The Johnson-Lindenstrauss Lemma for Clustering and Subspace Approximation: From Coresets to Dimension Reduction
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Bibliographic record
Abstract
We study the effect of Johnson-Lindenstrauss transforms in various projective clustering problems, generalizing results which only applied to center-based clustering [40]. We ask the general question: for a Euclidean optimization problem and an accuracy parameter ε ∈ (0,1), what is the smallest target dimension t ∈ ℕ such that a Johnson-Lindenstrauss transform Π : ℝd → ℝt preserves the cost of the optimal solution up to a (1 + ε )-factor. We give a new technique which uses coreset constructions to analyze the effect of the Johnson-Lindenstrauss transform. Our technique, in addition applying to center-based clustering, improves on (or is the first to address) other Euclidean optimization problems, including:
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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