Ordinal preserving projection: a novel dimensionality reduction method for image ranking

Learning to rank has been demonstrated as a powerful tool for image ranking, but the issue of the "curse of dimensionality" is a key challenge of learning a ranking model from a large image database. This paper proposes a novel dimensionality reduction algorithm named ordinal preserving projection (OPP) for learning to rank. We first define two matrices, which work in the row direction and column direction respectively. The two matrices aim at leveraging the global structure of the data set and ordinal information of the observations. By maximizing the corresponding objective functions, we can obtain two optimal projection matrices mapping original data points into low-dimensional subspace, in which both global structure and ordinal information can be preserved. The experiments are conducted on the public available MSRA-MM image data set and "Web Queries" image data set, and the experimental results demonstrate the effectiveness of the proposed method.