  Active learning (AL) repeatedly trains the classifier with the minimum
labeling budget to improve the current classification model. The training
process is usually supervised by an uncertainty evaluation strategy. However,
the uncertainty evaluation always suffers from performance degeneration when
the initial labeled set has insufficient labels. To completely eliminate the
dependence on the uncertainty evaluation sampling in AL, this paper proposes a
divide-and-conquer idea that directly transfers the AL sampling as the
geometric sampling over the clusters. By dividing the points of the clusters
into cluster boundary and core points, we theoretically discuss their margin
distance and {hypothesis relationship}. With the advantages of cluster boundary
points in the above two properties, we propose a Geometric Active Learning
(GAL) algorithm by knight's tour. Experimental studies of the two reported
experimental tasks including cluster boundary detection and AL classification
show that the proposed GAL method significantly outperforms the
state-of-the-art baselines.
