Practical Guide to Support
Vector Machines
Tingfan Wu
MPLAB, UCSD
Outline
Data Classification
High-level Concepts of SVM
Interpretation of SVM Model/Result
Use Case Study
What does it mean to learn?
Acquire new skills?
Make predictions about the world?
Making predictions is
fundamental to survival
Will that bear eat me?
Is there water in that canyon?
Is that person a good mate?
These are all examples of classification problems
Boot Camp Related
Motion classification
face recognition / speaker identification
Brain Computer Interface / Spikes Classification
Driver Fatigue Detection from Facial Expression
Data Classification
Sensor
Data
Preprocessing
features
Classifier
SVM
Adaboost
Neural Network
Prediction
Given training data (class labels known)
Predicts test data (class labels unknown)
Not just fitting generalization
Generalization
Many possible classification models
Which one generalize better ?
8
Generalization
Why SVM ? (my opinion)
With careful data preprocessing, and properly
use of SVM or NN similar performance.
SVM is easier to use properly.
SVM provides a reasonable good baseline
performance.
10
Outline
Data Classification
High-level Concepts of SVM
Interpretation of SVM Model/Result
Use case study
11
A Simple Dilemma
Who do I invite to my
birthday party?
12
Problem Formulation
training data as vectors: xi
binary labels [ +1, -1]
Name
Gift?
Income
Fondness
John
Mary
Yes
No
3k
5k
3/5
1/5
class
feature vector
y1=+1 x1 = [3000, 0.6]
y2= -1 x2 = [5000, 0.2]
13
x2
(Disposable Income)
Vector space
+ +
+
No Gift
+ Gift
+
+ ++
+
+
x1(Fondness)
14
A Line
The line : w T x
+ b= 0
x2(second feature)
Normal: w
++
+
+
+
+ ++
+
+
+
x1(first feature)
Hyperplane in high dimensional space
15
The inequalities and regions
T
w x + b= 0
+ + wT x + b> 0
i
- +
+
+
+
+
+
wT xi + b < 0
+
+
+
-
model
D eci si on funct i on f ( x ) = si gn( w T x n ew + b)
16
Large Margin
17
Maximal Margin
18
Data not linearly separable
Case 1
Case 2
19
Trick 1: Soft-Margin
These points are usually outliers. The hyperplane should not bias too much.
Penalty of
violating data
20
Soft-margin
21
[Ben-Hur & Weston 2005]
Support vectors
More important data that support (define) the hyperplane
22
Trick2: Map to Higher Dimension
x2
x 2 = x 21
x2
x 2 = x 21
M appi ng:
x1
x 21
23
Mapping to Infinite Dimension
Is it possible to create a universal mapping ?
What if we can map to infinite dimension ? Every problem is separable!
Consider Radial Basis Function (RBF):
=Kernel(x,y)
w : infinite number of variables!
24
Dual Problem
Primal
Dual
finite calculation
25
Gaussian/RBF Kernel
~ linear kernel
Overfitting
nearest neighbor?
26
27
[Ben-Hur & Weston 2005]
Recap
Soft-ness
Nonlinearity
28
Checkout the SVMToy
http://www.csie.ntu.edu.tw/~cjlin/libsvm/
-c (cost control softness of the margin/#SV)
-g (gamma controls the curvature of the
hyperplane)
29
Cross Validation
What is the best (C, ) ? Date dependent
Need to be determined by testing performance
Split training data into pseudo training, testing sets
Training
Split: training
Testing
Split: test
determine the best (C, )
Exhausted grid search for best (C, )
30
Outline
Machine Learning Classification
High-level Concepts of SVM
Interpretation of SVM Model/Result
Use Case Study
31
(1)Decision value as strength
D eci si on funct i on f ( x ) = si gn( w T x n ew + b)
32
Facial Movement Classification
Classes: brow up(+) or down(-)
Features: pixels of Gabor filtered image
33
Decision value as strength
Probability estimates from decision values also available
34
(2)Weight as feature importance
Magnitude of weight : feature importance
Similar to regression
35
(3)Weights as profiles
Fluorescent image of cells of
various dosage of certain drug
Various image-based features
Clustering the weights shows the
primal and secondary effect of the
drug
37
Outline
Machine Learning Classification
High-level Concepts of SVM
Interpretation of SVM Model/Result
User Case Study
38
The Software
SVM requires an constraint quadratic
optimization solver
not easy to implement.
Off-the-shelf Software
libsvm by Chih-Jen Lin et. al.
svmlight by Thorsten Joachims
Incorporated into many ML software
matlab / pyML / R
39
Beginners may
1. Convert their data into the format of a
SVM software.
2. May not conduct scaling
3. Randomly try few parameters and
without cross validation
4. Good result on training data, but poor in
testing.
40
Data scaling
Without scaling
feature of large dynamic range may dominate
separating hyperplane.
X Height Gender
x1 150 2
y2=1
y3=1
x2 180
x3 185
1
1
Gender
label
y1=0
Height
41
Parameter Selection
Contour of cross validation accuracy.
Good area
42
User case : Astroparticle scientist
User:
I am using libsvm in a astroparticle physics
application .. First, let me congratulate you to
a really easy to use and nice package.
Unfortunately, it gives me astonishingly bad
test results...
OK. Please send us your data
We are able to get 97% test accuracy. Is that
good enough for you ?
User:
You earned a copy of my PhD thesis
43
Dynamic Range Mismatch
A problem from astroparticle physics
<label> <index>:<value> <index>:<value>
1 1:2.6173e+01 2:5.88670e+01 3:-1.89469e-01 4:1.25122e+02
1 1:5.7073e+01 2:2.21404e+02 3:8.60795e-02 4:1.22911e+02
1 1:1.7259e+01 2:1.73436e+02 3:-1.29805e-01 4:1.25031e+02
1 1:2.1779e+01 2:1.24953e+02 3:1.53885e-01 4:1.52715e+02
1 1:9.1339e+01 2:2.93569e+02 3:1.42391e-01 4:1.60540e+02
1 1:5.5375e+01 2:1.79222e+02 3:1.65495e-01 4:1.11227e+02
1 1:2.9562e+01 2:1.91357e+02 3:9.90143e-02 4:1.03407e+02
#Training set 3,089 and #testing set 4,000
Large dynamic range of some features.
44
Overfitting
Training
$./svm-train train.1 (default parameter used)
optimization finished, #iter = 6131
nSV = 3053, nBSV = 724
Total nSV = 3053
Training Accuracy
$./svm-predict train.1 train.1.model o
Accuracy = 99.7734% (3082/3089)
Testing Accuracy
$./svm-predict test.1 train.1.model test.1.out
Accuracy = 66.925% (2677/4000)
nSV and nBSV: number of SVs and bounded SVs (i = C).
Without scaling. One feature may dominant the value overfitting
3053/3089 training data become support vectorOverfitting
Training accuracy high, but low testing accuracy Overfitting
45
Suggested Procedure
Data pre-scaling
scale range [0 1] or unit variance
Using (default) Gaussian(RBF) kernel
Use cross-validation to find the best parameter (C, )
Train your model with best parameter
Test!
All above done automatically in easy.py script provided with libsvm.
46
Large Scale SVM
(#training data >> #feature ) and linear kernel
Use primal solvers (eg. liblinear)
To approximated result in short time
Allow inaccurate stopping condition
svm-train e 0.01
Use stochastic gradient descent solvers
24
47
Resources
LIBSVM: http://www.csie.ntu.edu.tw/~cjlin/libsvm
LIBSVM Tools: http://www.csie.ntu.edu.tw/~cjlin/libsvmtools
Kernel Machines Forum: http://www.kernel-machines.org
Hsu, Chang, and Lin: A Practical Guide to Suppor t Vector
Classification
my email: tfwu@ucsd.edu
Acknowledgement
Many slides from Dr. Chih-Jen Lin , NTU
48
