Manifold Coordinates with Physical Meaning
Manifold Coordinates with Physical Meaning
复制标题
DOI：
--
复制
发表时间：
2018-11
期刊：
影响因子：
--
通讯作者：
Samson Koelle;Hanyu Zhang;M. Meilă;Yu-Chia Chen
中科院分区：
文献类型：
--
作者：
Samson Koelle;Hanyu Zhang;M. Meilă;Yu-Chia Chen
流形嵌入算法将高维数据映射到低维空间中的坐标。降维的目的之一是找到描述数据流形的内在坐标。嵌入算法返回的坐标是抽象的，找到它们的物理或领域相关的含义并没有形式化，通常留给领域专家。本文研究了以自动、有原则的方式恢复新的低维表示的含义的问题。我们提出了一种方法来将流形的嵌入坐标解释为来自用户定义字典的函数的非线性组合。我们证明这个问题可以设置为稀疏线性组套索恢复问题，找到足够的恢复条件，并证明其在数据上的有效性。
Manifold embedding algorithms map high-dimensional data down to coordinates in a much lower-dimensional space. One of the aims of dimension reduction is to find intrinsic coordinates that describe the data manifold. The coordinates returned by the embedding algorithm are abstract, and finding their physical or domain-related meaning is not formalized and often left to domain experts. This paper studies the problem of recovering the meaning of the new low-dimensional representation in an automatic, principled fashion. We propose a method to explain embedding coordinates of a manifold as non-linear compositions of functions from a user-defined dictionary. We show that this problem can be set up as a sparse linear Group Lasso recovery problem, find sufficient recovery conditions, and demonstrate its effectiveness on data.