Dimensionality Reduction for Cyclic Compositional Data

clrcycle learns a cyclic feature ordering by maximizing variance captured by the first Fourier mode and projects samples onto cosine/sine coordinates to assign each a phase and radius.

• Why it matters: Standard dimensionality reduction can detect periodic gene-expression variation but does not connect a sample’s position on a cycle to an ordering of molecular features defining it.
• What they did: The method applies a centered log-ratio transformation, fits a Fourier circle, and uses the resulting two-dimensional geometry to quantify phase and projection magnitude. It recovers temporal organization in a mouse circadian atlas, represents FUCCI cell-cycle phase more reliably than conventional 2D embeddings, and learns a circular coordinate from 250 highly variable genes in human endometrium.
• The result: In mice, it reveals tissue-specific differences in rhythmic timing; in FUCCI-profiled single cells, it more reliably represents independently measured cell-cycle phase; in human endometrium, it recovers menstrual-stage organization and can stage unseen biopsies.