CSE 5361 - Assignments - Assignment 4 (Programming 4)

Due date

Task

Loading and Processing Data

As in the previous assignment, you will use parts of the MNIST dataset. Please refer to Assignment 3 for instructions on how to download the package and use the data, and also for specifications on what data to use for training and what data to use for testing.

Implementing AdaBoost

Each strong classifier H that you construct (after you have finished its training) should be normalized, so that the absolute values of the weights of the weak classifiers that make up H sum up to 1. This should be a simple operation: every strong classifier H can be written as H= w1 * h1 + w2 * h2 + ... + wT * hT, where T is the number of weak classifiers in H, h1 to hT are the weak classifiers, and w1 to wT are the weights. Simply divide each weight by the sum |w1| + |w2| + ... + |wT|.

After you have constructed all classifiers, given a test image to classify, apply all 10 strong classifiers to that image, and find the one that gives the highest (most positive) response. Assign to the test image that class corresponding to that classifier with the highest response.

The AdaBoost algorithm, as can be seen in the above references, does not specify how to choose the next weak classifier. You should use rectangle filters as the basis for your weak classifiers. To choose the next weak classifier, at any point, try many random ones (say 1000 of them), and see which one gives the lowest WEIGHTED training error (where you use the current weights of the training samples to compute that error). To construct a classifier based on a random rectangle filter:

1. Choose randomly two numbers, width and height, from 2 to 10.
2. Choose randomly a direction (vertical, or horizontal).
3. If you chose the vertical direction, create a 2*height x width matrix, where the top half entries are all 1 and the bottom half entries are all -1. If you chose the horizontal direction, create a height x 2*width matrix, where the left half entries are all 1 and the right half entries are all -1.
4. Choose randomly a pixel coordinate (i,j) between (1,1) and (28-height_of_filter, 28-width_of_filter).
5. Create an image F that is all 0s, and then set value (i+i',j+j') of the image to value (i',j') of the filter.
6. For each test image T, compute (in Matlab notation) sum(sum(T.*F)).
7. Find the threshold M that minimizes the WEIGHTED classification error of the following rule: if sum(sum(T.*F)) < M, output -1, else output 1.
8. The weak classifier outputing, for each test image T, -1 and 1 as described in the previous step, is now ready.

Hints

Grading

10 points: correct implementation of rectangle filters.
• 10 points: correct identification of best threshold for each rectangle filter.
• 10 points: correct selection of the best next weak classifier.
• 10 points: correct implementation of AdaBoost, including correct labels for all training processes.
• 10 points: correct normalization of weak classifier weights for each strong classifier
• 30 points: correct implementation of classification algorithm (i.e., given the 10 strong classifiers, how to classify a test image).
• 20 points: preparing a good summary page, describing how to run your code, and summarizing your results (total classification error, and confusion matrix).

Submission guidelines