吳恩達機器學習 - 異常檢測

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						<p>題目連結：<a href="https://s3.amazonaws.com/spark-public/ml/exercises/on-demand/machine-learning-ex8.zip" rel="nofollow" target="_blank">點選開啟連結</a></p>
 

筆記：

資料視覺化：

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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效果圖：

求引數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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選擇最優的ε

這個用F1F1來衡量：

公式：

Code（selectThreshold.m）（注意這裡的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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效果圖（求出ε後，繼續執行ex8.m畫出的圖）：

另外還有多元高斯分佈這裡沒有實驗，但這也是一個很好的演算法，不要忘了！