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Tutorial-Logisticregression-MachineLearningclassification.doc (doc) DOWNLOAD

Tutorial-Logisticregression-MachineLearningclassification.pdf (pdf) DOWNLOAD

data_classification.zip (zip)

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and the dataset: zip

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Let’s create some random data that are split into two different classes, ‘class 0’ and ‘class 1’.

We will use these data as a training set for logistic regression.

This dataset represents 100 samples classified in two classes as 0 or 1 (stored in the third column), according to two parameters (stored in the first and second column):

Directly import your data in Scilab with the following command:

t=csvRead("data_classification.csv");

These data has been generated randomly by Scilab with the following script:

b0 = 10; t = b0 * rand(100,2); t = [t 0.5+0.5*sign(t(:,2)+t(:,1)-b0)]; b = 1; flip = find(abs(t(:,2)+t(:,1)-b0)<b); t(flip,$)=grand(length(t(flip,$)),1,"uin",0,1);

The data from different classes overlap slightly. The degree of overlapping is controlled by the parameter b in the code.

Before representing your data, you need to split them into two classes t0 and t1 as followed:

t0 = t(find(t(:,$)==0),:); t1 = t(find(t(:,$)==1),:); clf(0);scf(0); plot(t0(:,1),t0(:,2),'bo') plot(t1(:,1),t1(:,2),'rx')

We want to build a classification model that estimates the probability that a new, incoming data belong to the class 1.

First, we separate the data into features and results:

x = t(:, 1:$-1); y = t(:, $); [m, n] = size(x);

Then, we add the intercept column to the feature matrix

// Add intercept term to x x = [ones(m, 1) x];

The logistic regression hypothesis is defined as:

*h*(*θ, x*) = 1 / (1 + exp(−*θ ^{T}x*) )

It’s value is the probability that the data with the features *x* belong to the class 1.

The cost function in logistic regression is

*J* = [−*y ^{T}* log(

where `log`

is the “element-wise” logarithm, not a matrix logarithm.

If we use the gradient descent algorithm, then the update rule for the *θ* is

*θ* → *θ* − *α* ∇*J* = *θ* − *α* *x ^{T}* (

The code is as follows

// Initialize fitting parameters theta = zeros(n + 1, 1); // Learning rate and number of iterations a = 0.01; n_iter = 10000; for iter = 1:n_iter do z = x * theta; h = ones(z) ./ (1+exp(-z)); theta = theta - a * x' *(h-y) / m; J(iter) = (-y' * log(h) - (1-y)' * log(1-h))/m; end

Now, the classification can be visualized:

// Display the result disp(theta) u = linspace(min(x(:,2)),max(x(:,2))); clf(1);scf(1); plot(t0(:,1),t0(:,2),'bo') plot(t1(:,1),t1(:,2),'rx') plot(u,-(theta(1)+theta(2)*u)/theta(3),'-g')

Looks good.

The graph of the cost at each iteration is:

// Plot the convergence graph clf(2);scf(2); plot(1:n_iter, J'); xtitle('Convergence','Iterations','Cost')

Article kindly contributed by Vlad Gladkikh (Copyright owner)

Layout by Yann Debray @ Scilab

MOOC on Cousera about Machine Learning from Andrew Ng, Stanford University

https://www.coursera.org/learn/machine-learning/home/welcom