Principal Component Analysis
Principal Component Analysis
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DOI：
10.1142/9789812791764_0009
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发表时间：
2008-03
期刊：
影响因子：
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通讯作者：
Martin Sewell
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文献类型：
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作者：
Martin Sewell
主成分分析（也称为主分量分析）（PCA）是一种来自统计学的简化数据集的技术。它由皮尔逊（1901年）和霍特林（1933年）提出，而最好的现代参考文献是乔利夫（2002年）。该方法的目的是在尽可能保留相关信息的同时降低多元数据的维度。它是一种无监督学习形式，因为它完全依赖于输入数据本身，而不参考相应的目标数据（要最大化的标准是方差）。PCA是一种线性变换，它将数据转换到一个新的坐标系中，使得新的变量集（主成分）是原始变量的线性函数，它们不相关，并且数据的任何投影中方差最大的位于第一个坐标，方差第二大的位于第二个坐标，依此类推。在实践中，这是通过计算整个数据集的协方差矩阵来实现的。接下来，计算协方差矩阵的特征向量和特征值，并根据特征值降序排列。需要注意的是，PCA的偏差并不总是合适的；方差低的特征实际上可能具有较高的预测相关性，这取决于应用情况。
Principal component analysis (also known as principal components analysis) (PCA) is a technique from statistics for simplifying a data set. It was developed by Pearson (1901) and Hotelling (1933), whilst the best modern reference is Jolliffe (2002). The aim of the method is to reduce the dimensionality of multivariate data whilst preserving as much of the relevant information as possible. It is a form of unsupervised learning in that it relies entirely on the input data itself without reference to the corresponding target data (the criterion to be maximized is the variance). PCA is a linear transformation that transforms the data to a new coordinate system such that the new set of variables, the principal components, are linear functions of the original variables, are uncorrelated, and the greatest variance by any projection of the data comes to lie on the first coordinate, the second greatest variance on the second coordinate, and so on. In practice, this is achieved by computing the covariance matrix for the full data set. Next, the eigenvectors and eigenvalues of the covariance matrix are computed, and sorted according to decreasing eigenvalue. Note that PCA’s bias is not always appropriate; features with low variance might actually have high predictive relevance, it depends on the application.