  In the machine learning problems, the performance measure is used to evaluate
the machine learning models. Recently, the number positive data points ranked
at the top positions (Pos@Top) has been a popular performance measure in the
machine learning community. In this paper, we propose to learn a convolutional
neural network (CNN) model to maximize the Pos@Top performance measure. The CNN
model is used to represent the multi-instance data point, and a classifier
function is used to predict the label from the its CNN representation. We
propose to minimize the loss function of Pos@Top over a training set to learn
the filters of CNN and the classifier parameter. The classifier parameter
vector is solved by the Lagrange multiplier method, and the filters are updated
by the gradient descent method alternately in an iterative algorithm.
Experiments over benchmark data sets show that the proposed method outperforms
the state-of-the-art Pos@Top maximization methods.
