An Interactive Tool for Analyzing High-Dimensional Clusterings

Technological advances have spurred an increase in data complexity and dimensionality. We are now in an era in which data sets containing thousands of features are commonplace. To digest and analyze such high-dimensional data, dimension reduction techniques have been developed and advanced along with computational power. Of these techniques, nonlinear methods are most commonly employed because of their ability to construct visually interpretable embeddings. Unlike linear methods, these methods non-uniformly stretch and shrink space to create a visual impression of the high-dimensional data. Since capturing high-dimensional structures in a significantly lower number of dimensions requires drastic manipulation of space, nonlinear dimension reduction methods are known to occasionally produce false structures, especially in noisy settings. In an effort to deal with this phenomenon, we developed an interactive tool that enables analysts to better understand and diagnose their dimension reduction results. It uses various analytical plots to provide a multi-faceted perspective on results to determine legitimacy. The tool is available via an R package named DRtool.

Calibrating dimension reduction hyperparameters in the presence of noise

The goal of dimension reduction tools is to construct a low-dimensional representation of high-dimensional data. These tools are employed for a variety of reasons such as noise reduction, visualization, and to lower computational costs. However, there is a fundamental issue that is highly discussed in other modeling problems, but almost entirely ignored in the dimension reduction literature: overfitting. If we interpret data as a combination of signal and noise, prior works judge dimension reduction techniques on their ability to capture the entirety of the data, i.e. both the signal and the noise. In the context of other modeling problems, techniques such as feature-selection, cross-validation, and regularization are employed to combat overfitting, but no such precautions are taken when performing dimension reduction. In this paper, we present a framework that models dimension reduction problems in the presence of noise and use this framework to explore the role perplexity and number of neighbors play in overfitting data when applying t-SNE and UMAP. More specifically, we show previously recommended values for perplexity and number of neighbors are too small and tend to overfit the noise. We also present a workflow others may use to calibrate perplexity or number of neighbors in the presence of noise.