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Matlab

10 years ago
%% Machine Learning Online Class
% Exercise 8 | Anomaly Detection and Collaborative Filtering
%
% Instructions
% ------------
%
% This file contains code that helps you get started on the
% exercise. You will need to complete the following functions:
%
% estimateGaussian.m
% selectThreshold.m
% cofiCostFunc.m
%
% For this exercise, you will not need to change any code in this file,
% or any other files other than those mentioned above.
%
%% Initialization
clear ; close all; clc
%% ================== Part 1: Load Example Dataset ===================
% We start this exercise by using a small dataset that is easy to
% visualize.
%
% Our example case consists of 2 network server statistics across
% several machines: the latency and throughput of each machine.
% This exercise will help us find possibly faulty (or very fast) machines.
%
fprintf('Visualizing example dataset for outlier detection.\n\n');
% The following command loads the dataset. You should now have the
% variables X, Xval, yval in your environment
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)');
fprintf('Program paused. Press enter to continue.\n');
pause
%% ================== Part 2: Estimate the dataset statistics ===================
% For this exercise, we assume a Gaussian distribution for the dataset.
%
% We first estimate the parameters of our assumed Gaussian distribution,
% then compute the probabilities for each of the points and then visualize
% both the overall distribution and where each of the points falls in
% terms of that distribution.
%
fprintf('Visualizing Gaussian fit.\n\n');
% Estimate my and sigma2
[mu sigma2] = estimateGaussian(X);
% Returns the density of the multivariate normal at each data point (row)
% of X
p = multivariateGaussian(X, mu, sigma2);
% Visualize the fit
visualizeFit(X, mu, sigma2);
xlabel('Latency (ms)');
ylabel('Throughput (mb/s)');
fprintf('Program paused. Press enter to continue.\n');
pause;
%% ================== Part 3: Find Outliers ===================
% Now you will find a good epsilon threshold using a cross-validation set
% probabilities given the estimated Gaussian distribution
%
pval = multivariateGaussian(Xval, mu, sigma2);
[epsilon F1] = selectThreshold(yval, pval);
fprintf('Best epsilon found using cross-validation: %e\n', epsilon);
fprintf('Best F1 on Cross Validation Set: %f\n', F1);
fprintf(' (you should see a value epsilon of about 8.99e-05)\n\n');
% Find the outliers in the training set and plot the
outliers = find(p < epsilon);
% Draw a red circle around those outliers
hold on
plot(X(outliers, 1), X(outliers, 2), 'ro', 'LineWidth', 2, 'MarkerSize', 10);
hold off
fprintf('Program paused. Press enter to continue.\n');
pause;
%% ================== Part 4: Multidimensional Outliers ===================
% We will now use the code from the previous part and apply it to a
% harder problem in which more features describe each datapoint and only
% some features indicate whether a point is an outlier.
%
% Loads the second dataset. You should now have the
% variables X, Xval, yval in your environment
load('ex8data2.mat');
% Apply the same steps to the larger dataset
[mu sigma2] = estimateGaussian(X);
% Training set
p = multivariateGaussian(X, mu, sigma2);
% Cross-validation set
pval = multivariateGaussian(Xval, mu, sigma2);
% Find the best threshold
[epsilon F1] = selectThreshold(yval, pval);
fprintf('Best epsilon found using cross-validation: %e\n', epsilon);
fprintf('Best F1 on Cross Validation Set: %f\n', F1);
fprintf('# Outliers found: %d\n', sum(p < epsilon));
fprintf(' (you should see a value epsilon of about 1.38e-18)\n\n');
pause