Silvia D'Angelo, Trinity College Dublin
Title: Data compression for fast dimension reduction and clustering of high-dimensional discrete data
Date: Tuesday, July 28th 2026
Time: 1:30PM (PDT)
Location: ASB 10900
Abstract: High-dimensional discrete data are common in genomics, microbiomics, survey research, and digital behavioural analysis. Clustering such data is challenging because many existing methods are computationally expensive, sensitive to sparsity and discreteness, or designed for specific data types. We introduce a deterministic dimension-reduction framework for clustering high-dimensional discrete observations. The approach compresses observations into a low-dimensional continuous representation using weighted sums derived from a scaled positional encoding, yielding a numerically stable transformation applicable to both binary and count data. Several theoretical properties are established. The compression mapping is injective, ensuring that distinct observations remain distinguishable after transformation. Under mild regularity conditions, the compressed variables are approximately Gaussian, supporting the use of model-based clustering in the reduced space. We further show that separation between cluster centroids is preserved, indicating that location-based cluster structure remains identifiable following dimension reduction. Simulation studies demonstrate accurate cluster recovery across diverse settings, while achieving substantial computational savings compared with commonly used dimension-reduction techniques. Applications to microbiome data and United Nations rolling call voting data highlight the method's practical utility. Overall, the framework offers a scalable, efficient, and broadly applicable solution for clustering high-dimensional discrete data.
(Joint work with Michael Fop)