【人工智能】算法--Precision/Recall和ROC曲线原理以及Matlab源码

查准率和查全率是信息检索效率评价的两个定量指标，不仅可以用来评价每次检索的准确性和全面性，也是在信息检索系统评价中衡量系统检索性能的重要方面。

查准率（Precision ratio，简称为P），是指检出的相关文献数占检出文献总数的百分比。查准率反映检索准确性，其补数就是误检率。

查全率（Recall ratio，简称为R），是指检出的相关文献数占系统中相关文献总数的百分比。查全率反映检索全面性，其补数就是漏检率。

查全率＝（检索出的相关信息量/系统中的相关信息总量）*100%

查准率＝（检索出的相关信息量/检索出的信息总量）*100%

前者是衡量检索系统和检索者检出相关信息的能力，后者是衡量检索系统和检索者拒绝非相关信息的能力。两者合起来，即表示检索效率。

利用查准率和查全率指标，可以对每一次检索进行检索效率的评价，为检索的改进调整提供依据。利用这两个量化指标，也可以对信息检索系统的性能水平进行评价。要评价信息检索系统的性能水平，就必须在一个检索系统中进行多次检索。每进行一次检索，都计算其查准率和查全率，并以此作为坐标值，在平面坐标图上标示出来。通过大量的检索，就可以得到检索系统的性能曲线。实验证明，在查全率和查准率之间存在着相反的相互依赖关系–如果提高输出的查全率，就会降低其查准率，反之亦然。

网上源码有很多，这里找到了一个是Stefan Schroedl写的，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 arguments

num_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});

 end

end

 

[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 target

else

 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 bins

thresh = 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));

end

fpr = 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

 end

end