CS 276A Pattern Analysis and Machine Intelligence

A. Klinger Fall 1998 Boelter 5280

0. If you have missed any of the following dates, complete the item as soon as possible. Relate your planned text chapter readings to a possible in-depth study of key topics from recent Pattern Analysis research papers. ... Ask questions about relating different approaches to problems to each other. ... Present solve exercises in the class at the blackboard. ... Describe your likely term project to the class orally. ... Begin reading one research paper. ... List the key concepts you read about on a page with your name on it and hand it in at the fourth class meeting on Thursday 10/15/97 (end of second week): also see First Exercises re a 10/15 hand in of possible project title &, etc., ... supporting research papers ... reading. Four things are to appear on a 10/15 hand in, Chapters, Project, Research Papers, Research Reading Topics Relation to Chapters.

1. Use error correction to adjust a linear discriminant so it decides which of two classes is present. The scalar data is given as the list of six two-vectors (first coordinate is data, the second the class label):

( - 1.25, 1), ( - 1.50, 1), (- 0.80, 1), ( 1.40, 2), ( 0.80, 2), ( 1.20, 2).

The initial weight used is 2 and the initial threshold is 2.60. Find weight and threshold after two passes through the six-element data set for restrictions c) and then for d).

1. State any assumptions
2. List the misclassified patterns.
3. Unity error-correction.
4. harmonic error-correction (1, 1/2, 1/3 ... weights on at successive errors).

2. Construct a data set initially not linearly separable, but separable in a higher dimensional space. Find the separation-creating mapping. Begin with data in the real line or the plane.

3. Find the equation of a linear surface to separate two sets in (x,y)-space, a unit-radius sphere centered at the point (1,1) and the cone given by the set of all (x,y) with x < 0.1 and y < 0.1.

4. With three classes, there is just one learning set element, a three-vector (1, 1, 1), known to be in the class corresponding to the first discriminant. It is simultaneously input to all three linear discriminants. They are to be adjusted by error-correction to classify it correctly. The system result assigns data to the index of the largest of the three discriminants. Suppose the discriminant initial weights/[thresholds] are, respectively: (1, 2, 1) / [1]; (-6, 11, 2) / [3]; and (-8, -2, 3) / [4].

Assuming that the learning set vector is added to the discriminant that should be maximum when it is not, and subtracted from that incorrectly highest, what are the weight and threshold values after one correction?

5. This problem extends problem 4: here a vector in class 2, (2, -4, 1), and one in class 3, (-1, 2, -8), are also available.

Develop a set of all twelve-dimensional vectors needed for a learning set associated with treating the weights and thresholds for all the discriminants together.

6. A neural net is made up of seven linear discriminants. Each is associated to one class. The maximum-value discriminant index is the class membership decision.

Show how to use seven linearly separable learning set vectors to train this system to correctly classify all the given data.