模式識別課后習題英文

1、Pattern Recognition Theory and Its ApplicationPROBLEMS2.5 (1) 對C類情況推廣最小錯誤率貝葉斯決策規(guī)則； (2)指出此時使最小錯誤率最小等價于后驗概率最大，即 對一切。2.5 (1) Generalize the minimum error Bayes decision rule in case of class C; (2) Show that the minimum error rate is equivalent to the maximum posterior probability, namely where and .2.

2、6 對兩類問題，證明最小風險貝葉斯決策規(guī)則可表示為若 。2.6 In the two-category case, show that the minimum risk Bayes decision rule may be expressed as if .2.7 若，證明此時最小最大決策面是來自兩類的錯誤率相等。2.7 Consider minimax criterion for and.Prove that in this case .2.22 似然比決策準則為若 則 付對數(shù)似然比為，當是均值向量為 和協(xié)方差矩陣為的正態(tài)分布時：（1） 試推導出，并指出其決策規(guī)則；（2） 當時，推導及其決策

3、規(guī)則；（3） 分析（1），（2）兩種情況下的決策面類型。2.22 Likelihood ratio decision rules can be expressed as if .minus-log-likelihood ratio can be expressed as ,where .(1) Deduce and find the decision rule;(2) Let .Find the decision rule;(3)Analyze the decision surface types in question(1) and question(2).2.23 二維正態(tài)分布，,。試寫出

4、負對數(shù)似然比決策規(guī)則。2.23 Let ，,。Find the minus-log-likelihood ratio decision rule。2.24 在2.23中，若，寫出負對數(shù)似然比規(guī)則。2.24 Let ， .Find the minus-log-likelihood ratio decision rule under the condition of exercise 5 習題2.24 的情況下，若考慮損失函數(shù)，畫出似然比閾與錯誤率之間的關(guān)系。(1) 求出時完成Neyman-Pearson決策時總的錯誤率；(2) 求出最小最大決策的閾值和總的錯誤率。2.25 unde

5、r the condition of exercise 3.3，let ，.(1) Consider the Neyman-Pearson criterion , what is the error rate for ;(2) Calculate the threshold of the minimax decision and overall error rate.3.1 Consider the sample set with the distribution density, , where the prior distribution of is . Respectively calc

6、ulate the maximum likelihood estimate and the Bayesian estimation .3.2 Consider the sample set drawn from a multivariate normal population . Respectively calculate the maximum likelihood estimate of .3.3 Consider the sample set drawn from a binomial distribution , , , . Calculate the maximum likelih

7、ood estimate of the parameter.3.4 Suppose that the loss function is the quadratic function and the prior density of follows the uniform distribution , . Calculate the Bayesian estimation under the condition of exercise 4 Consider the sample set drawn from a multivariate normal distribution wh

8、ere is known. Calculate the maximum likelihood estimate of .4.4 Consider a two-dimensional linear discriminant（判別） function Transform the discriminant function into the form of , and describe the geometric figure（幾何圖形） of ;Map the discriminant function to obtain the generalized(廣義) homogeneous（齊次） l

9、inear discriminant function .Show that the X-space is actually a subspace of the Y-space, and the partition of the X-space by is the same as the partition of the X-space by in the original space. Describe it by a figure. 8.1 Given three partitions as shown in the figure below.Calculate .8.7 Given two sample sets Calculate the transform to obtain the biggest expressed by.9.1 Given two sample sets Respectively reduce the feature space dimension to and , then describe the positions of the samples in the feature space.10.5 Let , , and , and consider the following thre