This is an example of the partitioning described in the supplemental
document for Task 1.

For simplicity, we assume a data set of 10 samples; X1,X2,...,X10, each
Xi is a scalar rather than a vector, Yi denotes the class number of
Xi, and the number of classes is 3.

Let's assume Yi, i=1,...,10 are given as shown in the following table.
    X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
Yi:  3  1  2  3  2  1  2  3  3  1

(NB: The above shows, for example, Y1 is 3, which is the class number of X1,
Y2 is 1, which is the class number of X2,)

As you see, the number of samples for each class is:
N1 = 3,  N2 = 3,  N3 = 4

If the number of partitions we use is 3, i.e. K=3, Mc, c=1,2,3 are
given as follows. 
M1 = floor( N1 / K ) = 1
M2 = floor( N2 / K ) = 1
M3 = floor( N3 / K ) = 1

So, we assign X1,..., X10 to partitions as follows.
 Partition 1:
   Class 1:  X2
   Class 2:  X3
   Class 3:  X1

 Partition 2:
   Class 1:  X6
   Class 2:  X5
   Class 3:  X4

 Partition 3:
   Class 1:  X10
   Class 2:  X7
   Class 3:  X8, X9

From the above, you can obtain PMap as follows.
       X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
PMap:   1  1  1  2  2  2  3  3  3  3


If the number of partitions we use is 2, i.e. K=2, Mc, c=1,2,3 are
given as follows. 
M1 = floor( N1 / K ) = 1
M2 = floor( N2 / K ) = 1
M3 = floor( N3 / K ) = 2

So, we assign X1,..., X10 to partitions as follows.
 Partition 1:
   Class 1:  X2
   Class 2:  X3
   Class 3:  X1, X4

 Partition 2:
   Class 1:  X6, X10
   Class 2:  X5, X7
   Class 3:  X8, X9

From the above, you can obtain PMap as follows.
       X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
PMap:   1  1  1  1  2  2  2  2  2  2