  Sparse coding, which represents a data point as a sparse reconstruction code
with regard to a dictionary, has been a popular data representation method.
Meanwhile, in database retrieval problems, learning the ranking scores from
data points plays an important role. Up to now, these two problems have always
been considered separately, assuming that data coding and ranking are two
independent and irrelevant problems. However, is there any internal
relationship between sparse coding and ranking score learning? If yes, how to
explore and make use of this internal relationship? In this paper, we try to
answer these questions by developing the first joint sparse coding and ranking
score learning algorithm. To explore the local distribution in the sparse code
space, and also to bridge coding and ranking problems, we assume that in the
neighborhood of each data point, the ranking scores can be approximated from
the corresponding sparse codes by a local linear function. By considering the
local approximation error of ranking scores, the reconstruction error and
sparsity of sparse coding, and the query information provided by the user, we
construct a unified objective function for learning of sparse codes, the
dictionary and ranking scores. We further develop an iterative algorithm to
solve this optimization problem.
