AI-025: 练习：Anomaly Detection

通过数据的高斯分布来判断新数据是否是异常，步骤：

1. 根据公式计算高斯参数：mu和sigma
2. 计算交叉验证数据的F1 score评估，来获取最优阈值epsilon
3. 通过1、2获取的参数，可以预估新数据的数值；

原始数据：

数据分布：

1. 根据公式计算高斯参数：mu和sigma

estimateGaussian.m

function [mu sigma2] = estimateGaussian(X)
%ESTIMATEGAUSSIAN This function estimates the parameters of a 
%Gaussian distribution using the data in X
%   [mu sigma2] = estimateGaussian(X), 
%   The input X is the dataset with each n-dimensional data point in one row
%   The output is an n-dimensional vector mu, the mean of the data set
%   and the variances sigma^2, an n x 1 vector
% 

% Useful variables
[m, n] = size(X);

% You should return these values correctly
mu = zeros(n, 1);
sigma2 = zeros(n, 1);

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the mean of the data and the variances
%               In particular, mu(i) should contain the mean of
%               the data for the i-th feature and sigma2(i)
%               should contain variance of the i-th feature.
%

mu = 1/m.*sum(X,1)';%对每个特征的训练数据求均值, sum(X,1)是矩阵X每列求和, mu(n,1)
sigma2 = 1/m.*(sum((X-repmat(mu', m, 1)).^2))';%repmat 将mu‘(1,n) 复制m行1列，这样跟X(m,n)可以做减法运算；

%另一种计算方式
%mu = sum(X)' / m;
%temp = X' - repmat(mu, 1, m);
%sigma2 = sum(temp.^2,2) / m;

% =============================================================


end

根据计算的高斯参数绘制概率等高线：

2. 计算交叉验证数据的F1 score评估，来获取最优阈值epsilon

selectThreshold.m

function [bestEpsilon bestF1] = selectThreshold(yval, pval)
%SELECTTHRESHOLD Find the best threshold (epsilon) to use for selecting
%outliers
%   [bestEpsilon bestF1] = SELECTTHRESHOLD(yval, pval) finds the best
%   threshold to use for selecting outliers based on the results from a
%   validation set (pval) and the ground truth (yval).
%

bestEpsilon = 0;
bestF1 = 0;
F1 = 0;

stepsize = (max(pval) - min(pval)) / 1000;
for epsilon = min(pval):stepsize:max(pval)
    
    % ====================== YOUR CODE HERE ======================
    % Instructions: Compute the F1 score of choosing epsilon as the
    %               threshold and place the value in F1. The code at the
    %               end of the loop will compare the F1 score for this
    %               choice of epsilon and set it to be the best epsilon if
    %               it is better than the current choice of epsilon.
    %               
    % Note: You can use predictions = (pval < epsilon) to get a binary vector
    %       of 0's and 1's of the outlier predictions

	%方法1 矩阵形式
	cvPrediction = pval < epsilon;
	tp = sum((cvPrediction == 1) & (yval == 1));
	fp = sum((cvPrediction == 1) & (yval == 0));
	fn = sum((cvPrediction == 0) & (yval == 1));
	
	%方法2
	%m = size(yval, 1);
	%tp = 0;
	%fp = 0;
	%fn = 0;
	%for i=1:m
	
	%	if(yval(i,1) == 1 && pval(i,1) < epsilon)
	%		tp = tp + 1;
	%	end
	%	if(yval(i,1) == 0 && pval(i,1) < epsilon)
	%		fp = fp +1;
	%	end	
	%	if(yval(i,1) == 1 && pval(i,1) > epsilon)
	%		fn = fn + 1;
	%	end
	%end
	
	prec = tp / (tp + fp);
	rec = tp / (tp + fn);
	
	F1 = 2 * prec * rec / (prec + rec);
	
    % =============================================================

    if F1 > bestF1
       bestF1 = F1;
       bestEpsilon = epsilon;
    end
end

end

3. 通过1、2获取的参数，可以预估新数据的数值；

最后，通过编写的函数计算多维的数据：