Precision/Recall和ROC曲線原理以及Matlab源碼

查准率和查全率是資訊檢索效率評價的兩個定量指標，不僅可以用來評價每次檢索的準確性和全面性，也是在資訊檢索系統評價中衡量系統檢索效能的重要方面。

查准率（Precision ratio，簡稱為P），是指檢出的相關文獻數占檢出文獻總數的百分比。查准率反映檢索準確性，其補數就是誤檢率。

查全率（Recall ratio，簡稱為R），是指檢出的相關文獻數占系統中相關文獻總數的百分比。查全率反映檢索全面性，其補數就是漏檢率。

查全率＝（檢索出的相關資訊量/系統中的相關資訊總量）*100%

查准率＝（檢索出的相關資訊量/檢索出的資訊總量）*100%

前者是衡量檢索系統和檢索者檢出相關資訊的能力，後者是衡量檢索系統和檢索者拒絕非相關資訊的能力。兩者合起來，即表示檢索效率。

利用查准率和查全率指標，可以對每一次檢索進行檢索效率的評價，為檢索的改進調整提供依據。利用這兩個量化指標，也可以對資訊檢索系統的效能水平進行評價。要評價資訊檢索系統的效能水平，就必須在一個檢索系統中進行多次檢索。每進行一次檢索，都計算其查准率和查全率，並以此作為座標值，在平面座標圖上標示出來。通過大量的檢索，就可以得到檢索系統的效能曲線。實驗證明，在查全率和查准率之間存在著相反的相互依賴關係--如果提高輸出的查全率，就會降低其查准率，反之亦然。

網上源碼有很多，這裡找到了一個是Stefan Schroedl寫的，跟大家分享一下：

function [prec, tpr, fpr, thresh] = prec_rec(score, target, varargin)% PREC_REC - Compute and plot precision/recall and ROC curves.%%   PREC_REC(SCORE,TARGET), where SCORE and TARGET are equal-sized vectors,%   and TARGET is binary, plots the corresponding precision-recall graph%   and the ROC curve.%%   Several options of the form PREC_REC(...,'OPTION_NAME', OPTION_VALUE)%   can be used to modify the default behavior.%      - 'instanceCount': Usually it is assumed that one line in the input%                         data corresponds to a single sample. However, it%                         might be the case that there are a total of N%                         instances with the same SCORE, out of which%                         TARGET are classified as positive, and (N -%                         TARGET) are classified as negative. Instead of%                         using repeated samples with the same SCORE, we%                         can summarize these observations by means of this%                         option. Thus it requires a vector of the same%                         size as TARGET.%      - 'numThresh'    : Specify the (maximum) number of score intervals.%                         Generally, splits are made such that each%                         interval contains about the same number of sample%                         lines.%      - 'holdFigure'   : [0,1] draw into the current figure, instead of%                         creating a new one.%      - 'style'        : Style specification for plot command.%      - 'plotROC'      : [0,1] Explicitly specify if ROC curve should be%                         plotted.%      - 'plotPR'       : [0,1] Explicitly specify if precision-recall curve%                         should be plotted.%      - 'plotBaseline' : [0,1] Plot a baseline of the random classifier.%%   By default, when output arguments are specified, as in%         [PREC, TPR, FPR, THRESH] = PREC_REC(...),%   no plot is generated. The arguments are the score thresholds, along%   with the respective precisions, true-positive, and false-positive%   rates.%%   Example:%% x1 = rand(1000, 1);% y1 = round(x1 + 0.5*(rand(1000,1) - 0.5));% prec_rec(x1, y1);% x2 = rand(1000,1);% y2 = round(x2 + 0.75 * (rand(1000,1)-0.5));% prec_rec(x2, y2, 'holdFigure', 1);% legend('baseline','x1/y1','x2/y2','Location','SouthEast'); % Copyright @ 9/22/2010 Stefan Schroedl% Updated     3/16/2010 optargin = size(varargin, 2);stdargin = nargin - optargin; if stdargin < 2 error('at least 2 arguments required');end % parse optional argumentsnum_thresh = -1;hold_fig = 0;plot_roc = (nargout <= 0);plot_pr  = (nargout <= 0);instance_count = -1;style = '';plot_baseline = 1; i = 1;while (i <= optargin) if (strcmp(varargin{i}, 'numThresh')) if (i >= optargin) error('argument required for %s', varargin{i}); else num_thresh = varargin{i+1}; i = i + 2; end elseif (strcmp(varargin{i}, 'style')) if (i >= optargin) error('argument required for %s', varargin{i}); else style = varargin{i+1}; i = i + 2; end elseif (strcmp(varargin{i}, 'instanceCount')) if (i >= optargin) error('argument required for %s', varargin{i}); else instance_count = varargin{i+1}; i = i + 2; end elseif (strcmp(varargin{i}, 'holdFigure')) if (i >= optargin) error('argument required for %s', varargin{i}); else if ~isempty(get(0,'CurrentFigure')) hold_fig = varargin{i+1}; end i = i + 2; end elseif (strcmp(varargin{i}, 'plotROC')) if (i >= optargin) error('argument required for %s', varargin{i}); else plot_roc = varargin{i+1}; i = i + 2; end elseif (strcmp(varargin{i}, 'plotPR')) if (i >= optargin) error('argument required for %s', varargin{i}); else plot_pr = varargin{i+1}; i = i + 2; end elseif (strcmp(varargin{i}, 'plotBaseline')) if (i >= optargin) error('argument required for %s', varargin{i}); else plot_baseline = varargin{i+1}; i = i + 2; end elseif (~ischar(varargin{i})) error('only two numeric arguments required'); else error('unknown option: %s', varargin{i}); endend [nx,ny]=size(score); if (nx~=1 && ny~=1) error('first argument must be a vector');end [mx,my]=size(target);if (mx~=1 && my~=1) error('second argument must be a vector');end score  =  score(:);target = target(:); if (length(target) ~= length(score)) error('score and target must have same length');end if (instance_count == -1) % set default for total instances instance_count = ones(length(score),1); target = max(min(target(:),1),0); % ensure binary targetelse if numel(instance_count)==1 % scalar instance_count = instance_count * ones(length(target), 1); end [px,py] = size(instance_count); if (px~=1 && py~=1) error('instance count must be a vector'); end instance_count = instance_count(:); if (length(target) ~= length(instance_count)) error('instance count must have same length as target'); end target = min(instance_count, target);end if num_thresh < 0 % set default for number of thresholds score_uniq = unique(score); num_thresh = min(length(score_uniq), 100);end qvals = (1:(num_thresh-1))/num_thresh;thresh = [min(score) quantile(score,qvals)];% remove identical binsthresh = sort(unique(thresh),2,'descend');total_target = sum(target);total_neg = sum(instance_count - target); prec = zeros(length(thresh),1);tpr  = zeros(length(thresh),1);fpr  = zeros(length(thresh),1);for i = 1:length(thresh) idx     = (score >= thresh(i)); fpr(i)  = sum(instance_count(idx) - target(idx)); tpr(i)  = sum(target(idx)) / total_target; prec(i) = sum(target(idx)) / sum(instance_count(idx));endfpr = fpr / total_neg; if (plot_pr || plot_roc)  % draw  if (~hold_fig) figure if (plot_pr) if (plot_roc) subplot(1,2,1); end  if (plot_baseline) target_ratio = total_target / (total_target + total_neg); plot([0 1], [target_ratio target_ratio], 'k'); end  hold on hold all  plot([0; tpr], [1 ; prec], style); % add pseudo point to complete curve  xlabel('recall'); ylabel('precision'); title('precision-recall graph'); end if (plot_roc) if (plot_pr) subplot(1,2,2); end  if (plot_baseline) plot([0 1], [0 1], 'k'); end  hold on; hold all;  plot([0; fpr], [0; tpr], style); % add pseudo point to complete curve  xlabel('false positive rate'); ylabel('true positive rate'); title('roc curve'); %axis([0 1 0 1]); if (plot_roc && plot_pr) % double the width rect = get(gcf,'pos'); rect(3) = 2 * rect(3); set(gcf,'pos',rect); end end  else if (plot_pr) if (plot_roc) subplot(1,2,1); end plot([0; tpr],[1 ; prec], style); % add pseudo point to complete curve end  if (plot_roc) if (plot_pr) subplot(1,2,2); end plot([0; fpr], [0; tpr], style); end endend

源地址：

http://www.zhizhihu.com/html/y2010/2137.html