  Image ranking is to rank images based on some known ranked images. In this
paper, we propose an improved linear ordinal distance metric learning approach
based on the linear distance metric learning model. By decomposing the distance
metric $A$ as $L^TL$, the problem can be cast as looking for a linear map
between two sets of points in different spaces, meanwhile maintaining some data
structures. The ordinal relation of the labels can be maintained via classical
multidimensional scaling, a popular tool for dimension reduction in statistics.
A least squares fitting term is then introduced to the cost function, which can
also maintain the local data structure. The resulting model is an unconstrained
problem, and can better fit the data structure. Extensive numerical results
demonstrate the improvement of the new approach over the linear distance metric
learning model both in speed and ranking performance.
