1580
ANALYTICAL CHEMISTRY, VOL. 50, NO. 11, SEPTEMBER 1978
Comment on the Application of Feature Selection Method for Binary Coded Patterns Sir: Recently, various applications of pattern recognition techniques have been employed in the field of spectral interpretation and SAR (structure-activity relationship). However, it is pointed out by several authors (1-4) that deficiency in fundamental comprehension of the nonparametric classification method-especially the linear learning machine technique-resulted in misapplications of the technique. We have examined the feature selection method. by which the nonintrinsic dimensions are excluded. Those features which do not contribute to linear separability are called nonintrinsic ( I ) . Two different approaches are employed for this purpose; they are: (a) examination of importance of each dimension for class separability with the aid of class separation information (5-9), and (b) generation of new dimensions by making linear combination of original dimensions based on the variance of all data (Karhunen-Loeve transformation ( I O ) ) . The weight-sign feature selection method ( 5 ) known as an empirical technique for the former category is examined here. With the linear discriminant function, the pattern X,will be defined as class 1 or class 2 according t o the sign of the dot product si given by Equation 1,
where s, > 0, X, is categorized as class 1 and where s, < 0, X, is categorized as class 2. The weight vector W will be trained by a set of patterns whose class is known. Two weight vectors W+ and W- are to be trained for the weight-sign feature selection method. Their initial vectors are different from each other. The components of the two resultant weight vectors that correspond to the kth element of patterns are compared; and if both components have the same sign, then those components are retained. And components for which the signs are different are considered nonintrinsic and are discarded. This process is repeated as long as the feature selection routine can find nonintrinsic elements. We have found that two different patterns belonging to different classes could be made identical by reducing several features which are assigned as nonintrinsic by the feature selection routine. For example, two d + 1 dimensional binary patterns X1 (belonging to class 1) and X 2 (belonging to class 2) are given as follows;
X1 = (1, 0, x 3 , x4, ----,x d + J
class 1
X 2 = (0, 1, x3, x4, ----, x d + J
class 2
If the first and the second components of both patterns are eliminated, the two become identical. When two weight vectors W+ and W- are successfully trained, the following conditions should be satisfied for patterns X Iand X 2 . d
si+ =
x,’w+= ull++ kc=w3 k + x k + w + d + l > 0
d
S2+
=
xyw+ = w2+ + c W+k”k + W + d + l
0 SI- = ul- + w3-> 0 s2+ = wq+ + wy+ < 0 sp = w 2 -+ u y < 0 SI+
=
U$+
(2’1 (3’)
(4’) (5’)
1C1+Lc1-
