ISML Machine Learning, Lab 1 - Basic Matlab and Data Generation

This lab is about getting started with Matlab and data generation. The goal of the lab is to get familiar with Matlab syntax and to get a practical grasp of what we have discussed in class. Follow the instructions below. Think hard before you call the instructors!

• Check out getstart.pdf guide for a quick introduction to Matlab.

• Use the Matlab functions in the zip file.

1. Warm up - Welcome to Matlab!

• 1.A By using the Matlab shell, create a column vector v = [1; 2; 3] and a row vector u = [1,2,3]. What happens with the command v'?
  How is the operation “'“ called in matrix terms?
  Create z = [5;4;3].
  What happens by doing v + z?
  And u + z?

• 1.B Create the matrix A = [1 2 3; 4 5 6; 7 8 9] and the matrix B = A'; What kind of matrix is C = A + B?
  What happens typing A(:,1) and A(1,:)?
  By typing A(2:3,:) and A(:)?

• 1.C Play with the product “*”. What happens with 2*u, u*2, 2*v?
  What happens with u*v and v*u, why?
  With A*v, u*A and A*u?

• 1.D Use the pointwise operators “.*” and “./”. What happens with v.*z and v./z ? Why aren't A*A and A.*A the same?

• 1.E Use the following functions : zeros, ones, rand, randn (type help "function name" if needed).
  Create a 3x5 matrix of all zeros, all ones, random numbers uniformly distributed between 2 and 3 and random numbers distributed according to a Gaussian of variance 2.
  Finally, use the functions eye and diag, create a 3x3 identity matrix and a matrix whose diagonal is the vector v.

2. Core - data generation

Open the Matlab file MixGauss.m

• 2.A The function MixGauss(means, sigmas, n) generates datasets where the distribution of each class is a Gaussian with given a mean and variance.

• 2.B Have a look at the code or, for a quick help, type "help MixGauss" on the Matlab shell.

• 2.C Type on the Matlab shell the commands

[X1, Y1] = MixGauss([[0;0],[1;1]],[0.5,0.25],1000)
figure(1); scatter(X1(:,1),X1(:,2),25,Y1); %type "help scatter" to see what the parameters mean
title('dataset 1')

• 2.D Now generate a more complex dataset following the instructions below. 

  • Call MixGauss with appropriate parameters and produce a dataset with four classes: the classes must live in the 2D space and each should be centered on the corners of the unit square (0,0), (0,1) (1,1), (1,0), all with variance 0.2.
    
    [X2,C]=MixGauss(....)
    
    

  • Use the Matlab function "scatter" to plot the points.

  • Manipulate the data so to obtain a 2-class problem where data on opposite corners share the same class (if you produced the data following the centers order provided above, you may use the function "mod" for a quick result: Y2=mod(C,2) )

• 2.E Following the same procedure as above (section 2.D) generate a new set of data, from the same distribution, to be used as a test set: (X2t,Y2t)

3. If you have time - More experiments

• 3.A Generate more complex datasets with the MixGauss function, for instance by choosing larger variances, higher dimension, etc.

• 3.B You may also add noise to the data by randomly flipping the labels on the training set (set the percentage of flipped labels)

• 3.C Given a data set compute the distances among all input points (try not to use "for" loops): how does the mean distance change with the number of dimensions?

• 3.D Generate regression data considering a regression model defined by a linear function with Gaussian noise. Create a Matlab function with in input the number of points n, the number of dimensions D, a D dimensional coefficients vector w and a noise level delta. The output should be a n by d matrix X and an n by 1 vector Y. You might want to start with a 1 or 2 dimensional case, but also try higher dimensionalities.
  Plot the regression data.

• 3.E Generate regression data considering a 1-dimensional regression model defined by a non linear function.

• 3.F Generate a data-set (either for classification or regression) where most of the input variables are "noise", in the sense that they are unrelated to the output.