Machine Learning
19
i= 2 I
Transcript of Machine Learning
i=2I
i=
i=
i=arbitrary
Complex decision boundaries
Machine Learning
Design & Validation of ClassifiersDesign & Validation of Classifiers
Computer Vision
Detectionof
Errors
Sensor
Object
A/D Converter
Pattern of Data
+++ +
+
++
+
++
oo oo
o
o
o
o
o
o
X1
X2
Learning System
Samples Learning System Classifiers
Classification Systems
Data for classification
Classifier Decision Pertaining to class
Design of a classifier
Samples for training
Values ofvariables (xi)
Classes Pertaining to samples
LearningSystem
Classifier type
Classifier forSpecific
application
CaseVariables (Features)
Classes
Estimating the execution of a learning system
What is an error?
Class (+) Class (-)
Classification (+) Correct (+/+) Error (-/+)
Classification (-) Error (+/-) Correct (-/-)
Reason for error (estimate) = number of errors number of cases
Apparent and true error
Classifier
Samplesfor
training
Apparentreason for error
New cases
True error
Error estimationusing samples for training and samples for testing
Cases for training the classifier Cases for testing the classifier
Samples
Sample: Y1i ValueY11 .9846Y12 .-0449Y13 -.7652
Sample: X1i ValueX11 0.7635X12 -1.2667X13 -0.6141X14 1.0913X15 -0.5597
Sample: Y2i ValueY21 .2011Y22 .9438Y23 . 8135
Sample: X2i ValueX21 2.7123X22 1.5558X23 1.8327X24 0.3352X25 0.4325
Example: 1-d
Class 1: n1 = 5
X1 Train
Y1 Train
Class 2: n1 = 5
X2 Train
Y2 Test
Estimation of Parameters
ˆ k 1
ni
X kii1
n i
ˆ k2
1
n i 1X ki ˆ k 2
i1
n i
ˆ 1 .1171ˆ 1
2 1
ˆ 21.3737
ˆ 22 1
Classification ML Rule
f X/ wk 1
2k2
e
1
2
X k
k
2
X1i Value f(X/w1) f(X/w2) ClassX11 .7635 .2707 .3312 2X12 -1.2667 .2060 .0122 1X13 -.6141 .3526 .0553 1X14 1.0913 .1922 .3833 2X15 -.5597 .3617 .0615 1Y11 .9846 .2174 .3699 2Y12 -.0449 .3979 .1459 1Y13 -.7652 .3234 .0405 1
Class 1
Classification ML Rule
f X/ wk 1
2k2
e
1
2
X k
k
2
X2i Value f(X/w1) f(X/w2) ClassX21 2.7123 .0073 .1629 2X22 1.5558 .0984 .3924 2X23 1.8327 .0596 .3591 2X24 .3352 .3602 .2327 1X25 .4325 .3430 .2562 1Y21 .2011 .3792 .2006 1Y22 .9438 .2273 .3637 2Y23 .8135 .2587 .3410 2
Class 2
A simpler Classification ML Rule
X1i Value ClassX11 .7635 2X12 -1.2667 1X13 -.6141 1X14 1.0913 2X15 -.5597 1Y11 .9846 2Y12 -.0449 1Y13 -.7652 1
Class 1 T ˆ 1 ˆ 2
2.6283
Classification ML Rule
X2i Value ClassX21 2.7123 2X22 1.5558 2X23 1.8327 2X24 .3352 1X25 .4325 1Y21 .2011 1Y22 .9438 2Y23 .8135 2
Class 2 T ˆ 1 ˆ 2
2.6283
