模式识别Chapter 6-4 Fisher LD.pptVIP

* Pattern Recognition 北京交通大学 电子信息工程学院 * Contents Introduction Single layer neural networks Application single layer neural network Multi-layer neural networks * Application single layer neural network Problems of dimensionality -- Principal Component Analysis (PCA) -- Fisher Linear Discriminant (FLD) Polynomial Neural Network (PNN) * Problems of dimensionality Dimensionality reduction -- Principal Component Analysis (PCA) -- Fisher Linear Discriminant (FLD) * PCA finds components that are useful for representing data, there is no reason to assume that these components must be useful for discriminating between data in deferent classes. Principal Component Analysis (PCA) * * Fisher Linear Discriminant (FLD) 数据表示与数据分类 PCA 找到了在更低维空间的最精确的数据表示方法: -- 在最大方差的方向投影数据 。 但最大方差方向未必对于分类有用。 * Fisher Linear Discriminant (FLD) Main idea: find a best direction such that the projection onto this line can be easily separated. * Fisher Linear Discriminant (FLD) Suppose that we have a set of n d-dimensional samples . in the subset labeled in the subset labeled If , is the projection of the corresponding onto a line in the direction of . Find a best direction * Fisher Linear Discriminant (FLD) Find a best direction which will enable accurate classification. A measure of the separation between the projected points is the difference of the sample means. * Fisher Linear Discriminant (FLD) The sample mean for the projected points is given by: * Fisher Linear Discriminant (FLD) The sample mean for the projected points is given by: We can make this difference as large as we wish merely by scaling W * Fisher Linear Discriminant (FLD) Define the scatter for projected samples. * Fisher Linear Discriminant (FLD) Define the scatter for projected samples. is an estimate of the variance of the pooled data. is calle