Page 246 - Special Topic Session (STS) - Volume 1

STS426 Asis K.C.
significant in the data application of imputation techniques may result in loss
of accuracy and the severity of error increases with the increased proportion
of missing observations. To tackle this situation, they proposed this alternative
classification rule by including the proportion of missing observation in the
construction of classification rule.
For the redefined loss due to misclassification, the classification rule with
prior probabilities and would be to classify an observation (, ) to
1
2
group 1 if
log 1 (,) > log 2 (1|2) = log 2 1 (1− 1 ) ………Rule 2
2 (,)
1 (1|2)
1 2 (1− 2 )

else classify to group 2.
For Rule 2 the total cost of misclassification is less than that for Rule 1.
In order to compare the performances of the rules on the basis of above
mentioned astronomical data, the following exercise had been carried out.
As before, for the NGC 5128 data set, they have first performed a k-means
clustering with k=2 and formed two clusters( 55 observations in cluster 1 and
72 observations in cluster 2).Here the only difference was at each step they
have created few missing observations in the data.
Then they performed the classification in two different ways:
1. Rule 1a: The missing observations were discarded and Rule 1 was used
treating the resulting data set as a whole
2. Rule 2a: Rule 2 was used considering the missing proportions.
As earlier, they considered the three candidate distributions and found the
concerned TCM considering different choices of ( , ) and ( , ). Rule 1a
2
1
2
1
and Rule 2a are essentially the modified versions of Rule 1, adjusted for the
presence of missing observations. The resulting analysis is shown in Table-2
given below.

Table 2: TCM for NGC 5128 data with missing values
Rules Gamma TCM ( =0.9, =0.3) TCM ( =0.2, =0.8)
2
1
1
2
distribution ( = 0.06, = 0.15) ( = 0.06, = 0.15)
2
1
2
1
Rule 1a First form 0.170 0.045
Second form 0.050 0.019
Third form 0.029 0.004
Rule 2a First form 0.097 0.104
Second form 0.039 0.022
Third form 0.013 0.009

The important findings from the above tables are, the total cost of
misclassification for second and third form is less than the total cost of

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