  In this paper, we investigate the problem of optimization multivariate
performance measures, and propose a novel algorithm for it. Different from
traditional machine learning methods which optimize simple loss functions to
learn prediction function, the problem studied in this paper is how to learn
effective hyper-predictor for a tuple of data points, so that a complex loss
function corresponding to a multivariate performance measure can be minimized.
We propose to present the tuple of data points to a tuple of sparse codes via a
dictionary, and then apply a linear function to compare a sparse code against a
give candidate class label. To learn the dictionary, sparse codes, and
parameter of the linear function, we propose a joint optimization problem. In
this problem, the both the reconstruction error and sparsity of sparse code,
and the upper bound of the complex loss function are minimized. Moreover, the
upper bound of the loss function is approximated by the sparse codes and the
linear function parameter. To optimize this problem, we develop an iterative
algorithm based on descent gradient methods to learn the sparse codes and
hyper-predictor parameter alternately. Experiment results on some benchmark
data sets show the advantage of the proposed methods over other
state-of-the-art algorithms.
