Multidimensional Scaling With Very Large Datasets

Multidimensional scaling has a wide range of applications when observations are not continuous but it is possible to define a distance (or dissimilarity) among them. However, standard implementations are limited when analyzing very large datasets because they rely on eigendecomposition of the full distance matrix and require very long computing times and large quantities of memory. Here, a new approach is developed based on projection of the observations in a space defined by a subset of the full dataset. The method is easily implemented. A simulation study showed that its performance are satisfactory in different situations and can be run in a short time when the standard method takes a very long time or cannot be run because of memory requirements.

当观测值并非连续型数据，但可定义观测间的距离（或相异度）时，多维标度法（Multidimensional Scaling）具备广泛的应用场景。然而，标准实现方案在处理超大型数据集时存在局限：这类方案依赖完整距离矩阵的特征分解，不仅计算耗时极长，还需要占用大量内存空间。为此，本文提出一种全新方法，其核心是将观测值投影至由全数据集子集所定义的空间中。该方法易于实现。一项模拟仿真研究表明，该方法在各类场景下均能取得令人满意的性能表现，且在标准方法耗时极长或因内存限制无法运行的场景下，该方法可在短时间内完成计算。