PhD Thesis Semi-Supervised Ensemble Methods for Computer Vision

4.2. SemiBoost 49
SemiBoost
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Figure 4.3: SemiBoost combined with a learned similarity measure from given labeled
samples.
given a non-pair-wise classifier that is able to deliver confidence-rated predictions, for
instance, an object detector, which can already (partially) solve our problem. We will
denote such a classifier as prior or prior classifier F P (x). From a practical perspective
and as can be seen in Figure 4.3, it would be now beneficial to incorporate such a prior
into SemiBoost in order to exploit unlabeled data. Therefore, we have to approximate the
pair-wise similarity s(x, x ′ ) using the non-pair-wise prior F P (x).
In the following, we first show how the training can be done. Second, for evaluation
we can use the prior by combining it with the newly trained classifier. Thereby, we benefit
from the information which is already encoded in the prior classifier. Roughly speaking,
the newly trained classifier can be rather “small”, only correcting the mistakes of F P (x).
In more detail, we assume that we have access to a prior classifier F P (x) : X →
[−1, 1] (e.g., an already trained face detector). The classifier has to provide a confidence
measure of its classification. The more confident the decision is the higher the absolute
value of the response. We can use boosting for training such a classifier and the responds
can be translated into a probability [Friedman et al., 2000]. We can now incorporate this
classifier into SemiBoost using the following approximation
|F (x, x ′ )| ≈ |F (x) − F (x ′ )|. (4.17)
In other words, a discriminative pair-wise function measuring the distance between x
and x ′ is approximated by the difference of a conventional classification function for two
samples.