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| カーネル主成分分析× | 主成分分析× | |
|---|---|---|
| 分野 | 機械学習 | 機械学習 |
| 系統≠ | Latent structure | Machine learning |
| 提唱年≠ | 1998 | 2002 |
| 提唱者≠ | Schölkopf, B.; Smola, A. J.; Müller, K.-R. | Jolliffe, I.T. (textbook); Pearson & Hotelling (origins) |
| 種類≠ | Nonlinear dimensionality reduction via kernel trick | Unsupervised dimensionality reduction |
| 原典≠ | Schölkopf, B., Smola, A. J., & Müller, K.-R. (1998). Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10(5), 1299–1319. DOI ↗ | Jolliffe, I.T. (2002). Principal Component Analysis (2nd ed.). Springer. DOI ↗ |
| 別名 | KPCA, kernel PCA, nonlinear PCA via kernel trick, kernel eigenvalue decomposition | Temel Bileşenler Analizi (PCA), PCA, principal components analysis, Karhunen-Loève transform |
| 関連≠ | 5 | 3 |
| 概要≠ | 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. | Principal Component Analysis (PCA) is an unsupervised dimensionality-reduction method — given its modern textbook treatment by Ian Jolliffe (2002) — that compresses high-dimensional data into fewer dimensions while preserving the maximum possible variance. It re-expresses correlated variables as a small set of uncorrelated principal components ordered by how much of the data's variation each one captures. |
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