In this paper, we develop a local rank correlation (LRC) measure which quantifies the performance of dimension reduction methods. The LRC is easily interpretable, and robust against the extreme skewness of nearest neighbor distributions in high dimensions. Some benchmark datasets are studied. We find that the LRC closely corresponds to our visual interpretation of the quality of the output. In addition, we demonstrate that the LRC is useful in estimating the intrinsic dimensionality of the original data, and in selecting a suitable value of tuning parameters used in some algorithms.

中文翻译：

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非线性降维性能分析的新方法

在本文中，我们开发了一种局部秩相关（LRC）度量，该度量量化了降维方法的性能。LRC易于解释，并且在高维方面对最近邻分布的极端偏斜具有鲁棒性。研究了一些基准数据集。我们发现，LRC与我们对输出质量的视觉解释非常接近。此外，我们证明了LRC在估计原始数据的固有维数以及选择某些算法中使用的调整参数的合适值方面很有用。