Principal manifolds and nonlinear dimensionality reduction via tangent space alignment
Principal manifolds and nonlinear dimensionality reduction via tangent space alignment
复制标题
DOI：
10.1137/s1064827502419154
复制
发表时间：
2004-01-01
影响因子：
3.1
通讯作者：
Zha, HY
中科院分区：
文献类型：
--
作者：
Zhang, ZY;Zha, HY
我们提出了一种用于流形学习和非线性维度降低的新算法。基于一组无组织的数据点，并从参数化的歧管中采样了噪声，通过在每个数据点构建一个切线空间的近似值来学到歧管的局部几何形状，然后将这些切线空间对准以给出以提供的全局坐标。有关基础歧管的数据点。我们还对算法进行了错误分析，表明在某些情况下，重建错误可能很小。我们在二维/三维（2D/3D）欧几里得空间以及更高维的欧几里得空间中使用曲线和表面说明了算法。我们还讨论了几个理论和算法问题，以进行进一步的研究和改进。
We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approximation for the tangent space at each data point, and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases. We illustrate our algorithm using curves and surfaces both in two-dimensional/three-dimensional (2D/3D) Euclidean spaces and in higher-dimensional Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.