Support vector Machine (svm) ING SHEN SSE TONGJIUNIVERSITY SEP.2016
Support Vector Machine (SVM) Y I NG SH EN SSE, TO NG JI UNI VERSITY SEP. 2 0 1 6
What is a vector SVM= Support VECTOR Machine If we define a point a(3, 4 )in r2 we can plot it like this There exists a vector between the origin and a 5 1/27/2021 PATTERN RECOGNITION
What is a vector? SVM = Support VECTOR Machine If we define a point A(3,4) in ℝ 2 we can plot it like this. There exists a vector between the origin and A. 1/27/2021 PATTERN RECOGNITION 2
The magnitude of a vector The magnitude or length of a vector x is written alland is called its norm 1/27/2021 PATTERN RECOGNITION
The magnitude of a vector The magnitude or length of a vector x is written 𝒙 and is called its norm 1/27/2021 PATTERN RECOGNITION 3
The direction of a vector The direction of a vector u=(u,u2)is the vector w=( u 2 u=4 0.8 a 20=1 05 5 COs()=2_3 0.6 lull 5 050.6 cos(a)=2 4 =0.8 1/27/2021 PATTERN RECOGNITION
The direction of a vector The direction of a vector u=(u1 ,u2 ) is the vector w=( 𝑢1 𝑢 , 𝑢2 𝑢 ) 1/27/2021 PATTERN RECOGNITION 4 cos 𝜃 = 𝑢1 𝑢 = 3 5 = 0.6 cos 𝛼 = 𝑢2 𝑢 = 4 5 = 0.8
The dot product if we have two vectors x and y and there is an angle b between them, their dot product is x·y=‖ xlllyllcos(0) Talking about the dot product x y is the same as talking about the inner product (x y(in linear algebra scalar product 1/27/2021 PATTERN RECOGNITION
The dot product if we have two vectors x and y and there is an angle θ between them, their dot product is : 𝒙 ∙ 𝒚 = 𝒙 𝒚 𝑐𝑜𝑠(𝜃) Talking about the dot product x∙y is the same as talking about ◦ the inner product ⟨x,y⟩ (in linear algebra) ◦ scalar product 1/27/2021 PATTERN RECOGNITION 5