principle component analysis

In book Pattern Recognition and Machine Learning, two definitions of PCA that give rise to the same algorithm: PCA is the orthogonal projection of data onto a lower dimensional linear space, known as the principle subspace such that:

1. Maximum variance formulation: the variance of the projected data is maximized (Hotelling, 1993).
2. Minimum error formulatoin: the linear projection minimizes the average projection cost, which is the mean squared distance between the data points and their projections (Pearson, 1901).

Maximum Variance Formulation

Minimum Error Formulation

Reference

link[http://blog.codinglabs.org/articles/pca-tutorial.html]PCA的数学原理

線性判別分析（Linear Discriminant Analysis）