                 ###########################
                 # The Concentric database #
                 ###########################


1. Aim :

    Study of the linear separability of the classifier when some classes are 
    nested in other without overlapping.

2. Description :

    Bidimentional uniform concentric circular distributions with two classes.
    The database is entirely contained in the square (0,0), (1,1).

        2500 instances, 1579 in class 1 (63.2%), 921 in class 0 (36.8%).
 
    - The points of class 0 are uniformly distributed into a circle of 
      radius 0.3 centered on (0.5,0.5).

    - The points of class 1 are uniformely distributed into a ring    
      centered on (0.5,0.5) with internal and external radius respectively 
      egal to 0.3 and 0.5.


3. Best theoretical Bayes confusion : 

          Class     0      1  
           0      100      0
           1        0    100

   (The classes don't overlap).


4. Confusion obtained with the k_NN classifier (Leave_One_Out).
   k has been set to 7 in order to obtain 
   the best averaged error rate : 0.96 +/- 0.5%.

          Class         0               1  
           0      99.1 +/- 0.6%    0.9 +/- 0.6%
           1       1.0 +/- 0.5%   99.0 +/- 0.5%


