🤖 AI Summary
This work addresses the challenge of simultaneously preserving local neighborhoods, global structure, and population coherence when reducing the dimensionality of high-dimensional, sparse omics and lineage data. To this end, the authors propose a graph-based unsupervised dimensionality reduction method that constructs an initial neighborhood graph using cosine similarity and optimizes an attraction–repulsion objective in the embedding space via temperature-normalized contrastive affinities. A two-stage optimization strategy is introduced: first, an intermediate high-dimensional representation is used to refine the neighborhood graph and initialize the embedding; second, the final low-dimensional representation is fine-tuned. Evaluated on single-cell RNA-seq, handwritten digit, and large-scale lineage datasets, the method consistently outperforms existing approaches, yielding more coherent visualizations, superior neighborhood preservation, and clearer global structural organization.
📝 Abstract
Omics datasets, particularly single-cell RNA sequencing data, are high-dimensional, sparse, noisy, and dominated by zero values, making faithful low-dimensional representation challenging. Existing dimensionality-reduction methods may distort local neighbourhoods, global organization, or the cohesion of meaningful populations, with similar limitations arising in genealogical data. We introduce Contrastive Manifold Approximation and Projection (CosMAP), a graph-based unsupervised dimensionality-reduction method for producing faithful and interpretable embeddings. CosMAP extends the graph-based framework of UMAP by combining cosine-similarity neighbourhoods with temperature-normalized contrastive affinities, which are optimized in the embedding space using an attractive--repulsive objective. It further employs a two-phase refinement strategy: an intermediate higher-dimensional representation is first learned and then used to reconstruct the neighbourhood graph and initialize the final low-dimensional embedding. We evaluate CosMAP on MNIST and USPS handwritten-digit datasets, mouse retina and cortex single-cell RNA-sequencing datasets, and a large genealogical kinship dataset derived from BALSAC-CARTaGENE. Compared with state-of-the-art dimensionality-reduction methods, CosMAP produces more coherent visual representations, improves neighbourhood preservation, and provides clearer global organization of digit classes, biological cell populations, and regional genealogical patterns. These results indicate that CosMAP offers a robust framework for exploratory analysis of complex, sparse, high-dimensional data. The implementation is publicly available at https://github.com/FenosoaRandrianjatovo/CosMAP-dr.