Geoscience Reference
In-Depth Information
BIBLIOGRAPHICAL NOTES
Transductive SVMs, as S3VMs were originally called, were proposed by Vapnik [
176
]. Due to its
non-convex nature, early implementations were limited by the problem size they could solve [
18
,
58
,
68
]. The first widely used implementation was by Joachims [
89
]. Since then, various non-
convex optimization techniques have been proposed to solve S3VMs [
34
], including semi-definite
programming [
55
,
54
,
188
,
189
], gradient search with smooth approximation to the hat function [
36
],
deterministic annealing [
157
], continuation method [
32
], concave-convex procedure (CCCP) [
42
],
difference convex (DC) programming [
182
], fast algorithm for linear S3VMs [
156
], Branch and
Bound [
33
], and stochastic gradient descent which also combines with the manifold assumption [
96
].
Some recent work relaxes the assumption on unlabeled data [
190
].
The idea that unlabeled data should not be very close to the decision boundary is a general
one, not limited to S3VMs. It can be implemented in Gaussian Processes with the null category
noise model [
106
,
40
], as information regularization [
169
,
44
,
45
], maximum entropy discrimination
approach [
87
], or entropy minimization [
79
,
108
,
122
].
