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| Locally Linear Embedding (LLE)（局所線形埋め込み）× | カーネル主成分分析× | |
|---|---|---|
| 分野 | 機械学習 | 機械学習 |
| 系統≠ | Machine learning | Latent structure |
| 提唱年≠ | 2000 | 1998 |
| 提唱者≠ | Sam Roweis & Lawrence Saul | Schölkopf, B.; Smola, A. J.; Müller, K.-R. |
| 種類≠ | Nonlinear manifold dimensionality reduction | Nonlinear dimensionality reduction via kernel trick |
| 原典≠ | Roweis, S. T., & Saul, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500), 2323–2326. DOI ↗ | Schölkopf, B., Smola, A. J., & Müller, K.-R. (1998). Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10(5), 1299–1319. DOI ↗ |
| 別名 | LLE, manifold learning, nonlinear dimensionality reduction, yerel doğrusal gömme | KPCA, kernel PCA, nonlinear PCA via kernel trick, kernel eigenvalue decomposition |
| 関連≠ | 3 | 5 |
| 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. | Kernel Principal Component Analysis (Kernel PCA) is a nonlinear dimensionality-reduction method introduced by Bernhard Schölkopf, Alexander Smola, and Klaus-Robert Müller in 1997–1998. It extends classical linear PCA to curved, non-linear data manifolds by implicitly mapping input data into a high-dimensional feature space via a kernel function, then performing standard PCA in that space — all without ever computing the mapping explicitly. |
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