  Retrieving the most similar objects in a large-scale database for a given
query is a fundamental building block in many application domains, ranging from
web searches, visual, cross media, and document retrievals. State-of-the-art
approaches have mainly focused on capturing the underlying geometry of the data
manifolds. Graph-based approaches, in particular, define various diffusion
processes on weighted data graphs. Despite success, these approaches rely on
fixed-weight graphs, making ranking sensitive to the input affinity matrix. In
this study, we propose a new ranking algorithm that simultaneously learns the
data affinity matrix and the ranking scores. The proposed optimization
formulation assigns adaptive neighbors to each point in the data based on the
local connectivity, and the smoothness constraint assigns similar ranking
scores to similar data points. We develop a novel and efficient algorithm to
solve the optimization problem. Evaluations using synthetic and real datasets
suggest that the proposed algorithm can outperform the existing methods.
