Hand-Written Character Recognition Solution

Description

For this project you will be solving the hand-written character recognition (classi cation) problem we discussed in class.

You will be turning in 3 les (possibly more but will be discussed further below)

• 1. There should be a Matlab script called \Training Lastname.m” (where Lastname is replaced by your last name) which will have the optimization code that created all 45 hyperplanes in the form of a’s and b’s.

• 2. There should be a Matlab script called \Testing Lastname.m” (where Lastname is replaced by your last name) which will have the Directed-Acyclic-Graph (DAG) code and also your analysis on how well your classi cation performed.

• 3. There should be a Matlab .mat le called \DAG Lastname.mat” (where Lastname is replaced by your last name) which will include all a’s and b’s representing the 45 hyperplanes. This .mat le will be used to perform veri cation analysis to compare with your own analysis.

You must save your hyperplanes (a’s and b’s) in the following manner for me to be able to analyze your classi cation solution:

• 1. Store all your a’s in an upper-triangular “cell” called A (in Matlab you use curly brackets f g ) … so Af1,10g will store the a vector that represent the hyperplane between 0 and 9 and Af9,10g represent 8 vs 9.

• 2. Store all your b’s in an upper-triangular “cell” called B… so Bf1,10g will store the b scalar that represents 0 vs 9 etc.

• 3. Here is example code to make the mat- le: >>save DAG_Ruben A B

So the cell-array should look something like this:

• A

A =

[] ’0 vs 1’ ’0			vs 2’	…	’0 vs 9’
[]	[]	’1	vs 2’	…	’1 vs 9’
[]	[]		[]	…	’2 vs 9’
[]	[]		[]	…	’3 vs 9’
[]	[]		[]	…	’4 vs 9’
[]	[]		[]	…	’5 vs 9’
[]	[]		[]	…	’6 vs 9’
[]	[]		[]	…	’7 vs 9’
[]	[]		[]	…	’8 vs 9’

It is crucial for my ability to analyze your classi cation that Set1, in the above code, is the smaller of the two numbers you are comparing. So when nding the hyperplane between 0 and 9 (or Af1,10g and Bf1,10g), Set1 should be zeros and Set2 should be nines.

Here is my sample code for checking between zeros and nines in the DAG:

Not9 = find(double(images_test)* A{1,10} – B{1,10}>0); % so maybe zero

Here is the sample code for displaying an image from its 784 long feature vector:

• Load Data

load mnist;

• Plotting a HandWritten Digit

%for ii = 1:10

nHold = 7, % I chose the 7th image to show

IMAGE = reshape(images(nHold,:),28,28)’;

labels(nHold)

figure,imagesc(IMAGE)

colormap(flipud(gray(256)))

axis equal

set(gca, ’YTick’, []);

set(gca, ’XTick’, []);

axis off

Now that you have nished solving the problem as described above, by solving for the 45 hyperplanes using the un-altered 784 features, you are now to play with the problem. When I say \play”, I mean try to alter the problem in the following possible two ways (at least choose one):

• 1. Reduce (or change) the features in a logical way so as to maintain the essence of the image. One example would be to cut the border pixels and reduce the problem by 2 28 + 2 26 = 108. Another option would be to do some image processing on the images (although this may not change the size of the feature vector). Come up with other options! When reducing the feature size, the gain in speed will most likely result in a loss of accuracy but by how much?

• 2. Increase the features in a logical way so as to give more more ways for the hy-perplane to compare digits. One example would be to append to the original 784 feature another 784 features that come the original image low passed and another 784 features that come from the original image high passed (image processing toolbox will have some of these tools) giving a total of 3 784 = 2352 features. This increase in feature size will de nitely increase the time needed to solve the problem but will most likely result in a high accuracy.

After changing the features in both the training and testing image, and produced new corresponding a’s and b’s, I need you to save the following items to the .mat le called \DAG Lastname.mat” you already made (and already saved the A and B cell array):

• 1. Save your new a’s and b’s in cell arrays name Ap and Bp (where p is for \play”)

• 2. Save your new, altered, \images test” as \images test play”

Don’t forget about the report :). Although it only get one bullet in the write-up, it is a crucial part of this project. Remember that clearly presenting your results to your peers is an important part of any project. When writing a report or paper, try to ask yourself if another engineering could recreate your results by reading your paper.

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