Principal Components Analysis

目录

• Principal Components Analysis
  • Intuition
  • Formalization

Intuition

PCA tries to identify the subspace in which the data approximately lies.

Intuitively, we choose a direction for projection and we reserve the most variance / difference.

Formalization

\[\frac{1}{m}\sum_{i=1}^m (x^{{(i)}^T} u)^2=u^T(\frac{1}{m}\sum_{i=1}^m x^{(i)}x^{(i)^T})u \]

so the problem is transferred to choosing a eigenvector that maximize eigenvalue.

choose top k eigenvalue to reduce data dimension from \(\R^n\) down to \(\R^k\)

标签：分析,eigenvalue,frac,sum,成分,choose,Components,data
来源： https://www.cnblogs.com/BUAA-Stargazer/p/16625526.html