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Efficient Inter-Geodesic Distance Computation and Fast Classical Scaling

机译:高效的大地间距离计算和快速经典缩放

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Multidimensional scaling (MDS) is a dimensionality reduction tool used for information analysis, data visualization and manifold learning. Most MDS procedures embed data points in low-dimensional euclidean (flat) domains, such that distances between the points are as close as possible to given inter-point dissimilarities. We present an efficient solver for classical scaling, a specific MDS model, by extrapolating the information provided by distances measured from a subset of the points to the remainder. The computational and space complexities of the new MDS methods are thereby reduced from quadratic to quasi-linear in the number of data points. Incorporating both local and global information about the data allows us to construct a low-rank approximation of the inter-geodesic distances between the data points. As a by-product, the proposed method allows for efficient computation of geodesic distances.
机译:多维缩放(MDS)是一种降维工具,用于信息分析,数据可视化和多种学习。大多数MDS程序将数据点嵌入到低维欧氏(平坦)域中,以使这些点之间的距离尽可能接近给定的点间差异。通过外推从点的子集到其余部分的距离所提供的信息,我们提出了一种有效的求解器,适用于经典缩放,特定的MDS模型。因此,新的MDS方法的计算和空间复杂度在数据点数量上从二次线性降低为准线性。结合有关数据的本地和全局信息,我们可以构建数据点之间大地间距的低阶近似。作为副产品,提出的方法可以有效计算测地距离。

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