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The goal of dimension reduction tools is to construct a low-dimensionalrepresentation of high-dimensional data. These tools are employed for a varietyof reasons such as noise reduction, visualization, and to lower computationalcosts. However, there is a fundamental issue that is highly discussed in othermodeling problems, but almost entirely ignored in the dimension reductionliterature: overfitting. If we interpret data as a combination of signal andnoise, prior works judge dimension reduction techniques on their ability tocapture the entirety of the data, i.e. both the signal and the noise. In thecontext of other modeling problems, techniques such as feature-selection,cross-validation, and regularization are employed to combat overfitting, but nosuch precautions are taken when performing dimension reduction. In this paper,we present a framework that models dimension reduction problems in the presenceof noise and use this framework to explore the role perplexity and number ofneighbors play in overfitting data when applying t-SNE and UMAP. Morespecifically, we show previously recommended values for perplexity and numberof neighbors are too small and tend to overfit the noise. We also present aworkflow others may use to calibrate perplexity or number of neighbors in thepresence of noise.

Calibrating dimension reduction hyperparameters in the presence of noise