Master Thesis - Department of Computer Science

generated for obtaining goatishness and lambishness measures for each subject. Thus
for each (l, k) pair, we will obtain C goatishness and lambishness pairs corresponding
to every subject, and therefore (G
(l, k)
i
, L
(l, k)
i
the i th subject. Now a two step search is performed on (G
) represents the corresponding pair for
(l, k)
i
, L
(l, k)
i
)’s for each
subject over all (l, k) pairs (l = 0, 1, .., L and k = (l + 1), ..., K). First the set,
denoted as MGi, of all (l, k) pairs giving minimum Gi for i th subject is obtained.
MGi can be written as,
k)
MGi = {(l, k) | (l, k) = arg min G(l, i }. (3.9)
(l, k)
Among all the pairs in MGi, a single pair denoted as (li, ki) is selected which gives
minimum value for Li. So, (li, ki) represents the optimal subband face for subject i
and is obtained by,
where ˆ L
(l, k)
i
(li, ki) = arg min
(l, k)
ˆL
(l, k)
i | (l, k) ∈ MGi. (3.10)
’s are the lambishness values of the pairs selected in MGi. This operation
is repeated for all subjects. So final output of subband selection algorithm provides
C optimal (l, k) pairs, where (li, ki) or (Ali − Aki ) represents optimal subband face
for i th subject in the database.
The two step searching procedure discussed above, can be considered equivalent
to minimizing a weighted cost function with Gi and Li, for all (l, k) pairs, by assigning
weights say, 0.8 and 0.2 , respectively. The reason behind using a two-step search,
with Gi being minimized prior to Li, instead of giving equal weightage to both of the
measures is two-fold:
(l, k)
1. The minima of the sum, S i
(l, k)
= G i
+ L
(l, k)
i
, may not contain any of the
minima from Gi or Li. Thus it has a large scope of not detecting the local
minima’s from both set and can give a suboptimal result.
2. Searching with two-steps in a reverse way (Li prior to Gi) does not work well
due to the presence of a very few (single in almost all cases) minima’s for Li’s,
which provides no scope of minimizing Gi in any sense. Hence, an initial search
for Gi gives a rich collection of local minima’s from which searching for min(Li)
yields good results.
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