Principal Component Analysis (PCA)
Principal Component Analysis (PCA)
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DOI：
10.1201/b10345-5
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发表时间：
2010-11
期刊：
影响因子：
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通讯作者：
Kim-Anh Lê Cao;Z. Welham
中科院分区：
文献类型：
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作者：
Kim-Anh Lê Cao;Z. Welham
·高维空间中的模式识别-当在高维空间（例如，（Curse of Dimensionality）显著的改进可以通过首先将数据映射到低维空间来实现。x = a 1 a 2. a N −−>降维−−> y = B 1 B 2. B K降维（K << N）-PCA的目标是降低数据的维数，同时尽可能多地保留原始数据集中存在的变化。PCA允许我们计算线性变换，将数据从高维空间映射到低维空间。B 1 = t 11 a 1 + t 12 a 2 +.+ t 1n a N B 2 = t 21 a 1 + t 22 a 2 +.+ t 2n a N. B K = t K 1 a 1 + t K 2 a 2 +.+ t KN a N or y = Tx其中T = 11 t 21. t K 1 t 12 t 22.
• Patternrecognition in high-dimensional spaces-P roblems arise when performing recognition in a high-dimensional space (e.g., curse of dimensionality).-S ignificant improvements can be achievedb yfi rst mapping the data into a lower-dimensionality space. x = a 1 a 2 ... a N −−> reduce dimensionality −−> y = b 1 b 2 ... b K (K << N)-The goal of PCA is to reduce the dimensionality of the data while retaining as much as possible of the variation present in the original dataset. • Dimensionality reduction-PCA allows us to compute a linear transformation that maps data from a high dimensional space to a lower dimensional space. b 1 = t 11 a 1 + t 12 a 2 +...+t 1n a N b 2 = t 21 a 1 + t 22 a 2 +...+t 2n a N ... b K = t K 1 a 1 + t K 2 a 2 +...+t KN a N or y = Tx where T = t 11 t 21 ... t K 1 t 12 t 22 ...