MACHINE LEARNING QUESTION

A Latin square over the set L{1,2,3} is a 3x3 array such that each row and column contains exactly one element from L. Train an artificial neural network (with only one hidden layer containing two units) which decides whether a given array is a Latin square or not.

Notes:

1) Use excel to initialize the weights (in a normal distribution) or just assign random initial values.

2) Use the sigmoid function for all activation units.

3) Use cross-entropy as discussed in class.

4) There should be at least couple of steps in gradient-descent and your solution should have the (initial and updated) weights after every step.

Training-data:

1 2 3

2 3 1 A latin square

3 1 2

-------

2 1 3

3 2 1 Not a latin square

2 3 1

-------

2 1 3

1 2 3 Not a latin square

3 1 2

-------

1 2 3

3 1 2 A latin square

2 3 1

---------

1 3 2

2 1 3 A latin square

3 2 1

----------

2 2 1

3 1 3 Not a latin square

1 2 3

-----------

1 3 2

3 2 1 A latin square

2 1 3

----------

3 2 1

1 2 2 Not a latin square

3 1 3

------------

1 1 2

1 2 3 Not a latin square

2 3 3

---------

2 1 3

1 3 2 A latin square

3 2 1