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(solution) part 2 in the project and I need report


part 2 in the project and I need report ............................


ECE505 Computer Project I

 

Due Date: Nov. 8, ?16 In this project you will experiment with various algorithms that you have learned in class for unconstrained

 

optimization.

 

Implement your procedures on a computer. Use any programming language at will. At the end you will

 

submit a project report, in which you should by all means document your implementation clearly and

 

concisely. For example, what is the principle of your algorithm? how would you determine its parameter(s)

 

if necessary? Be sure to discuss and comment on your test results. Your results should be presented using

 

graphs and tables whenever applicable.

 

You project report will be graded based on the following bases: correct, clear, and concise. Limit your

 

report to no more than 10 pages (It takes forests to make paper!).

 

Part 1. Algorithmic Implementation

 

1. Steepest Descent Algorithm. See Problem 10 in the document ?prob10.pdf? for details. For 10.(a) you

 

may use any of the linear search algorithms covered in class.

 

2. Newton Algorithm. Test your algorithm using the same problems as in 10.(d).

 

3. BFGS Quasi-Newton Algorithm. See Problem 11 in the document ?prob11.pdf? for details. For 11.(a)

 

you may use any of the linear search algorithms covered in class.

 

4. Conjugate Gradient Algorithm. For line search, you may use any of the linear search algorithms covered

 

in class.

 

Part 2. Application (optional)

 

Assume the intensity value (i.e. brightness) of a pixel in a cancerous region in a mammogram image can be

 

modeled by a Gaussian N ( 1 , 12 ) , where 1 , 12 are the mean and variance of the intensity, respectively,

 

while that in a harmless background is modeled by a Gaussian N ( 2 , 22 ) . A uniform random sampling of

 

a mammogram image (shown below) yields 200 intensity values from the image (listed in a separate

 

spreadsheet). Based on this information, estimate the proportion of cancerous pixels in this image. Hint: Let P1 denote the proportion of cancerous pixels in the image. Then a

 

randomly chosen pixel from the image has the following distribution p( x; 1 , 12 , 2 , 22 , P ) P1 1

 

2 2

 

1 e x 1 2

 

2 12 . 1 P1 1

 

2 2

 

2 e The problem then is to estimate the unknowns 1 , 12 , 2 , 22 , P1 x 2 2

 

2 22 from the given image samples. You may consider finding the maximumlikelihood estimate (MLE) 200 2

 

, , ,

 

P arg

 

max

 

p xi ; 1 , 12 , 2 , 22 , P , 1

 

2

 

2

 

1 i 1 where xi , i 1,2, ,200, denote the image samples. , 2

 

1

 


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