tailieunhanh - Computational Statistics Handbook with MATLAB phần 7

Chúng tôi bắt đầu bằng cách thành lập các tỷ lệ khả năng sử dụng các mục tiêu không (ω 2) quan sát và qua xác nhận để có được sự phân bố của các tỷ lệ khả năng xảy ra khi các thành viên lớp học thực sự là ω 2. | FIGURE In this figure we see the decision regions for deciding whether a feature corresponds to the target class or the non-target class. Lr x P x 1 - --- . P x 2 We start off by forming the likelihood ratios using the non-target ffl2 observations and cross-validation to get the distribution of the likelihood ratios when the class membership is truly ffl2. We use these likelihood ratios to set the threshold that will give us a specific probability of false alarm. Once we have the thresholds the next step is to determine the rate at which we correctly classify the target cases. We first form the likelihood ratio for each target observation using cross-validation yielding a distribution of likelihood ratios for the target class. For each given threshold we can determine the number of target observations that would be correctly classified by counting the number of Lr that are greater than that threshold. These steps are described in detail in the following procedure. cross-validation for specified false alarm rate 1. Given observations with class labels ffl1 target and ffl2 nontarget set desired probabilities of false alarm and a value for k. 2002 by Chapman Hall CRC 2. Leave k points out of the non-target class to form a set of test cases denoted by TEST. We denote cases belonging to class 2 as x 2 . 3. Estimate the class-conditional probabilities using the remaining n2- k non-target cases and the n1 target cases. 4. For each of those k observations form the likelihood ratios Lr X2 x ĩ1 x 2 in TEST. P x 2 2 5. Repeat steps 2 through 4 using all of the non-target cases. 6. Order the likelihood ratios for the non-target class. 7. For each probability of false alarm find the threshold that yields that value. For example if the P FA then the threshold is given by the quantile of the likelihood ratios. Note that higher values of the likelihood ratios indicate the target class. We now have an array of thresholds corresponding to each probability of false .