CS392 MATLAB Workshop 2 – SVM’s 08/10/2003
© David Lindsay 2003 www.david-lindsay.co.uk Page 4 of 17
L Matrices, vectors and constants
I will try to use consistent notation to distinguish between matrices, vectors and constants
throughout this document. I will usually use capital bold notation for matrices (e.g.
Α, Β,
K ), lower case bold for vectors (e.g.
,,
K ) and italicised for constants (e.g.
bc,, K ). It is very important that you can distinguish between these mathematical objects!
Copy data sets and programs into local directory
As stated in the previous workshop we have created for you a shared directory of resources
under the /CS/courses/CS392/ directory
Copy the files that you need for this session into your local directory
cp /CS/courses/CS392/ex2SVM/* .
You should find the files firstsvm1.m, tennisweather2AttSVMTrain.txt and
tennisweather2AttSVMTest.txt in your home directory. The file firstsvm1.m is
a slightly modified version of the program that you developed in workshop 1. Open this file
for editing by typing emacs firstsvm1.m &
³ Classes represented as ±1 for SVM’s
The two dataset files that you have copied is the same data as you worked with in the previous
workshop on assessing good ‘tennis playing’ days. Look at the data, you will notice that I
have changed the classes to ±1 so that it can be analysed by an SVM directly. It will become
clearer later why it is useful to encode the classes in this manner. We have also separated the
last example from the original data to make a separate training and test file.
³ Return of the hyper-plane
One of the most important concepts to get your head around is that of a hyper-plane in n
dimensional space [see Class 2 Slide 8]! We consider our attribute vectors
1
,
i
x=
i
x K as
the n dimensionals vectors for the ith example in the data set. We have a a training set of l
examples (information pairs attribute vector + label) as
()()
1
,,,
l
y
11
xxK where the labels
{}
1,1−∈
i
y . The equation of a hyperplane H is
00 11
)
nn
Hwxwx wxb b=++++=⋅+=wxL
using the dot product notation. The hyperplane is defined by the “weights” which are
contained in the n dimensional vector w and the constant b.
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