论文标题
关于线性子空间的预测
On Projections to Linear Subspaces
论文作者
论文摘要
将数据投射到线性子空间上的优点是从缩小尺寸降低中众所周知的。已经对子空间预测的最大保留（主要组件分析）的一个关键方面进行了彻底研究，并且随机线性投影对诸如固有维度等度量的措施的影响仍然是一项持续的努力。在本文中，我们研究了较少探索的线性投影深度，这些尺寸的明确子空间以及随之而来的方差期望。结果是欧几里得距离和内部产品的新界限。我们展示了这些边界的质量，并研究了与内在维度估计的密切关系。
The merit of projecting data onto linear subspaces is well known from, e.g., dimension reduction. One key aspect of subspace projections, the maximum preservation of variance (principal component analysis), has been thoroughly researched and the effect of random linear projections on measures such as intrinsic dimensionality still is an ongoing effort. In this paper, we investigate the less explored depths of linear projections onto explicit subspaces of varying dimensionality and the expectations of variance that ensue. The result is a new family of bounds for Euclidean distances and inner products. We showcase the quality of these bounds as well as investigate the intimate relation to intrinsic dimensionality estimation.
