Much of Michael Mahoney's current research focuses on developing geometric network analysis tools, i.e., using scalable approximation algorithms with a geometric or statistical flavor to analyze the structure and dynamics of large informatics graphs; developing approximate computation and regularization methods for large informatics graphs; and applications to community detection, clustering, and information dynamics in large social and information networks. Mahoney is also continuing work on randomized matrix algorithms, as well as applications to DNA single nucleotide polymorphism (SNP) data, and large-scale statistical data analysis more generally.
In the past, he has developed and analyzed algorithms for large matrix, graph, and regression problems, and applied these and related tools to the statistical data analysis of extremely large scientific and Internet data sets. For example, he worked on large-scale web analytics, machine learning, and query log analysis; applications of graph partitioning algorithms to clustering and community identification; and applications of randomized matrix algorithms to hyperspectral medical image data, DNA microarray data, and DNA SNP data. In the more distant past, Mahoney also worked on developing and analyzing Monte Carlo algorithms for performing useful computations on extremely large matrices, e.g., the additive-error and relative-error CUR matrix decompositions. Past research has included work in computational statistical mechanics on the development and analysis of the TIP5P model of liquid water, as well as work in both computational and experimental biophysics on proteins and protein-nucleic acid interactions.