Consensus dimension reduction via multi-view learning

Dimension reduction methods are a fundamental class of techniques in data analysis, which aim to find a lower-dimensional representation of higher-dimensional data while preserving as much of the original information as possible. These methods are extensively used in practice, including in exploratory data analyses to visualize data--arguably, one of the first and most vital steps in any data analysis (Ray et al., 2021). Notably, in genomics, dimension reduction methods are ubiquitously applied to visualize high-dimensional single-cell RNA sequencing data in two dimensions (Becht et al., 2019). Beyond visualization, dimension reduction methods are also frequently employed to mitigate the curse of dimensionality (Bellman, 1957), engineer new features to improve downstream tasks like prediction (e.g., Massy, 1965), and enable scientific discovery in unsupervised learning settings (Chang et al., 2025). For example, many researchers have used dimension reduction in conjunction with clustering to discover new cell types and cell states (Wu et al., 2021), new cancer subtypes (Northcott et al., 2017), and other substantively-meaningful structure in a variety of domains (Bergen et al., 2019; Traven et al., 2017). Given the widespread use and need for dimension reduction methods, numerous dimension reduction techniques have been developed. Popular techniques include but are not limited to principal component analysis (PCA) (Pearson, 1901; Hotelling, 1933), multidimensional scaling (MDS) (Torgerson, 1952; Kruskal, 1964a), Isomap (Tenenbaum et al., 2000), locally linear embedding (LLE) (Roweis and Saul, 2000), t-distributed stochastic neighbor embedding (t-SNE) (van der 1