Dimensionality reduction techniques map values from a high dimensional space to one with a lower dimension. The result is a space which requires less physical memory and has a faster distance calculation. These techniques are widely used where required properties of the reduced-dimension space give an acceptable accuracy with respect to the original space. Many such transforms have been described. They have been classified in two main groups: linear and topological. Linear methods such as Principal Component Analysis (PCA) and Random Projection (RP) define matrix-based transforms into a lower dimension of Euclidean space. Topological methods such as Multidimensional Scaling (MDS) attempt to preserve higher-level aspects such as the nearest-neighbour relation, and some may be applied to non-Euclidean spaces. Here, we introduce nSimplex Zen, a novel topological method of reducing dimensionality. Like MDS, it relies only upon pairwise distances measured in the original space. The use of distances, rather than coordinates, allows the technique to be applied to both Euclidean and other Hilbert spaces, including those governed by Cosine, Jensen-Shannon and Quadratic Form distances. We show that in almost all cases, due to geometric properties of high-dimensional spaces, our new technique gives better properties than others, especially with reduction to very low dimensions.

翻译：从高维空间到低维度减少技术的地图值,从高维空间到低维空间。 结果是空间需要较少物理内存, 并且有更快的距离计算。 这些技术被广泛使用, 需要的缩小空间的特性使得原始空间具有可接受的准确性。 许多这样的变异已经被描述过。 它们被分为两大类: 线性和地形学。 线性方法, 如主元分析( PCA) 和随机预测( Randoman Project) 等, 定义基于矩阵的变换为欧几里德空间的较低维度。 诸如MDS( MDS) 等地形学方法, 试图保存更高级别的方面, 如最近的邻里关系, 有些技术被广泛应用到非欧几里德空间。 在这里, 我们引入 nSoproadx Zen, 这是一种新型的减空格方法。 与MDS一样, 它仅仅依靠在原始空间测量的对等距离。 使用距离, 而不是坐标, 使得技术技术技术可以适用于厄里德和希尔伯特空间,, 包括由Cosine, ent- dismostrual- develop ex- develop ex