数据高维波动y=xsinx
低维数据线性y=xsinx
纷乱的空间降维方法和算法，存在一个共同点，那就是数据点的拟合思路有问题，线性化思维，空间线性化，面对波动的点数据无所适从，计算重复，假如面对一堆“无关”的实验数据点，从基本波动的角度去分析，线性空间的误差或可转化为波动（量子化）精确值，不同维度未知的外在因素的影响从暗处明朗化：所有的实验数据都是精确的.
附：Daniel Ting, Michael I. Jordan
(Submitted on 6 Mar 2018)
We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using existing NLDR theory for deriving new algorithms. We provide a novel framework for analysis of NLDR via a connection to the statistical theory of linear smoothers. This allows us to both understand existing methods and derive new ones. We use this connection to smoothing to show that asymptotically, existing NLDR methods correspond to discrete approximations of the solutions of sets of differential equations given a boundary condition. In particular, we can characterize many existing methods in terms of just three limiting differential operators and boundary conditions. Our theory also provides a way to assert that one method is preferable to another; indeed, we show Local Tangent Space Alignment is superior within a class of methods that assume a global coordinate chart defines an isometric embedding of the manifold.
Subjects:Machine Learning (stat.ML)
Cite as:arXiv:1803.02432 [stat.ML]
(or arXiv:1803.02432v1 [stat.ML] for this version)
Submission history
From: Daniel Ting [view email]
[v1] Tue, 6 Mar 2018 21:35:16 UTC (300 KB)
Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)
我们发展了非线性降维理论（NLDR）。已经开发了许多NLDR方法，但是对这些方法的工作和它们之间的关系的理解是有限的。现有的NLDR理论推导新算法的基础有限。我们提供了一个新的框架分析NLDR通过连接到统计理论的线性平滑器。这使我们既能理解现有的方法，又能得到现有的方法。我们使用这个连接来平滑，表明渐近的，现有的NLDR方法对应于给定边界条件的微分方程组解的离散逼近。特别地，我们仅用三个有限微分算子和边界条件来描述许多已有的方法。我们的理论也提供了一种断言一种方法比另一种方法更好的方法；事实上，我们表明局部切空间对齐在一类假设AgbAbar坐标图定义歧管的等距嵌入的方法中是优越的。
网友评论