A New Method for Performance Analysis in Nonlinear Dimensionality Reduction
This provides a new tool for researchers and practitioners in machine learning and data analysis to better evaluate and optimize dimensionality reduction techniques, though it is incremental as it builds on existing performance analysis methods.
The paper tackles the problem of evaluating nonlinear dimensionality reduction methods by introducing a local rank correlation measure that is interpretable and robust to high-dimensional nearest neighbor skewness, and demonstrates its utility for assessing output quality, estimating intrinsic dimensionality, and tuning parameters.
In this paper, we develop a local rank correlation measure which quantifies the performance of dimension reduction methods. The local rank correlation 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 local rank correlation closely corresponds to our visual interpretation of the quality of the output. In addition, we demonstrate that the local rank correlation is useful in estimating the intrinsic dimensionality of the original data, and in selecting a suitable value of tuning parameters used in some algorithms.