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| Locally Linear Embedding (LLE)（局所線形埋め込み）× | 行列補完× | |
|---|---|---|
| 分野 | 機械学習 | 機械学習 |
| 系統 | Machine learning | Machine learning |
| 提唱年≠ | 2000 | 2009 |
| 提唱者≠ | Sam Roweis & Lawrence Saul | Emmanuel Candès & Benjamin Recht |
| 種類≠ | Nonlinear manifold dimensionality reduction | Convex low-rank recovery |
| 原典≠ | Roweis, S. T., & Saul, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500), 2323–2326. DOI ↗ | Candès, E. J., & Recht, B. (2009). Exact matrix completion via convex optimization. Foundations of Computational Mathematics, 9(6), 717–772. DOI ↗ |
| 別名 | LLE, manifold learning, nonlinear dimensionality reduction, yerel doğrusal gömme | Nuclear Norm Minimization, Collaborative Filtering via Low-Rank Recovery, Inductive Matrix Completion, Matris Tamamlama |
| 関連≠ | 3 | 2 |
| 概要≠ | Locally linear embedding, introduced by Sam Roweis and Lawrence Saul in 2000, is a manifold-learning method for nonlinear dimensionality reduction. It assumes that although data may curve through a high-dimensional space, each point and its neighbours lie approximately on a flat patch. LLE captures each point as a weighted combination of its neighbours and then finds a low-dimensional layout that preserves those same local relationships, unrolling curved structure into a faithful low-dimensional map. | Matrix Completion is a technique for recovering a low-rank matrix from a small, possibly random subset of its entries. Introduced by Emmanuel Candès and Benjamin Recht in 2009, it reformulates the problem as nuclear norm minimization — a convex surrogate for rank minimization — and provides theoretical guarantees that exact recovery is achievable when entries are observed uniformly at random and the matrix satisfies an incoherence condition. |
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