NMF

Non-negative matrix factorization is a useful method for additive decomposition of signal within a dataset. However, NMF of concatenated datasets does not cleanly resolve batch effects, sources of heterogeneity, and common signal. Linked NMF implicitly couples independent factorizations of multiple datasets to recover models describing shared and unique signal.

Finding the best discoverable solution for a non-negative matrix factorization from a random initialization requires multiple random restarts. NNDSVD has previously been proposed as a “head-start” for NMF, but I show that it is not always a head start, and can be a dangerous local minima. I further explore the use of random uniform or random gaussian models for NMF initialization.

L1- and L2-regularized non-negative matrix factorizations have special properties. Here I show how L1 is a sparsifying regularization that promotes a k-means clustering-like model, while L2 is a densifying regularization that promotes convergence of all factors towards the first singular vector.

In this post I review four distinctly different methods for cross-validation of NMF, each with strengths and weaknesses for different applications, and discuss how to use these methods effectively.

Use the Hawaii Birds dataset to show how to annotate factors in NMF models using metadata, with some interesting UMAP visualizations and applications to ecology along the way.

DNA methylation signatures in patients with Acute Myelogenous Leukemia are compared to healthy cell types to determine cell-of-origin. This is a great example of why source separation is necessary to integrate mixed or heterogenous signals. By using subsets of NMF factors, similarities between these signals are exposed.