A Practical Guide to Sparse K-Means Clustering for Studying Molecular Development of the Human Brain

Abstract Studying the molecular development of the human brain presents unique challenges for selecting a data analysis approach. The rare and valuable nature of human postmortem brain tissue, especially for developmental studies, means the sample sizes are small ( n ), but the use of high throughput genomic and proteomic methods measure the expression levels for hundreds or thousands of variables (e.g. genes or proteins ( p )) for each sample. This leads to a data structure that is high dimensional ( p >> n ) and introduces the curse of dimensionality, which poses a challenge for traditional statistical approaches. In contrast, high dimensional analyses, especially cluster analyses developed for sparse data, have worked well for analyzing genomic datasets where p >> n. Here we explore applying a lasso-based clustering method developed for high dimensional genomic data with small sample sizes. Using protein and gene data from the developing human visual cortex, we compared clustering methods. We identified an application of sparse K -means clustering (Robust Sparse K -means Clustering (RSKC)) that partitioned samples into age-related clusters that reflect lifespan stages from birth to aging. RSKC adaptively selects a subset of the genes or proteins contributing to partitioning samples into age-related clusters that progress across the lifespan. This approach addresses a problem in current studies that could not identify multiple postnatal clusters. Moreover, clusters encompassed a range of ages like a series of overlapping waves illustrating that chronological- and brain-age have a complex relationship. In addition, a recently developed workflow to create plasticity phenotypes (Balsor et al., 2020) was applied to the clusters and revealed neurobiologically relevant features that identified how the human visual cortex changes across the lifespan. These methods can help address the growing demand for multimodal integration, from molecular machinery to brain imaging signals, to understand the human brain’s development.