[SOLVED] C matlab python graph theory PRIMMAL FORMULATION OF A NONLINEAR CLASSIFIER WITH MMSE

PRIMMAL FORMULATION OF A NONLINEAR CLASSIFIER WITH MMSE
Use the attached function to reconstruct the example of lesson 6.1.In particular,you must:
1Construct a traindataset and represent them.Your representation may be rotated 90 with respect to the one of the slides.
2 Construct a function to directly map the data into a 10 dimension Hilbert space using the Volterra expansion.
3 Compute the weights of the MMSE solution, and representthe boundary as indicated in the video.
Provide a document that summarizes the theory and a graph of the result. Comment your results.
MATLAB CODE
X,ydata100,0.2

i1findy1;
i2findy1;
figure1
plotX1,i1,X2,i1,s
hold on
plotX1,i2,X2,i2,r
xlabelxn1
ylabelxn

function X,ydataN,a
NN1;
ysignrandn1,N;
xfilter1 a,1,y0.2randnsizey;
Xbufferx,2,1,nodelay; Convolution
yy2:end
end

DUAL FORMULATION OF A NONLINEAR MMSE CLASSIFIER
Use the functions of the previous assignmentto reconstruct the example of lesson 6.1 but using a dual representation an the polynomial kernel
1Construct a traindataset and represent them.
2 Construct a function that computer the kernel matrixK.
3 Compute the dual weightsof the MMSE solution.
4 Write an estimator in dual form as a function of kernel dot products between the trainikng and test data.
5 Plot the boundary,
6 Repeat the experiment, but using the Ridge Regression solution, this is

whereis a small number. Show the result for different values of the parameter that are able to produce different solutions. Comment the results.
Provide a document that summarizes the theory and a graph of the result. Comment your results.

NONLINEAR SVM CLASSIFIER
Use anSVMclassifier to solve the classification problem of assignment 6.1
A. How to use the svmtrainfunction:
If you type svmtrainyou will see that the option t 4 exists, which allows the user to compute a kernel matrix and use it as an input instead of introducing the data. We will use this option to precompute the kernel matrix and place it in the position traininginstancematrix. A similar option is present in Python
B. Work out a function whose input is the data matrix X and woseoutput is the matrix of kernel dot products for
Linear kernel.
Order 3 polynomial kernel.
Square exponential or Gaussian kernel with variable parameter.
Constructa training set of 100 samples and train a Support Vector Machine.
Validate the parameter of the square exponential kernel and C with avalidatinset of 110 samples.
Construct a test set of 1000 samples.Computethe kernel matrix between training and test sets.
Compute the test error.
Do it for all three kernels.
Provide the following
A draw of the classification boundaryfor the best values of validation parameters.
Comments on the results.