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where 
This is the same data set as in the example collec- tion where straightforward linear regression was attempted and shown not to produce any result meaningful for discrimination.
Use the LS-method to determine ?. Determine and draw the decision boundary defined by ?.
c) What is the effect on the decision boundary of changing y4 to ?0.5.
d) Use the LMS-method to determine ?. Choose the starting point ?(1) = (1 1 1)t. Set the threshold value to ? = 1, and let ? = 0.5. Remember that the learning rate is updated according to ?(i) = ?/i. Compute ?(i) for i = 2,3,4, ... until convergence and sketch the decision boundary defined by ?. Compare the resulting decision boundary with the one you found in subtask
Trygve Eftestøl, Professor Faculty of Science and Technology University of Stavanger Telephone: +47 51 83 10 00. Department of Electrical and Computer Engineering N-4036 Stavanger. Telefax: +47 51 83 17 50. E-mail: trygve.eftestol@uis.no Kjølv Egelands hus www.ux.his.no/ ?trygve-e
Problem 2
The problem of defining a generalised linear discriminant function to discriminante the vectors in a labelled two-class problem can be expressed
X? = y (1) where X is the N × ˆl matrix1 where the nth row is the vector xnT and y be the vector y = (y1,...,yN)T.
a) Explain why this equation is not generally solvable.
b) Show that the vector ? giving the best approximation in the sense of the minimum squared error
between the right and left side in the equation is given by
c) Find an expression for the quadratic distance using the solution from theprevious task.
d) Show that the problem is linearly separable if
where I is the identity matrix.
Problem 3
Consider the data sets with samples xi
for class ?2. We want to find the discriminant function g(x) = ?Tx that solves the inequalities ?Txi > 0.
The batch perceptron algorithm is given:
Algorithm 3. (Batch Perceptron)
a) Augment the data and determine the labels for each sample.
b) Plot the lines defined by ?Txi = 0 for all the samples.
c) Indicate the positive and negative sides of the lines and identify the solution region.
d) Apply the algorithm letting the initial values be ?(1) =0,?(1) = 1, criterion ? = 0. Let ?(i) = 1.
e) As above, but let let ?(i)=1/i.
Machine Learning - Electrical Engineering and Computer Science Assignment Help
Task: Problem 1 We shall design a pattern recognition system to classify 2-dimensional feature vectors {x} to class ?1 (’×’), or class ?2 (’?’). As a basis for this work, we have performed measurements so that 4 feature vectors are available as training vectors:
- a) Plot the training vectors in the x1x2–plane translated to the augmented feature
where
This is the same data set as in the example collec- tion where straightforward linear regression was attempted and shown not to produce any result meaningful for discrimination.
Use the LS-method to determine ?. Determine and draw the decision boundary defined by ?.
c) What is the effect on the decision boundary of changing y4 to ?0.5.
d) Use the LMS-method to determine ?. Choose the starting point ?(1) = (1 1 1)t. Set the threshold value to ? = 1, and let ? = 0.5. Remember that the learning rate is updated according to ?(i) = ?/i. Compute ?(i) for i = 2,3,4, ... until convergence and sketch the decision boundary defined by ?. Compare the resulting decision boundary with the one you found in subtask
Trygve Eftestøl, Professor Faculty of Science and Technology University of Stavanger Telephone: +47 51 83 10 00. Department of Electrical and Computer Engineering N-4036 Stavanger. Telefax: +47 51 83 17 50. E-mail: trygve.eftestol@uis.no Kjølv Egelands hus www.ux.his.no/ ?trygve-e
Problem 2
The problem of defining a generalised linear discriminant function to discriminante the vectors in a labelled two-class problem can be expressed
X? = y (1) where X is the N × ˆl matrix1 where the nth row is the vector xnT and y be the vector y = (y1,...,yN)T.
a) Explain why this equation is not generally solvable.
b) Show that the vector ? giving the best approximation in the sense of the minimum squared error
between the right and left side in the equation is given by
c) Find an expression for the quadratic distance using the solution from theprevious task.
d) Show that the problem is linearly separable ifwhere I is the identity matrix.
Problem 3
Consider the data sets with samples xi
for class ?2. We want to find the discriminant function g(x) = ?Tx that solves the inequalities ?Txi > 0.
The batch perceptron algorithm is given:
Algorithm 3. (Batch Perceptron)
a) Augment the data and determine the labels for each sample.
b) Plot the lines defined by ?Txi = 0 for all the samples.
c) Indicate the positive and negative sides of the lines and identify the solution region.
d) Apply the algorithm letting the initial values be ?(1) =0,?(1) = 1, criterion ? = 0. Let ?(i) = 1.
e) As above, but let let ?(i)=1/i.
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