# Coursera: Machine Learning (Week 9) [Assignment Solution] - Andrew NG

▸ Anomaly detection algorithm to detect failing servers on a network.

▸ Collaborative filtering to build a recommender system for movies.

I have recently completed the Machine Learning course from Coursera by Andrew NG.

While doing the course we have to go through various quiz and assignments.

Here, I am sharing my solutions for the weekly assignments throughout the course.

In this exercise, you will implement the anomaly detection algorithm and apply it to detect failing servers on a network. In the second part, you will use collaborative filtering to build a recommender system for movies. Before starting on the programming exercise, we strongly recommend watching the video lectures and completing the review questions for the associated topics.

I tried to provide optimized solutions like

▸ Collaborative filtering to build a recommender system for movies.

I have recently completed the Machine Learning course from Coursera by Andrew NG.

While doing the course we have to go through various quiz and assignments.

Here, I am sharing my solutions for the weekly assignments throughout the course.

**These solutions are for reference only.****> It is recommended that you should solve the assignments by yourself honestly then only it makes sense to complete the course.****>**

**But, In case you stuck in between, feel free to refer to the solutions provided by me.**

**NOTE:**

Don't just copy paste the code for the sake of completion.

Even if you copy the code, make sure you understand the code first.

**Click here to check out**__week-8__assignment solutions,__Scroll down__for the solutions for__week-9__assignment.In this exercise, you will implement the anomaly detection algorithm and apply it to detect failing servers on a network. In the second part, you will use collaborative filtering to build a recommender system for movies. Before starting on the programming exercise, we strongly recommend watching the video lectures and completing the review questions for the associated topics.

**It consist of the following files:****ex8.m -**Octave/MATLAB script for first part of exercise**ex8 cofi.m -**Octave/MATLAB script for second part of exercise**ex8data1.mat -**First example Dataset for anomaly detection**ex8data2.mat -**Second example Dataset for anomaly detection**ex8 movies.mat -**Movie Review Dataset**ex8 movieParams.mat -**Parameters provided for debugging**multivariateGaussian.m -**Computes the probability density function for a Gaussian distribution**visualizeFit.m -**2D plot of a Gaussian distribution and a dataset**checkCostFunction.m -**Gradient checking for collaborative filtering**computeNumericalGradient.m -**Numerically compute gradients**fmincg.m -**Function minimization routine (similar to fminunc)**loadMovieList.m -**Loads the list of movies into a cell-array**movie ids.txt -**List of movies**normalizeRatings.m -**Mean normalization for collaborative filtering**submit.m -**Submission script that sends your solutions to our servers**[*] estimateGaussian.m -**Estimate the parameters of a Gaussian distribution with a diagonal covariance matrix**[*] selectThreshold.m -**Find a threshold for anomaly detection**[*] cofiCostFunc.m -**Implement the cost function for collaborative filtering**Video -**YouTube videos featuring Free IOT/ML tutorials

*****indicates files you will need to complete**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))';
sigma2 = ((1/m)*sum((X-mu').^2))';
% =============================================================
end
```

**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
cvPredictions = (pval < epsilon); % m x 1
tp = sum((cvPredictions == 1) & (yval == 1)); % m x 1
fp = sum((cvPredictions == 1) & (yval == 0)); % m x 1
fn = sum((cvPredictions == 0) & (yval == 1)); % m x 1
prec = tp/(tp+fp);
rec = tp/(tp+fn);
F1 = 2*prec*rec / (prec + rec);
% =============================================================
if F1 > bestF1
bestF1 = F1;
bestEpsilon = epsilon;
end
end
end
```

**Check-out our free tutorials on IOT (Internet of Things):**

**cofiCostFunc.m :**

```
function [J, grad] = cofiCostFunc(params, Y, R, num_users, num_movies, ...
num_features, lambda)
%COFICOSTFUNC Collaborative filtering cost function
% [J, grad] = COFICOSTFUNC(params, Y, R, num_users, num_movies, ...
% num_features, lambda) returns the cost and gradient for the
% collaborative filtering problem.
%
% Unfold the U and W matrices from params
X = reshape(params(1:num_movies*num_features), num_movies, num_features);
Theta = reshape(params(num_movies*num_features+1:end), ...
num_users, num_features);
% You need to return the following values correctly
J = 0;
X_grad = zeros(size(X)); % Nm x n
Theta_grad = zeros(size(Theta)); % Nu x n
% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost function and gradient for collaborative
% filtering. Concretely, you should first implement the cost
% function (without regularization) and make sure it is
% matches our costs. After that, you should implement the
% gradient and use the checkCostFunction routine to check
% that the gradient is correct. Finally, you should implement
% regularization.
%
% Notes: X - num_movies x num_features matrix of movie features
% Theta - num_users x num_features matrix of user features
% Y - num_movies x num_users matrix of user ratings of movies
% R - num_movies x num_users matrix, where R(i, j) = 1 if the
% i-th movie was rated by the j-th user
%
% You should set the following variables correctly:
%
% X_grad - num_movies x num_features matrix, containing the
% partial derivatives w.r.t. to each element of X
% Theta_grad - num_users x num_features matrix, containing the
% partial derivatives w.r.t. to each element of Theta
%
%% %%%%% WORKING: Without Regularization %%%%%%%%%%
Error = (X*Theta') - Y;
J = (1/2)*sum(sum(Error.^2.*R));
X_grad = (Error.*R)*Theta; % Nm x n
Theta_grad = (Error.*R)'*X; % Nu x n
%% %%%%% WORKING: With Regularization
Reg_term_theta = (lambda/2)*sum(sum(Theta.^2));
Reg_term_x = (lambda/2)*sum(sum(X.^2));
J = J + Reg_term_theta + Reg_term_x;
X_grad = X_grad + lambda*X; % Nm x n
Theta_grad = Theta_grad + lambda*Theta; % Nu x n
% =============================================================
grad = [X_grad(:); Theta_grad(:)];
end
```

**vectorized implementation**for each assignment. If you think that more optimization can be done, then put suggest the corrections / improvements.--------------------------------------------------------------------------------

Click here to see solutions for all **Machine Learning**Coursera Assignments.

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Click here to see more codes for **Raspberry Pi 3**and similar Family.

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Click here to see more codes for **NodeMCU ESP8266**and similar Family.

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Feel free to ask doubts in the comment section. I will try my best to solve it.

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This is the simplest way to encourage me to keep doing such work.

Thanks and Regards,

**-Akshay P. Daga**

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