CosMAP: Contrastive Manifold Approximation and Projection for Dimensionality Reduction of Omics and Genealogical Data

Modern high-dimensional datasets—such as single-cell RNA sequencing and large genealogical kinship records—are typically sparse, noisy, and challenging to project into low-dimensional spaces without distorting local neighborhoods or global organization. Existing graph-based dimensionality reduction methods often rely on fixed neighborhood graphs constructed from raw metrics, making them vulnerable to the curse of dimensionality and unstable edges.

To address this, the authors introduce Contrastive Manifold Approximation and Projection (CosMAP). CosMAP extends standard graph-based frameworks by utilizing cosine-similarity neighborhoods combined with temperature-normalized contrastive affinities. To mitigate the impact of unstable high-dimensional graph edges, CosMAP introduces a two-phase refinement strategy: it first learns an intermediate higher-dimensional representation, reconstructs a more reliable neighborhood graph from this intermediate space, and then initializes and optimizes the final low-dimensional embedding.

The authors evaluate CosMAP across diverse datasets, including MNIST and USPS handwritten digits, mouse retina and cortex single-cell RNA-sequencing data, and a large genealogical kinship dataset derived from BALSAC-CARTaGENE. Compared with state-of-the-art dimensionality reduction methods such as t-SNE, UMAP, PaCMAP, and LocalMAP, CosMAP produces more visually coherent representations. It improves neighborhood preservation and provides clearer global organization of distinct classes, biological cell populations, and regional genealogical patterns without requiring class labels during optimization.

Exploratory data analysis in genomics, single-cell biology, and genealogy heavily depends on reliable low-dimensional visualizations to uncover hidden cell states, tumor heterogeneity, or population structures. By integrating cosine similarity, contrastive learning principles, and a multi-phase graph refinement strategy, CosMAP offers a robust framework that reduces structural distortions in sparse, high-dimensional settings, thereby supporting more trustworthy data-driven discoveries.