()=+1P(x)<PB Example 2 [-1otherwise +1 if p,lv-mu]< p,c Find the equation of the1-1otherwise line: v=mu+C Answer:c=2,m=(6-2)/10=0.4,So Assume Polarity Pt is 1 V=04u+2 Assume polarity Pt=1, classify P1, 2, 3, 4. I V -mutC P1 P1(u=5,V=9) Answer:V-mu=9-0. 4*5=7. since c=2 so v-mu>c, so it is class:-1 2(u=9V=4): Answer: V-mu=4-0.4*9=0. 4. since C=2. s0 v-mu<c, so it is class +1 9876543 Class-1 V-muEC V-ma>c P4 P3(u=6,v=3) P2 P4(u=2,v=3): P3 Repeat using Pt=-1 Class +1 V-musc 23456 8910 U Adaboost, Vga
Example 2 : • Find the equation of the line :v=mu+c – Answer: c=2, m=(6-2)/10=0.4, So v=0.4u+2 • Assume polarity Pt=1, classify P1,2,3,4. • P1(u=5,v=9) – Answer: V-mu=9-0.4*5=7, since c=2, so v-mu>c, so it is class: -1 • P2(u=9,v=4): – Answer: V-mu=4-0.4*9=0.4, since c=2, so v-mu<c, so it is class:+1 • P3 (u=6,v=3): • P4(u=2,v=3): • Repeat using Pt= -1 Adaboost , V9a 11 ( ) 1 otherwise 1 if ( ) ( ) 1 otherwise 1 if ( ) ( ) ib p v mu p c h x i p f x p h x t t t t t t t t − − − − − − − − − − + − = − − − − − − − − − − + = Class +1: V-mu<c Class -1: V-mu>c Assume Polarity Pt is 1 v=mu+c or v-mu=c
Answer for exercise 2 P3(u=6,V=3) V-mu=3-0.4*6=0.6. since c=2, so v-musc, so it is class +1 24(u=2V=3)} V-mu=3-0. 42=2.2 since c=2, Sov-mu>c, so it is class -1 Adaboost, Vga
Answer for exercise 2 ◼ P3(u=6,v=3): • V-mu=3-0.4*6=0.6, since c=2, so v-mu<c, so it is class +1 • P4(u=2,v=3): • V-mu=3-0.4*2=2.2, since c=2, so v-mu>c, so it is class -1 Adaboost , V9a 12
Learn what is h (), a weak classifier. Decision stump Decision stump definition Exampl e a decision stump is a machine learning model consisting of a one-level decision tree. 1 That is, it is a decision tree with Temperature T one internal node the root) which is immediately connected to the terminal nodes. a decision stump makes a prediction based on the value of just a single input feature. Sometimes they are T<=1010<T<28T>=28 also called 1-rules. 21 Cold mild Fromhttp:llen.wikipediaorg/wiki/decisionstump Adaboost, Vga
Learn what is h( ), a weak classifier. Decision stump • Decision stump definition • A decision stump is a machine learning model consisting of a one-level decision tree.[1] That is, it is a decision tree with one internal node (the root) which is immediately connected to the terminal nodes. A decision stump makes a prediction based on the value of just a single input feature. Sometimes they are also called 1-rules.[2] • From http://en.wikipedia.org/wiki/Decision_stump • Example Adaboost , V9a 13 Temperature T T<=10oc 10oc<T<28oc T>=280c Cold mild hot
a Weak learner(classifier is a decision stump Define weak learners based on rectangle features The function fi(x)of a decision-lipe in space (x)= ∫+1fp/(x)<P othewise 0 = threshold olarity(+1, -1] Decision Select which 1 region Ine side separated by the line you pr reter +1 region Adaboost vga
Adaboost , V9a 14 A weak learner (classifier ) is a decision stump • Define weak learners based on rectangle features − + = 1 othewise 1 if ( ) ( ) t t t t t p f x p h x The function ft (x) of a decision-line in space pt= polarity{+1,-1} Select which side separated by the line you prefer t =threshold Decision line +1 region -1 region
Weak classifier we use here Axis parallel weak classifier In order to simplify the t-1, err of this classifier=0. 125, alpha= 0. 97296, following Ds are D att+1 2638 derivation we will use the D(1)=0.071 D(5)=0.500 D(2)=0071 simple"axis parallel weak 30 classifier" that means m=0 20 If polarity p(=1, this region is-1 for v=mu+c, hence v=c If polarity p =-1, this region is +1 42.10) (V=input, c=constant D(4)=0071 3) It assumes gradient(m)of (3}=0.071 the decisⅰ on line is =o(horizontal)or oo(vertical) The decision line is parallel to either the horizontal or =0071 D8)=0071 4-33) ertical axis D(6=0071 use v=6=threshold (x=(0)=() , (r=(u, +1 if P (v)<P, o If polarity pF1, this region is +1 1 otherwise If polarity pa-1, this region is-1 Adaboost, Vga
Weak classifier we use here: Axis parallel weak classifier • In order to simplify the derivation, we will use the simple “axis parallel weak classifier”. That means m=0 for v=mu+c, hence v=c; (v=input, c=constant) • It assumes gradient (m) of the decision line is =0(horizontal) or (vertical). • The decision line is parallel to either the horizontal or vertical axis. ( ) ( ) − + = = = = = = 1 otherwise 1 if ( ) ( , ) ( , ) ( ) use 0 0 p v p v h x u v f x u v v v threshold t t t t t Adaboost , V9a 15 ht (x) v0 If polarity pt=1, this region is +1 If polarity pt=-1, this region is -1 If polarity pt=1, this region is -1 If polarity pt=-1, this region is +1