  PageRank for Semi-Supervised Learning has shown to leverage data structures
and limited tagged examples to yield meaningful classification. Despite
successes, classification performance can still be improved, particularly in
cases of fuzzy graphs or unbalanced labeled data. To address such limitations,
a novel approach based on powers of the Laplacian matrix $L^\gamma$ ($\gamma >
0$), referred to as $L^\gamma$-PageRank, is proposed. Its theoretical study
shows that it operates on signed graphs, where nodes belonging to one same
class are more likely to share positive edges while nodes from different
classes are more likely to be connected with negative edges. It is shown that
by selecting an optimal $\gamma$, classification performance can be
significantly enhanced. A procedure for the automated estimation of the optimal
$\gamma$, from a unique observation of data, is devised and assessed.
Experiments on several datasets demonstrate the effectiveness of both
$L^\gamma$-PageRank classification and the optimal $\gamma$ estimation.
