Following the manifold hypothesis we develop and employ methodologies for understanding the topology of high dimensional data in it's native space. Our techniques span from the application of the diffusion operator to neural manifold learning

We learn representations of complex affinities by creating easy to represent spaces. We make these spaces amenable for downstream analysis and apply these procedures to challenges such as drug discovery and neuroscience. Often this includes construction of graphs and signal processing thereon to denoise, impute, and study our data.

The data acquisition method can restrict insights gained, such as static snapshots hindering analysis of continuous processes. We specializatize in characterizing data representations, constructing a unified representation of static snapshots respecting the entire process, and leveraging optimal transport (OT) for understanding data dynamics.

We explore Multiscale Graph Signal Processing, applying graph theory to dissect complex signals across various scales. We design innovative tools for robust signal analysis, aiding in anomaly detection, community detection, and graph visualization.

Combining all our prior efforts, we apply them to high dimensional, high throughput data to unravel the mysteries of biomedical systems including: stem cell development, behavioral neuroscience, molecular neuroscience, immunology, cancer, and structural biology.