Assignment 7 information

• Announcements
• Support code
• Generate your own synthetic data
• Questions & Answers

• Submit/test your code to the web tester

• [12/2] If you depend upon the perceptron-epoch procedure for your learn-perceptron procedure, you must include it in your file for Problem 2. The pretester does not check for the perceptron-epoch procedure because you are not required to use it.

• [11/30] For Problem 3 (where it says that I will provide a data set specifically for creating a learning curve), you may use either the B1 and B2 data from the lsd.scm file, or you can use the bc-data-l1, bc-data-l2, bc-data-l3 data from the bc-data.scm file. The synthetic data might converge so quickly that you don't get a very wide learning curve; the breast cancer data might not converge to 100%, but you'd probably get a good learning curve from it. Either will be fine.

• [11/30] The web testers are up for problems 1 and 2. Also see the "Generate your own data" section below...

• [11/30] A student pointed out that I made a mistake in class on Thursday with the convention using a -1 for the first input which makes the first weight the threshold value.

• [11/27] I've put together some synthetic data you can use to test your procedures. See the support code section below and the comments in the file.

• [11/27] Since I didn't get to perceptrons in class yesterday, here's some information on learning perceptrons. The text is not so forthcoming about training perceptrons instead focusing on multilayer networks of sigmoid units (which we'll get to), although it does basically cover the material.

  • The "basic" algorithm for training a perceptron is, for each epoch, to take each example in turn, compute the perceptron's output with the current weights, compute the error from the correct answer, and then apply the perceptron learning rule to adjust the weights.

  • In the perceptron learning rule, the vector "w" is the vector of weights and the vector "I" is the vector of inputs. (Sometimes, I may use the variable "x" instead of "I")

• [11/26] Support code is out. I've provided one collection of data sets; I should have at least one more out shortly.

• The support code for this problem is in the file a7code.scm. This file contains a version of the code in the assignment handout that has some error checking on the arguments passed to procedures. See the code for details.

• The file bc-data.scm contains the Wisconsin Breast Cancer Database, converted for use with perceptrons. The only difference is that instead of the symbols b and m (for benign and malignant), a number is used (-1 for benign and 1 for malignant.)

  These data may not be linearly separable (although the documentation for the data set says that they are). I will be providing at least one synthetic data set which will be linearly separable.

• The file lsd.scm (that stands for "linearly separable data" by the way) contains synthetic data you can yous for training your perceptron. Some of the data contains some noise, but most is linearly separable. See the comments in the file for details.

(define h (pick-hyperplane 2))

h
;Value: ((-.8925898031763745 -.45086965218958913) .15687006660372727)
; the format of the hyperplane is (normal offset) so that:
;
; output = 1 if  the dot product of the "normal" and the "input" is
;            greater than the "offset"
;         -1 otherwise

(define d (lsdata h 10))
Of 10 examples, 5 are positive examples.

d
;Value: ((-1 (.8667412929548199 .17378869975659605))
         (-1 (-.09185614144878473 -.1411371356122395))
	 (1 (-.14720896904730352 -.44910735200288165))
	 (1 (-.24302071105109146 .12993139718884072))
	 (1 (-.7104105489682528 .9972802749803293))
	 (1 (-.698340137603623 .8554353330464048))
	 (1 (-.23009130827860358 -8.647936173537651e-3))
	 (-1 (.5941178449361095 .7622703851227071))
	 (-1 (.15212484490140898 .4744542207038662))
	 (-1 (.17650231762847657 .12650541626674294)))

(test-perceptron (cons (second h) (first h)) d)
;Value: 1.
; i.e. it classified 100% of the examples in d correctly