Xfredhd 2021 < Cross-Platform >

Theoretical guarantee: With high probability, for any two samples i , j :

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 xfredhd

[ \textsim_X (x_i, x_j) \approx \textsim_Z (f(x_i), f(x_j)) ] Theoretical guarantee: With high probability, for any two

| 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 | Theoretical guarantee: With high probability

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