模式识别学习笔记（3）——高斯概率密度

概率密度估计方法

参数法：只需将均值和协方差矩阵保存下来，就可知道其分布。

半参数法：GM通过解析求解；期望最大化是极大似然估计的特例，多次迭代才能求得

高斯密度函数

牢记密度函数公式！！！

把协方差矩阵对角化，即将其变为对角矩阵，除主对角线上的元素外其余元素全为0.

马氏距离相等的点构成的是等密度点轨迹.

白化变换参考：https://www.cnblogs.com/kevinGaoblog/archive/2012/06/20/2556335.html

The whitening transformation is a decorrelation method which transforms a set of random variables having the covariance matrix Σ into a set of new random variables whose covariance is aI, where a is a constant and I is the identity matrix. The new random variables are uncorrelated and all have variance 1. The method is called "whitening" because it transforms the input matrix to the form of white noise, which by definition is uncorrelated and has uniform variance. It differs from decorrelation in that the variances are made to be equal, rather than merely making the covariances zero. That is, where decorrelation results in a diagonal covariance matrix, whitening produces a scalar multiple of the identity matrix.

linear discrimination function（3 cases）

学习笔记2、3，总的内容：

贝叶斯决策的错误率是理论上的，因为贝叶斯是理想的（最优）分类器。但这个错误率很重要，因为贝叶斯错误率是我们做研究时的错误率下限，即我们的错误率一定比贝叶斯错误率高！

参考资料：

中国科学院大学硕士课《模式识别》ppt