Geoscience Reference
In-Depth Information
Positive labeled data
Negative labeled data
Unlabeled data
Supervised decision boundary
Semi−supervised decision boundary
−1.5
−1
−0.5
0
0.5
1
1.5
2
x
Figure 2.1:
A simple example to demonstrate how semi-supervised learning is possible.
2.3
INDUCTIVE VS. TRANSDUCTIVE SEMI-SUPERVISED
LEARNING
There are actually two slightly different semi-supervised learning settings, namely inductive and
transductive semi-supervised learning. Recall that in supervised classification, the training sample is
fully labeled, so one is always interested in the performance on future test data. In semi-supervised
classification, however, the training sample contains some unlabeled data. Therefore, there are two
distinct goals. One is to predict the labels on future test data. The other goal is to predict the labels on
the unlabeled instances in the training sample. We call the former
inductive semi-supervised learning
,
and the latter
transductive learning
.
l
i
=
Definition 2.1.
Inductive semi-supervised learning
.
Given a training sample
{
(
x
i
,y
i
)
}
1
,
l
+
u
{
x
j
}
j
=
l
+
1
, inductive semi-supervised learning learns a function
f
:
X
→
Y
so that
f
is expected
l
+
u
to be a good predictor on future data, beyond
{
x
j
}
j
=
l
+
1
.
Like in supervised learning, one can estimate the performance on future data by using a
separate test sample
k
=
1
, which is not available during training.
{
(
x
k
,y
k
)
}
l
+
u
i
=
1
,
Definition 2.2. Transductive learning
.
Given a training sample
{
(
x
i
,y
i
)
}
{
x
j
}
j
=
l
+
1
, trans-
l
+
u
l
+
u
ductive learning trains a function
f
:
X
→
Y
so that
f
is expected to be a good predictor
l
+
u
on the unlabeled data
j
=
l
+
1
. Note
f
is defined only on the given training sample, and is not
required to make predictions outside. It is therefore a simpler function.
{
x
j
}
There is an interesting analogy: inductive semi-supervised learning is like an in-class exam,
where the questions are not known in advance, and a student needs to prepare for all possible
questions; in contrast, transductive learning is like a take-home exam, where the student knows the
exam questions and needs not prepare beyond those.
