Limitations of Clustering with PCA and Correlated Noise

It is now common to have a modest to large number of features on individuals with complex diseases. Unsupervised analyses, such as clustering with and without preprocessing by Principle Component Analysis (PCA), is widely used in practice to uncover subgroups in a sample. However, in many modern studies features are often highly correlated and noisy (e.g. SNP's, -omics, quantitative imaging markers, and electronic health record data). The practical performance of clustering approaches in these settings remains unclear. Through extensive simulations and empirical examples applying Gaussian Mixture Models and related clustering methods, we show these approaches (including variants of kmeans, VarSelLCM, HDClassifier, and Fisher-EM) can have very poor performance in many settings. We also show the poor performance is often driven by either an explicit or implicit assumption by the clustering algorithm that high variance features are relevant while lower variance features are irrelevant, called the variance as relevance assumption. We develop practical pre-processing approaches that improve analysis performance in some cases. This work offers practical guidance on the strengths and limitations of unsupervised clustering approaches in modern data analysis applications.