Machine learningDimensionality reduction
随机投影
随机投影通过与随机矩阵相乘来降低维度，它依赖于 Johnson-Lindenstrauss 引理（1984），该引理保证将数据投影到足够多的随机方向上可以近似保留所有成对距离。与 PCA 不同，它根本不分析数据——投影是随机的且与数据无关——这使得它成本极低，非常适合高维数据以及流式或隐私敏感的场景。
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来源
- Johnson, W. B., & Lindenstrauss, J. (1984). Extensions of Lipschitz mappings into a Hilbert space. Contemporary Mathematics, 26, 189–206. DOI: 10.1090/conm/026/737400 ↗
- Achlioptas, D. (2003). Database-friendly random projections: Johnson-Lindenstrauss with binary coins. Journal of Computer and System Sciences, 66(4), 671–687. DOI: 10.1016/S0022-0000(03)00025-4 ↗
如何引用本页
ScholarGate. (2026, June 2). Random Projection (Johnson-Lindenstrauss Dimensionality Reduction). ScholarGate. https://scholargate.app/zh/machine-learning/random-projection
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