【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