白化
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下面我们先用前文的2D例子描述白化的主要思想,然后分别介绍如何将白化与平滑和PCA相结合。 | 下面我们先用前文的2D例子描述白化的主要思想,然后分别介绍如何将白化与平滑和PCA相结合。 | ||
在前文计算<math>x_{rot}^{(i)}=U^Tx^{(i)}</math>时我们实际上已经消除了输入特征<math>x^{(i)}</math>之间的相关性。得到的新特征<math>x_{rot}</math>的分布如下图所示: | 在前文计算<math>x_{rot}^{(i)}=U^Tx^{(i)}</math>时我们实际上已经消除了输入特征<math>x^{(i)}</math>之间的相关性。得到的新特征<math>x_{rot}</math>的分布如下图所示: | ||
+ | |||
+ | [[File:PCA-rotated.png | 600px]] | ||
+ | |||
+ | :【原文】: | ||
+ | The covariance matrix of this data is given by: | ||
+ | |||
+ | <math>\begin{align} | ||
+ | \begin{bmatrix} | ||
+ | 7.29 & 0 \\ | ||
+ | 0 & 0.69 | ||
+ | \end{bmatrix}. | ||
+ | \end{align}</math> | ||
+ | |||
+ | (Note: Technically, many of the | ||
+ | statements in this section about the "covariance" will be true only if the data | ||
+ | has zero mean. In the rest of this section, we will take this assumption as | ||
+ | implicit in our statements. However, even if the data's mean isn't exactly zero, | ||
+ | the intuitions we're presenting here still hold true, and so this isn't something | ||
+ | that you should worry about.) | ||
+ | |||
+ | :【初译】: | ||
+ | 数据的协方差矩阵如下: | ||
+ | |||
+ | (注: 严格地讲, 这部分许多关于“协方差”的陈述仅当数据以0为均值时成立。接下来,我们将这一假设作为隐含条件。然而,即使数据不以0为均值,我们在这里提出的仍然保持正确,因此读者无需担心。) | ||
+ | |||
+ | :【一校】: | ||
+ | 数据的协方差矩阵如下: | ||
+ | |||
+ | (注: 严格地讲, 这部分许多关于“协方差”的陈述仅当数据均值为0时成立。下文的论述都隐式地假定这一条件成立。不过即使数据均值不为0,下文的说法仍然成立。) |