Master Thesis - Department of Computer Science

• Product Rule: Product Rule computes the soft class label vectors as:
˜d j (x) = d j
Null (x) ∗ djRange
(x), j = 1, ...., C (4.33)
4.4.2 Proposed Technique for Decision Fusion
Unlike sum rule and product rule, our technique of decision fusion learns each of
the classifier’s behavior by using training data at decision level. Learning a classifier
involves training with the response of that classifier. So the response vectors on a
validation set of a database which is disjoint from training and testing set can be
used as training information at decision level for learning the behavior of a classifier.
We employ LDA and nonparametric LDA on training information at decision level to
build up discriminative eigenmodel. Then response vectors of the input test images
are projected in that eigenmodel and for each test response vector, the similarity
measures for the respective classes in the eigenmodel provide a new response vector
which replaces the old test response vector.
To accomplish the whole task, we divide our database into three disjoint subsets,
training, validation and testing sets. Now the training set along with validation set
and testing set respectively constructs the “training response vector set” and “testing
response vector set”, respectively at classifier output space. Then “training response
vector set” is used as training data to construct a LDA or nonparametric LDA-based
eigenmodel at classifier response level.
Here, we formally define validation and testing set which are independent of any
classifier. Let, the validation and testing set of a database are denoted by XV A and
XT S and can be defined as,
XV A = [vx 1 1 , vx12 , . . . , vx1V , vx21 , . . . , vxij , . . . , vxCV ], (4.34)
XT S = [tx 1 1, tx 1 2, . . . , tx 1 S, tx 2 1, . . . , tx i j, . . . , tx C S ]. (4.35)
where vx i j represents the jth validation sample from class i and V is the number of
validation samples per class. Similarly, j th testing sample from class i is denoted
by tx i j
and number of testing samples per class is represented as S. The “training
response vector set” and “testing response vector set” for null space classifier are
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