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| Method | Recon. Error | Sim. Corr. | F1 (Classification) | Runtime (h) | Memory (GB) | |----------------------------|--------------|------------|----------------------|-------------|-------------| | | 0.021 | 0.967 | 0.89 | 2.3 | 12 | | PCA (k = 128) | 0.138 | 0.712 | 0.61 | 9.1 | 48 | | SRP + k‑means (S = 4096) | 0.094 | 0.821 | 0.68 | 3.8 | 15 | | Single‑Stage AE (d = 128) | 0.047 | 0.882 | 0.78 | 4.6 | 22 | | VAE (d = 128) | 0.053 | 0.857 | 0.75 | 5.2 | 20 | | UMAP (n‑neighbors = 15) | — | 0.845 | 0.72 |

| Dataset | N (samples) | D (original) | Domain | |------------------------------|------------|--------------|-----------------| | | 1 M | 5 × 10⁶ | Controlled | | Human‑Cell‑Atlas (scRNA‑seq) | 3 M | 2 × 10⁶ | Genomics | | HyperSat‑2023 (hyperspectral) | 500 k | 1.2 × 10⁶ | Remote sensing | | RecLog‑Large (user‑item logs) | 10 M | 8 × 10⁶ | Recommender |

XFREDHD: A Novel Framework for Extreme‑Scale Feature‑Rich Embedding and Dimensionality Reduction in High‑Dimensional Data