available at https://github.com/alanxuji/DeLaLA.