A new method for performance analysis in nonlinear dimensionality reduction
Jiaxi Liang, Shojaeddin Chenouri, Christopher G. Small · Statistical Analysis and Data Mining The ASA Data Science Journal · 2020
Abstract 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.