Geodesic distance matrices can reveal shape properties that are largely
invariant to non-rigid deformations, and thus are often used to analyze and
represent 3-D shapes. However, these matrices grow quadratically with the
number of points. Thus for large point sets it is common to use a low-rank
approximation to the distance matrix, which fits in memory and can be
efficiently analyzed using methods such as multidimensional scaling (MDS). In
this paper we present a novel sparse method for efficiently representing
geodesic distance matrices using biharmonic interpolation. This method exploits
knowledge of the data manifold to learn a sparse interpolation operator that
approximates distances using a subset of points. We show that our method is 2x
faster and uses 20x less memory than current leading methods for solving MDS on
large point sets, with similar quality. This enables analyses of large point
sets that were previously infeasible.

本文提出了一种利用双调和插值有效地表示测地距离矩阵的稀疏方法，用于在大数据点集上进行多维缩放分析，相比目前领先的方法，该方法运行速度更快，占用内存更少，可使先前不可行的大数据点集的分析成为可能。