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

源地址：

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