  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.
