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with hyper‑parameters (\lambda_k, \lambda_g) tuned via Bayesian optimization.

High‑dimensional data arise in numerous domains:

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| Metric | Definition | |----------------------------|------------------------------------------| | | ‖X − \hatX‖₂ / ‖X‖₂ | | Similarity Preservation | Pearson correlation of pairwise cosine similarities (pre‑ vs. post‑embedding) | | Downstream Accuracy | Classification F1 (for labeled subsets) | | Runtime | End‑to‑end wall‑clock time (hours) | | Memory Footprint | Peak GPU memory usage (GB) |

tackles these obstacles by:

[ \tildex i[b] = \sum f:h(f)=b s(f) \cdot x_i[f] ]

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

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