一种基于全局和局部特征匹配的流形对齐算法

A manifold alignment algorithm based on global and local feature matching

不同流形样本点之间的关联性挖掘是决定流形对齐算法效率的关键问题。提出了一种新的思路,利用测地距离初步构造不同流形样本点之间的关联性,再利用样本点之间局部几何结构的相似性进行修正,以更为准确地挖掘不同流形样本点之间的关联性。进一步提出一种新的半监督流形对齐算法,利用已知对应点信息和所挖掘样本点之间的关联性,将多个流形数据投影到共同的低维空间。与传统的半监督流形对齐算法相比,本算法在先验信息不充分的情况下,能更准确地联结不同流形数据集。最后通过在实际数据集上的实验验证了算法的有效性。

A key issue that determines the effectiveness of the manifold alignment approaches is to discover the correlations between the points sampled from different manifolds.This paper proposes a new idea,which uses the geodesic distances to originally construct the correlations between the points sampled from different manifolds,and then uses the similarities measured by the local geometric structures of the samples to modify the correlations,thus discovering the correlations between the data points sampled from different manifolds more accurately.Further more,the paper proposes a new semi-supervised manifold alignment algorithm,which projects multiple manifold data sets to acommon low-dimensional space by using the known correspondences information and the discovered correlations between the sample points.Compared with the traditional semi-supervised manifold alignment algorithms,the proposed algorithm can find the matching points of different manifold data in the low-dimensional space more accurately when the prior information is not sufficient.Finally,the effectiveness of the proposed algorithm is validated by the experiments on real-world data sets.