Hi all,

The assignments bellow was also given in today's 
Pattern Recognition course (Thursday 15th October).

The due date is the same as the previous homework.

Akira,

---------- 8< ---------- 8< ---------- 8< ----------

We now assume two classes in which variance matrix
is not a diagonal one, that is,

==============================================
        1.1  0.3
Sigma =              ,mu-1 = (0, 0)  <=  class-1
        0.3  1.9
==============================================
        1.1  0.3
Sigma =              ,mu-2 = (3, 3)  <=  class-2
        0.3  1.9
==============================================

Example 100 points from each of the two classes
are attoched below. 

(1) Plot all of the 200 points on an appropriate
    coordinate of (x1, x2).

(2) Obtain the equation of the border of these 
    two classes and draw it on the coordinate of (1).

(3) We now want to classify a vector x = (1.0, 2.2).
    Answer the following question.

   i) Plot x on the coordinate of (1)

  ii) Calculate Eucledean distance to both of 
      the center of the two classes, i.e. 
      mu-1 and mu-2. Answer your geuss which class 
      do you think x is classified from the calculation?

 iii) Calculate Mahalanobis distance to both of 
      the center of the two classes, i.e. 
      mu-1 and mu-2. Answer if you change your decision
      in (ii).

4) Draw the line from which the Mahalanobis distance to
   mu-1 is 0.5, 1.0, 1.5, and 2.0 respectively on 
   the coordinate of (1).

5) Same as (4) but the Mahalanobis distance to mu-2.

class-1:
============
 0.08,  0.63
-0.57, -1.95
 0.04,  1.60
-0.62,  0.76
 0.62,  1.88
-0.64, -0.62
 0.85,  1.41
-0.35, -1.82
-0.66,  2.69
-0.28, -1.10
 0.24, -0.69
-0.33, -3.18
 0.83, -0.57
-1.44, -0.44
 2.54,  0.09
 1.00,  0.48
 0.18,  0.74
 1.49,  0.22
 0.59, -1.58
-1.74, -2.38
-0.31,  0.41
 1.58,  2.90
-0.03, -2.36
 1.21,  1.62
-0.02, -1.81
 0.34, -1.44
-0.58, -1.25
-0.40,  0.41
-0.80, -0.46
 0.31, -1.08
-1.81, -1.77
 0.13,  0.45
-0.09, -0.68
-0.60,  1.48
-0.43, -1.77
-0.39, -0.16
 0.97,  1.52
-0.32,  1.86
-0.53,  0.29
 1.33,  0.77
-2.15,  0.52
-0.04,  1.02
-0.38, -0.29
-0.74, -0.36
-0.13,  1.01
 0.23,  2.65
 0.40,  1.29
-0.25, -2.31
-0.34,  0.90
-2.06,  0.39
 0.31,  1.99
 0.01, -1.70
-0.12, -2.74
 0.16, -0.22
 0.83,  1.16
-1.44, -0.96
 0.61,  0.11
 0.65,  1.32
 0.07, -1.02
-1.50, -0.86
 1.15,  1.48
-2.55, -0.25
-1.96, -0.02
 0.24,  0.58
 0.70,  0.29
-0.36,  0.44
-1.07, -2.29
-1.03, -0.70
 2.29,  1.13
 2.19, -1.48
-0.83,  2.45
 1.15, -1.79
 1.46, -0.43
 0.47, -0.80
 0.21, -1.01
 0.45,  1.10
 0.68,  0.59
-0.37, -1.46
-0.30,  0.28
 1.34,  3.70
 0.91,  0.82
 0.69, -1.04
-0.72,  0.15
 0.73, -0.60
 0.84, -1.75
 0.72, -0.78
 1.21,  1.56
-0.75,  0.34
 0.82, -0.12
-0.09,  1.29
-0.08, -2.56
 0.13, -0.04
-0.16,  0.21
-2.31,  1.34
 2.01, -1.22
-1.48,  1.28
 0.64,  2.08
-0.82, -0.70
-1.13,  1.62
-0.14,  1.14

class-2:
============
 2.76,  3.26
 3.61,  6.35
 4.27,  4.01
 4.44,  6.03
 1.99,  2.43
 2.74,  3.65
 3.80,  5.82
 4.61,  6.21
 2.73,  4.33
 2.81,  5.60
 1.34,  2.16
 2.58,  4.15
 2.05,  3.11
 2.16,  4.82
 3.76,  6.14
 1.66,  3.66
 2.67,  2.22
 2.67,  4.82
 3.93,  4.87
 3.99,  3.40
 2.64,  5.57
 3.13,  5.69
 2.28,  3.75
 4.78,  2.69
 2.43,  2.34
 3.92,  5.82
 2.82,  5.40
 3.00,  1.59
 1.89,  2.68
-0.01,  3.29
 3.18,  1.68
 5.15,  2.39
 2.82,  2.87
 2.97,  3.41
 2.40,  0.49
 2.96,  6.46
 3.60,  4.93
 4.02,  3.94
 4.32,  3.88
 3.55,  5.83
 2.39,  2.27
 3.92,  5.77
 2.49,  2.25
 1.85,  2.55
 3.94,  4.55
 2.35,  4.28
 1.72,  2.37
 1.90,  3.96
 3.11,  5.83
 3.16,  5.34
 3.44,  6.26
 1.89,  5.36
 2.45,  5.40
 4.67,  5.14
 2.86,  2.40
 2.25,  1.24
 5.94,  5.28
 3.57,  3.46
 2.84,  2.36
 1.80,  3.19
 2.34,  4.08
 4.28,  4.93
 3.89,  2.84
 3.43,  1.65
 3.10,  5.12
 4.37,  5.34
 5.24,  2.92
 3.61,  0.96
 4.73,  3.10
 3.67,  4.74
 2.19,  2.77
 2.71,  4.83
 2.17,  2.27
 4.30,  6.17
 0.68,  3.90
 2.57,  3.82
 3.35,  3.31
 2.21,  3.22
 2.48,  4.02
 4.78,  4.32
 2.37,  1.55
 2.09,  4.10
 4.10,  5.93
 2.55,  4.30
 3.11,  6.27
 4.98,  4.11
 3.67,  6.53
 3.09,  2.18
 2.22,  4.57
 4.87,  4.76
 4.07,  3.61
 1.25,  2.75
 4.65,  4.84
 3.45,  4.24
 2.64,  5.46
 4.86,  3.97
 3.58,  3.55
 4.59,  4.43
 4.19,  5.89
 3.94,  3.35