一种流形仿射对齐算法

An algorithm for affine alignment of manifolds

研究了高维数据集中共享隐空间的寻找和对齐问题,提出了半监督的流形仿射对齐算法.未匹配点的局部分布信息被有效地利用起来,以改善在匹配点比例较低情况下的学习效果;扩展的谱回归技术的应用,使得线性对齐也能较好地保持高维数据的局部几何信息.实验表明该算法能够找出高维数据的相关性方向,并将其内部隐空间较好地对齐在一起,映射新点的开销也很小.

For the problem of finding and aligning the shared hidden structure of high-dimensional data sets, a semi-supervised algorithm for affine alignment of manifolds was presented. Un-matching points were used to improve the learning effect when the proportion of matching points was small. The extended spectral regression technique was applied, which made it possible for linear aligning algorithm to preserve the local geometry information of high-dimensional data. The experiments showed that the embedded manifolds could be successfully found and aligned when the proportion of matching points was small, and less cost was needed to project a new point.