Machine Learning Week 2

Multivariate Linear Regression

Build up the model(Matrix notion)

notions used to describe the model:
n=variable numbers, m=training example numbers
x(i)jwhich i denotes No.i training examples j denotes No.j variable

in order to do the vectorise, we need to change the model a little bit which create a constant variable x0=1 and make the parameters vector into θT(1*(n+1)matrix) and make the variables vector into X ((n+1)*1 matrix )with the n denotes amount of variables.

Skills used to do the gradient descent

Skill used on training data:

gradient decsent

Important skill in doing the gradient descent:
make the variable into the same scale(approximately near to [-1,1])

mean normalization

Choose the right learning rate:

make sure the gradient descent is working correctly

choose the right learning rate not too big or too small

too small will cause the J(θ)decrease slow too big may not decrease

Polynomial Regression

Some times not only linear but also have quadratic or polynomial regression

Tips: Feature scaling without mean normalisation is only divided by the scale

Normal Equation

Use the same notion with gradient descent to calculate the parameters vector by normal equation

By using the normal equation, don’t need to do the feature scaling or mean normalisation, and the corresponding Matlab syntax is also in the graf

Compare the gradient descent and normal equation
The normal equation don’t need to choose learning rate and do the iteration but Gradient descent may work well when the number of features is large i.e. n=106

Matlab Syntax

Input/Output/Change Route

>>cd'/Users/lyking/Desktop'>>ls>>who>>whos>>clear>>save hello.txt/hello.mat variable -ascii %human readable format, if don't use this will be binary format>>load hello.txt % hello.dat/('shit.dat') is also OK

Build Up Matrix

>>A=[1 2;3 4;5 6]>>A(3,2)ans=    6>>A(:,2)ans=    2    4    6>>A([1 3],:)%take the corresponding rows in the vectorans=    1 2    5 6>>A(:,2)=[10;11;12]%change valueA=    1 10    3 11    5 12>>A=[A,[101;102;103]]%append another columnA=    1 10 101    3 11 102    5 12 103>>A(:)ans=    1    3    5    10    11    12    101    102    103>>A=[1;2]>>B=[3;4]>>C=[A B]C=    1 3    2 4>>C=[A;B]C=    1    2    3    4

Matrix Operation

>>A=[1 2;3 4;5 6]>>B=[11 12;13 14;15 16]>>C=[1 1;2 2]>>A*Cans=    5 5    11 11    17 17>>A.*B%element wiesans=    11 24    39 56    75 96>>A.^2ans=    1 4    9 16    25 36>>V=[1;2;3]>>1./V>>log(V)>>exp(V)>>abs(V)>>-V>>V+ones(length(V),1)>>V+1>>A'%transpose>>max(V)>>[r,c]=max(V)>>A=magic(3)%magic matrix>>[r,c]=find(A>=7)>>a=[1 2 3 4]>>sum(a)>>prod(a)%time all the elements together>>floor(a)%used for decimal>>ceil(a)%used for decimal>>rand(3)%like magic matrix but is randomly generated between (0,1)>>max(A,[],1)%find the biggest in the column>>max(A,[],2)%find the biggest in the row>>max(A(:))%find out the biggest in all elements>>sum(A,1)%column sum>>sum(A,2)%row sum>>eye(9)%identity matrix>>flipud(eye(9))%flip up down>>A.*eye(9)%only left the value in the diagonal>>pinv(a)%inverse of matrix a