On a Connection between Maximum Variance Unfolding, Shortest Path Problems and IsoMap
On a Connection between Maximum Variance Unfolding, Shortest Path Problems and IsoMap
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发表时间：
2012-03
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通讯作者：
A. Paprotny;J. Garcke
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作者：
A. Paprotny;J. Garcke
我们提出了一个等价的最大方差展开（MVU）方法来非线性降维的距离矩阵。这产生了一个新的解释MVU问题作为一个正规化版本的最短路径问题的图。这种解释使我们能够建立一个渐近收敛的结果的情况下，基本的数据是从黎曼流形是等距的凸子集的欧几里德空间。
We present an equivalent formulation of the Maximum Variance Unfolding (MVU) approach to nonlinear dimensionality reduction in terms of distance matrices. This yields a novel interpretation of the MVU problem as a regularized version of the shortest path problem on a graph. This interpretation enables us to establish an asymptotic convergence result for the case that the underlying data are drawn from a Riemannian manifold which is isometric to a convex subset of Euclidean space.