Xfredhd -

Resulting sketch (\tildeX) ∈ ℝ^N × S is , can be computed on‑the‑fly, and fits comfortably in GPU memory for S ≈ 10³–10⁴.

XFREDHD: A Novel Framework for Extreme‑Scale Feature‑Rich Embedding and Dimensionality Reduction in High‑Dimensional Data Authors: Dr. A. M. Sanchez¹, Prof. L. K. Rao², Dr. J. H. Miller³ xfredhd

| Domain | Typical Dimensionality | Example | |----------------------------|------------------------|-----------------------------------------| | Genomics & Transcriptomics | 10⁶ – 10⁸ | Single‑cell RNA‑seq expression matrices | | Remote Sensing | 10⁴ – 10⁶ | Hyperspectral cubes (hundreds of bands) | | Recommender Systems | 10⁶ – 10⁹ | User–item interaction tensors | | Natural Language Processing| 10⁵ – 10⁷ | Contextualized token embeddings | Resulting sketch (\tildeX) ∈ ℝ^N × S is

[ \mathcalL \textGPR = \frac1\sum (i,j)\in E\bigl(\textsim Z(z_i, z_j) - \textsim \tildeX(\tildex_i, \tildex_j)\bigr)^2 ] j)\in E\bigl(\textsim Z(z_i

¹ Department of Computer Science, University of Valencia, Spain ² Department of Electrical Engineering, Indian Institute of Technology Delhi, India ³ Data Science Lab, Stanford University, USA