原
吴恩达机器学习 - 异常检测
笔记：
数据可视化：
load('ex8data1.mat');
% Visualize the example dataset
plot(X(:, 1), X(:, 2), 'bx');
axis([0 30 0 30]);
xlabel('Latency (ms)');
ylabel('Throughput (mb/s)');
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效果图：
求参数μ和σ2σ2：
公式：
Code（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 = mean(X)';
sigma2 = (sum(bsxfun(@minus,X,mu').^2)./m)';
% =============================================================
end
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选择最优的ε
这个用F1F1来衡量：
公式：
Code（selectThreshold.m）（注意这里的true position,false position,false negative的求法）：
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
predictions = pval < epsilon;
tp = sum((predictions == 1) & (yval == 1)); %true positive
fp = sum((predictions == 1) & (yval == 0)); %false positive
fn = sum((predictions == 0) & (yval == 1)); %false negative
prec = tp/(tp+fp); %precision
rec = tp/(tp+fn); %recall
F1 = 2*prec*rec/(prec+rec);
% =============================================================
if F1 > bestF1
bestF1 = F1;
bestEpsilon = epsilon;
end
end
end
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效果图（求出ε后，继续运行ex8.m画出的图）：
另外还有多元高斯分布这里没有实验，但这也是一个很好的算法，不要忘了！