Active learning method for multi-class classifiers
View Patent ↗A method trains a multi-class classifier by iteratively performing the following steps until a termination condition is reached. The probabilities of class membership for unlabeled data obtained from an active pool of unlabeled data are estimated. A difference between a largest probability and a second largest probability is determined. The unlabeled data with the lowest difference is selected, labeled and then added to a training data set for training the classifier.
1. A method for training a multi-class classifier, comprising a processor for performing steps of the method iteratively until a termination condition is reached, comprising the steps of:
estimating probabilities of class membership for unlabeled data obtained from an active pool of unlabeled data;
determining a difference between a largest probability and a second largest probability;
selecting the unlabeled data with the lowest difference;
labeling the selected unlabeled data;
adding the labeled data to a training data set; and
training the classifier with the training data set.
2. The method of claim 1 , wherein the classifier is trained with a seed set of labeled data.
3. The method of claim 2 , wherein the seed set includes two samples of the labeled data.
4. The method of claim 1 , further comprising:
evaluating, after the training, a performance of the classifier with a test data set to determine whether the termination condition is satisfied.
5. The method of claim 1 , wherein the multi-class classifier uses a support vector machine.
6. The method of claim 1 , wherein a number of the classes is unknown.
7. The method of claim 1 , wherein the estimating uses a sigmoid function.
8. The method of claim 1 , wherein the probability of a sample x is
p
(
x
)
=
1
1
+
exp
(
Af
(
x
)
+
B
)
,
where ƒ(x) is a decision function, A and B are parameters to be estimated.
9. The method of claim 8 , estimating the parameters using maximum likelihood estimation is used to solve for the parameters according to
max
(
A
,
B
)
[
∑
i
=
1
l
(
t
i
log
(
p
i
)
+
(
1
-
t
i
)
log
(
p
i
)
)
]
where l is the number of samples in the active pool, and t is a parameter for each sample to adjust the importance of the positive and negative labeled examples, min is a function that selects a smallest value, i is a number of samples in the training data set, and
p
i
=
1
1
+
exp
(
Af
(
x
i
)
+
B
)
,
t
i
=
{
N
p
+
1
N
p
+
2
if
y
i
=
1
1
N
n
+
2
if
y
i
=
-
1
,
and
N p and N n are positive 103 and negative 104 samples in the training data set, respectively.
10. The method of claim 9 , wherein the maximum likelihood is determined using Newton's gradient method and a backtracking line search.
11. The method of claim 5 , wherein comparisons by the support vector machine is pair-wise.
12. The method of claim 8 , wherein a number of the classes is k and a number samples in the training data set is I, and a discrete entropy of a class membership Y is
H
(
Y
)
=
-
∑
i
=
1
k
p
i
log
(
p
i
)
.
13. The method of claim 6 , wherein a number of the classes is greater than one hundred, and a number of samples in the training data set is greater than sic thousand.
14. The method of claim 1 , further comprising:
evaluating, after the training, a performance of the classifier with a validation data set to determine whether the termination condition is satisfied.
15. The method of claim 1 , further comprising:
evaluating a maturity score to as the termination condition.
16. The method of claim 15 , further comprising:
determining a ratio of the number of newly discovered classes over a fixed number of most recent training cycles; and
assigning the inverse of the ratio as the maturity score.
17. The method of claim 15 , further comprising:
determining an average score of the lowest difference over a fixed number of most recent training cycles; and
assigning the average score as the maturity score.
18. The method of claim 14 , further comprising:
applying the trained classifier to the validation or test data,
computing a ratio of correctly classified samples using labels;
assigning the ratio of correctly classified samples as a maturity score; and
evaluating the maturity score to as the termination condition.
19. The method of claim 1 , further comprising:
initializing the training data with labeled seed data.
20. The method of claim 19 , where in the seed data set includes two labeled samples.