  Over the past few decades, we have witnessed a large family of algorithms
that have been designed to provide different solutions to the problem of
dimensionality reduction (DR). The DR is an essential tool to excavate the
important information from the high-dimensional data by mapping the data to a
low-dimensional subspace. Furthermore, for the diversity of varied
high-dimensional data, the multi-view features can be utilized for improving
the learning performance. However, many DR methods fail to integrating multiple
views. Although the features from different views are extracted by different
manners, they are utilized to describe the same sample, which implies that they
are highly related. Therefore, how to learn the subspace for high-dimensional
features by utilizing the consistency and complementary properties of
multi-view features is important in the present. In this paper, we propose an
effective multi-view dimensionality reduction algorithm named Multi-view Smooth
Preserve Projection. Firstly, we construct a single view DR method named Smooth
Preserve Projection based on the Smooth Representation model. The proposed
method aims to find a subspace for the high-dimensional data, in which the
smooth reconstructive weights are preserved as much as possible. Then, we
extend it to a multi-view version in which we exploits Hilbert-Schmidt
Independence Criterion to jointly learn one common subspace for all views. A
plenty of experiments on multi-view datasets show the excellent performance of
the proposed method.
