Incremental learning has been investigated by many researchers. However, only few works have considered the situation where class imbalance occurs. In this paper, class imbalanced incremental learning was investigated and an ensemble-based method, named Selective Further Learning (SFL) was proposed. In SFL, a hybrid ensemble of Naive Bayes (NB) and Multilayer Perceptrons (MLPs) were employed. For the ensemble of MLPs, parts of the MLPs were selected to learning from the new data set. Negative Correlation Learning (NCL) with Dynamic Sampling (DyS) for handling class imbalance was used as the basic training method. Besides, as an additive model, Naive Bayes was employed as an individual of the ensemble to learn the data sets incrementally. A group of weights (with the number of the classes as the length) are updated for every individual of the ensemble to indicate the 'confidence' of the individual learning about the classes. The ensemble combines all of the individuals by weighted average according to the weights. Experiments on 3 synthetic data sets and 10 real world data sets showed that SFL was able to handle class imbalance incremental learning and outperform a recently related approach.
Citation: Minlong Lin, Ke Tang. 2017: Selective further learning of hybrid ensemble for class imbalanced increment learning, Big Data and Information Analytics, 2(1): 1-21. doi: 10.3934/bdia.2017005
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Incremental learning has been investigated by many researchers. However, only few works have considered the situation where class imbalance occurs. In this paper, class imbalanced incremental learning was investigated and an ensemble-based method, named Selective Further Learning (SFL) was proposed. In SFL, a hybrid ensemble of Naive Bayes (NB) and Multilayer Perceptrons (MLPs) were employed. For the ensemble of MLPs, parts of the MLPs were selected to learning from the new data set. Negative Correlation Learning (NCL) with Dynamic Sampling (DyS) for handling class imbalance was used as the basic training method. Besides, as an additive model, Naive Bayes was employed as an individual of the ensemble to learn the data sets incrementally. A group of weights (with the number of the classes as the length) are updated for every individual of the ensemble to indicate the 'confidence' of the individual learning about the classes. The ensemble combines all of the individuals by weighted average according to the weights. Experiments on 3 synthetic data sets and 10 real world data sets showed that SFL was able to handle class imbalance incremental learning and outperform a recently related approach.
Normal machine learning problems require learning model to learn information from all the achieved data and all the data are stored. However, in practice, the data are usually updated all the time and new information is necessary to be learned from the new data [19]. It is usually time consuming to learn new information with accessing to the previous data and storing the learned data is also expensive. In this situation, the learning model is required to have the ability of learning new information from new data and preserving the previously learned information without accessing the previous data. This learning model is called incremental learning [8], [21].
In incremental learning, the whole data set is not available in a lump. In another word, we can only get a part of the whole data set every time. We suppose that the whole data set S is divided into T subsets, i.e.,
In our assumption, even though the rules are different between different data subsets, the target rules (i.e., R) are not changed. This phenomenon was also called virtual concept drift [28] and it is different from real concept drift, in which the target concept is changed when new data subsets are available. Virtual concept drift was called sampling shift in [22] and it will be referred to in this paper. There are some additive models that can be easily adopted to learn incrementally when sampling shift occurs. For example, in Bayes Decision Theory, the rules can be represented by some parameters and the parameters of the whole data set can be combined by those of all the data subsets. In this way, the models can learn the data subsets respectively to form a same learner of learning the whole data set. However, these kinds of methods often require assumptions about the data distribution and the decision boundaries are always simple. Neural networks have strong abilities to learn complex classification boundary. Unfortunately, they are not additive. By training with new data subsets, the model tends to perform well on the new data subsets but poorly on the previous ones [8]. In other words, the model forgets the previously learned rules. Therefore, it is a challenge to employ neural networks to learn incrementally in this situation.
To exploit neural networks for incremental learning, some ensemble based approaches have been proposed. In our previous work, i.e., Selective Negative Correlation Learning (SNCL) [26], selective ensemble method was employed to pre-vent the model from forgetting previously learned information. There are also other ensemble based methods for incremental learning, such as Fixed Size Negative Correlation Learning (FSNCL), Growing Negative Correlation Learning (GNCL) [15], and Learn++ methods [21], [17], [5]. In SNCL and FSNCL (size-fixed methods), the model was able to learn new information from new data subsets with the size of the model fixed. How-ever, the ability of preserving previously learned information was not as good as Learn++ methods and GNCL (size-grown methods), in which the sizes of the models grown larger as new data subsets were learned. Since the new data subsets always become available all the time in practice, the sizes of the models will become too large in Learn++ methods and GNCL. Therefore, it is worthy to design a method with the benefits of both size-fixed methods and size-grown methods.
Besides sampling shift, there is another issue in incremental learning, i.e., class imbalance. In normal learning model, class imbalance problem has been studied by many researchers and there are plenty of literatures addressing class imbalance problems [11], [4], [9]. Class imbalance problems may also occur in incremental learning and this kind of issue has also been investigated [5], [6]. There are mainly two cases for class imbalance incremental learning:
(1) If the class distribution of the whole data set
(2) Even though the class distribution of
In this paper, we focus on class imbalance cases, in which sampling shift also occurs. Specifically, when sampling shift occurs, new classes may come up in the new data subset and some previous classes may be lost in the new data subset. When class distribution of the whole data set is imbalanced, this phenomenon will be more likely to happen to the minority classes. This is also the main issue in this paper.
The rest of the paper is organized as follows. In Section Ⅱ, we will briefly review some existing methods for incremental learning. Our methods, i.e., Selective Further Learning (SFL) will be described in Section Ⅲ. Then in Section Ⅳ, the experimental studies will be presented. Finally, we will conclude this paper and discuss the future work in Section Ⅴ.
Some neural network based methods, such as the Adaptive Resonance Theory modules map (ARTMAP) [3], [23], [29], [2] and Evolving Fuzzy Neural Network (EFuNN) [12] have been proposed for incremental learning. Both ARTMAP and EFuNN can learn new rules by changing the architecture of the models, such as self-organize new clusters (in ARTMAP) and create new neurons (in EFuNN) when new data are sufficiently different from previous ones. However, it is usually a non-trivial task to estimate the difference between new data and previous ones. Moreover, both of them are very sensitive to the parameters of the algorithms.
Researches have shown the good performance of ART-MAP and EFuNN in incremental learning. However, their abili-ties of learning incrementally in class imbalance situation have not been well investigated. In [5], where Learn++.UDNC was proposed for class imbalance incremental learning, fuzzy ARTMAP [2] was presented with poor performance when class imbalance occurs. Learn++.UDNC is an ensemble based method. It is one of the Learn++ series methods [21], [20] which were based on AdaBoost [7]. Besides Learn++.UDNC, many versions of Learn++ methods have been proposed, such as Learn++.MT [16], Learn++.MT2 [16], Learn++.NC [18] and Learn++.SMOTE [6]. In these versions, Learn++.MT and Learn++.NC was proposed for handling the problem of "out-voting" when learning new classes. Learn++.MT2 was pro-posed for handling the imbalance of examples between data subsets. These versions did not consider class imbalance situations. Class imbalance in incremental learning was addressed only in Learn++.UDNC and Learn++.SMOTE. In Learn++.UDNC, it was assumed that no real concept drift will happen, while in Learn++.SMOTE, real concept drift in class imbalanced data was investigated. Therefore, the former matches the issue in this paper but the later dose not.
Besides Learn++, another type of ensemble based methods, i.e., methods based on Negative Correlation Learning (NCL) [14], have also been proposed for incremental learning [26], [15]. NCL is a method to construct neural networks ensemble. It is capable of improving the generalization performance of the ensemble by decreasing the error of every neural network and increasing the diversities between neural networks simultaneously. In [15], tow NCL-based methods, i.e., FSNCL and GNCL were proposed. In FSNCL, the size of the ensemble is fixed and all of the neural networks are trained when new data subsets become available. In GNCL, the size of the ensemble grows as the data sets are incrementally learned and only new added neural networks are trained when new data subsets become available. In our previous work [26], SNCL was proposed. In SNCL, new neural networks are added and trained when new data subsets become available and then a pruning method was employed to prune the ensemble to make the size of the ensemble fixed. Comparing to Learn++ methods and GNCL, FSNCL and SNCL can make the size of the ensemble fixed as more and more data sets come up while their abilities of preserving previously learned information are poorer than Learn++ and GNCL.
There are also some other methods with ability of incremental learning. Self-Organizing Neural Grove (SONG) [10] is an ensemble based method with Self-Generating Neural Net-works (SGNNs) [27] as the individual learners. Incremental Backpropagation Learning Networks (IBPLN) [8] employed neural networks for incremental learning by making the weights of the neural network bounded and adding new nodes. However, they did not consider the class imbalance in incremental learning.
In this paper, class imbalance is considered in incremental learning. In the existing work, Learn++.UDNC [5] was pro-posed for addressing this issue and it has been shown more effective than other incremental learning methods which did not consider class imbalance situation. However, as a size-grown method, the size of the ensemble in Learn++.UDNC increases all the way as new data sets become available. The size of the ensemble may become too large. In our method, ensemble based method is also considered and at the same time, we aim at controlling the size of ensemble at an acceptable level.
In our previous work, i.e., SNCL [26], selective ensemble was used to keep the size of the ensemble fixed. When new data subset comes up, it is used to train the copy of the previous ensemble. The two ensembles are combined and half of the individuals in the ensemble are pruned to keep the size of the ensemble fixed. However, in this model, previous information loss may easily occur due to the pruning process based on the latest data subset. The ensemble will be biased to the latest data subset. Furthermore, if the rules of the latest data subset is quite different from that of the previous data subset, i.e., high sampling shift occurs, all of the individuals of the previous ensemble might be pruned. On the other hand, since SNCL was designed without considering class imbalance situation, it might not be good at handling class imbalance incremental problems.
To overcome the above drawbacks, we propose a new en-semble based approach for incremental learning, i.e., Selective Further Learning (SFL). In SFL, a hybrid ensemble with two kinds of base classifiers was used. First of all, a group of Multi-Layer Perceptrons (MLPs) are used. When new data subsets become available, half of the MLPs in the current ensemble are selected to be trained with the new data subsets. After training, the selected MLPs are laid back to the ensemble. No pruning process will be executed so that the risk of previous information forgetting is reduced. At the same time, as an additive model, Naive Bayes (NB) is used as a component of the ensemble to incrementally learn from new data subsets. In this way, the strong incremental learning ability of NB will help the ensemble to preserve the previous information if high sampling shift occurs.
In addition, a group of weights (namely impact weights) are constructed for every individual (including MLPs and NB). The weights and the outputs of the
yk=M∑i=1wikoik/M∑i=1wik,k=1,2,...,C, | (1) |
where
On one hand, the grade that the
Fik=2RikPikRik+Pik | (2) |
where
Rik=N(i)kk∑Cm=1N(i)km | (3) |
and
Pik=N(i)kk∑Cm=1N(i)mk | (4) |
where
On the other hand, since MLPs could be easily biased to the latest data subset, if some classes in the previous data subsets do not come up in the new data subset, the output of the MLPs that are selected to be trained with the new data subset should be suspectable. Therefore, a coefficient
μi=ntnc, | (5) |
where nt is the number of classes that are contained in the new data subset, nc is the number of classes in all the coming up data subsets.
By considering both of the above issues,
wik=Fikμi. | (6) |
For the model of NB,
The pseudo-code for the approach is presented in Fig. 1. In the pseudo-code, Select is the selecting process for selecting MLPs from the ensemble to be trained with the new data sub-set, MLPs-Training and NB-Training were the training process for training the MLPs and NB in the ensemble. The details of these processes are described in the following subsection.
The selecting process is based on the current data subset
If the current data subset does not contain some classes that have appeared in the previous data subsets, the selection process should ensure that not all the MLPs that have been trained with the data of the lost classes are added to
Πk∈L(∑iwik)≠0. | (7) |
where
In this way, the MLPs that are not well trained are selected to be further trained. Besides, the MLPs that are reserved in
According to Bayes Decision Theory, the probability of an testing example
P(k|x)=P(x|k)P(k)P(x)=P(x|k)P(k)∑Ck=1P(x|k)P(k) | (8) |
where
P(k|x)=Πdi=1P(xi|k)∑Ck=1Πdi=1P(xi|k). | (9) |
In incremental learning mode,
The estimation of
We have proposed a Dynamic Sampling (DyS) method for class imbalance problems [13], which can be used for training the ensemble of MLPs. Similarly to the approach proposed in [13], the main process of DyS for an ensemble is presented as follows (in one epoch):
step1. Randomly fetch an example
step2. Estimate the probability
step3. Generate a uniform random real number
step4. If
step5. Repeat steps 1 to 3 until there is no example in the training set.
The above steps will be repeated until stop criterion is satisfied. The following shows the method for estimating
In a problem with
The same to [13], the probability that an example belonging to class
p={1,if δ<0,e−δrkmini{ri},otherwise | (10) |
where
By employing DyS, the MLPs in the ensemble are able to accommodate to class imbalance situations.
In general, there are several essentials inside SFL that would make SFL successful, including the selective training of MLPs, the use of NB, the setting of impact weights for comb-ing the individuals in the ensemble, and the consideration of class imbalance in training process.
To analyze the reason for the success of SFL, two especial cases in incremental learning are considered, i.e., new classes in the new data subsets and the loss of previous classes in the new data subsets. The ensemble are divided into three parts:
After learning a new data subset which contains new classes,
After learning a new data subset which loses some previous classes,
Besides, as we discuss before, NB is able to learn incrementally without forgetting previous information. The use of NB will help to prevent the ensemble from catastrophic forgetting. Furthermore, in the training of NB and MLPs, the situation of class imbalance is considered. Therefore, SFL is able to deal with class imbalance in the new data subsets.
To assess the performance of SFL, some synthetic data sets and real-world data sets were used to conduct the experiments. First of all, three types of synthetic data sets were generated to simulate the incremental learning process. Then, 5 real-world data sets with imbalanced class distributions from UCI repository [1] were used to simulate incremental learn-ing by randomly dividing the data sets. Finally, another 5 real-world data sets from UCI repository, including 3 class imbalanced data sets and 2 class balanced data sets, were used to simulate the incremental learning process by dividing the data sets. In this part, the dividing of the data sets considered new classes and the loss of previous classes in the new data subsets. The purpose of this part of experiment is to assess the ability of SFL learning form new classes and preserving previous in-formation when some classes are lost in the new data subsets. As a recently proposed approach which also addressed for class imbalanced incremental learning, Learn++.UDNC [5] was used for the comparison. Besides, in order to find out the efficiency of MLPs and NB to SFL, the model of ensembles with only MLPs (referred as SFL.MLP) and the model of NB are also compared with SFL. The recall of every class and the arithmetic mean values over recalls of all classes are used as the metric.
The synthetic data were generated as follows. Data of four 2-dimensional Normal Distributions were generated for four classes. The means were
10 MLPs with 20 hidden nodes of every MLP was used in SFL and SFL.MLP. The training stop error was 0.05 and the coefficient of the penalty term of NCL (referred as
The results on Type B data set are presented in TABLE Ⅲ. When comparing to Learn++.UDNC, the similar observations can be made and we can also conclude that SFL outperforms Learn++.UDNC in this data set. When comparing to SFL.MLP and NB, some values of SFL are between the values of SFL.MLP and NB (always closer to the larger ones), some values of SFL are significantly larger than both SFL.MLP and NB. Observing the results on Type C data set in TABLE Ⅳ, the similar observations can be made. All these results show that SFL outperforms Learn++.UDNC and is capable of combining the advantages of both MLPs and NB to make a better model.
The experiments on real-world data sets include three parts. First of all, 5 class imbalanced data sets were divided randomly to simulate the incremental learning process. Secondly, 3 class imbalanced data sets were divided with considering new classes and the loss of classes in the new data subsets. Finally, 2 class balanced data sets were divided into some class imbalanced subsets to simulate the incremental learning process. The situations of new classes and the loss of classes in the new data subsets were also considered.
The class distributions of the 5 class imbalanced data sets that were randomly divided are presented in TABLE Ⅴ. Each one of these data sets was firstly stratified divided into training set (
For all the data sets, 10 MLPs with 20 hidden nodes of every MLP was used in SFL and the coefficient
It can be observed form TABLE Ⅶ that SFL can outperform Learn++.UDNC on most of the data sets, including Soybean, Splice, Thyroid-allrep, Car, Nursery, Optdigits and Vehicle. On the other data sets, SFL also does not perform significantly worse than Learn++.UDNC. When comparing with SFL.MLP and NB, the performance of SFL usually leans to the better one of SFL.MLP and NB and sometimes SFL outperforms both of them, such as the performance on Soybean, Nursery, Optdigits and Vehicle. These observations go a step further to support that SFL is capable of combing the advantages of both MLPs and NB to make a better model.
On Car, Nursery, Page-blocks, Optdigits and Vehicle, the data sets were divided according the distribution presented in TABLE Ⅵ, where coming up new classes or losing previous classes usually occurs in the new data subsets. It will be worthy to see the detailed results of each class on these data sets. Therefore, the detailed results on two of them, i.e., Nursery (class imbalanced) and Optdigits (class balanced) were further presented.
The means and standard deviations over 30 executions of Nursery are presented in TABLE Ⅷ. Wilcoxon signed-rank test with the level of significance
The means and standard deviations over 30 executions of Optdigits are presented in TABLE Ⅸ. Wilcoxon signed-rank test with the level of significance
The experimental results indicate that the performance of Learn++.UDNC usually leans to majority classes. Even though it sometimes performs better on minority classes, the performance on other classes are usually degraded too much. On contrary, SFL can usually get more balanced performance on different classes and get better overall performance. This is because of the different processing methods of SFL and Learn++.UDNC for handling class imbalance problems. In SFL, class imbalance is considered when training the model. The method for training MLPs has been shown to be effective for class imbalance problems. In Learn++.UDNC, the training process did not consider class imbalance and a transfer function with consideration of class imbalance was applied to the outputs. The effectiveness of the method has not been well proved. Even in the results presented in [5], the performance on minority classes was much worse than that of majority classes. Therefore, it is not surprising that SFL can outperform Learn++.UDNC on most of the data sets.
The computational time of SFL and Learn++.UDNC on all the data sets is presented in TABLE X. It can be observed from TABLE X that SFL usually takes less computational time than Learn++.UDNC. In the experiments, the structures of MLPs were the same for SFL and Learn++.UDNC and the stop criterion were also the same. However, more MLPs were trained for Learn++.UDNC for every new data subset. On the other hand, the training process of SFL usually meet the stop criterion earlier than that of Learn++.UDNC. Therefore, SFL is usually faster than Learn++.UDNC.
In SFL, two kinds of base classifiers, i.e., MLPs and NB, are employed to construct the ensemble. The results have shown that SFL is capable of outperforming the models with only MLPs and the models with only NB. To find out the reason, the differences of SFL and its components (MLPs and NB) and the influences of the differences are investigated in detail.
After every data subset is learned, four numbers are estimated on testing data set: the number of the examples that are correctly classified by only MLPs(
{ρ1=(#1+#2)/#tρ2=#1/(#1+#2)ρ3=#2/(#1+#2)ρ4=#3/(#1+#2) | (11) |
where
There are some parameters in SFL, including the number of MLPs, the number of hidden nodes in every MLP, the stop criterion for training MLPs and the coefficient
Extra executions of SFL with
This paper investigates incremental learning in class imbalance situation. An ensemble-based method, i.e., SFL, which is a hybrid of MLPs and NB, was proposed. A group of impact weights (with the number of the classes as the length) was updated for every individual of the ensemble to indicate the 'confidence' of the individual learning about the classes. The weights affect the outputs of the ensemble by weighted aver-age of all individuals outputs. The training of MLPs and NB considered class imbalance so that the ensemble can adapt the situation of class imbalance.
The experimental studies on 3 synthetic data sets and 10 real-world data sets have shown that the performance of SFL was better than that of a recently proposed approach for class imbalance incremental learning, i.e. Learn++.UDNC[9]. The experimental results have also shown that SFL can combine the advantages of both MLPs and NB to make a better model.
SFL has successfully combined MLPs and NB. The experimental studies have shown that combining additive models can make progress in incremental learning. However, this is just an ordinary trial. Other additive models, such as parame-ter estimation model might also help to improve SFL. This would be a direction of our future work.
[1] | A. Asuncion and D. Newman, Uci machine learning repository, 2007. |
[2] |
Carpenter G. A., Grossberg S., Markuzon N., Reynolds J. H., Rosen D. B. (1992) Fuzzy artmap: A neural network architecture for incremental supervised learning of analog multidimensional maps. IEEE Transactions on Neural Networks 3: 698-713. doi: 10.1109/72.159059
![]() |
[3] |
G. A. Carpenter, S. Grossberg and J. H. Reynolds,
ARTMAP: Supervised Real-Time Learning and Classification of Nonstationary Data by a Self-Organizing Neural Network Elsevier Science Ltd. , 1991.
10.1109/ICNN.1991.163370 |
[4] | Chawla N. V., Japkowicz N., Kotcz A. (2004) Editorial: Special issue on learning from imbalanced data sets. Acm Sigkdd Explorations Newsletter 6: 1-6. |
[5] |
Ditzler G., Muhlbaier M. D., Polikar R. (2010) Incremental learning of new classes in unbalanced datasets: Learn?+?+?.UDNC. International Workshop on Multiple Classifier Systems, Multiple Classifier Systems 33-42. doi: 10.1007/978-3-642-12127-2_4
![]() |
[6] |
Ditzler G., Polikar R., Chawla N. (2010) An incremental learning algorithm for non-stationary environments and class imbalance. International Conference on Pattern Recognition 2997-3000. doi: 10.1109/ICPR.2010.734
![]() |
[7] | Freund Y., Schapire R. E. (1999) A short introduction to boosting. Journal of Japanese Society for Artificial Intelligence 14: 771-780. |
[8] | Fu L., Hsu H.-H., Principe J. C. (1996) Incremental backpropagation learning networks. IEEE Transactions on Neural Networks 7: 757-761. |
[9] | He H., Garcia E. A. (2009) Learning from imbalanced data. IEEE Transactions on Knowledge and Data Engineering 21: 1263-1284. |
[10] |
Inoue H., Narihisa H. (2005) Self-organizing neural grove and its applications. IEEE International Joint Conference on Neural Networks 2: 1205-1210. doi: 10.1109/IJCNN.2005.1556025
![]() |
[11] | N. Japkowicz and S. Stephen, The Class Imbalance Problem: A Systematic Study IOS Press, 2002. |
[12] |
Kasabov N. (2001) Evolving fuzzy neural networks for supervised/unsupervised online knowledge-based learning. IEEE Transactions on Systems Man & Cybernetics Part B Cybernetics A Publication of the IEEE Systems Man & Cybernetics Society 31: 902-918. doi: 10.1109/3477.969494
![]() |
[13] | Lin M., Tang K., Yao X. (2013) Dynamic sampling approach to training neural networks for multiclass imbalance classification. IEEE Transactions on Neural Networks and Learning Systems 24: 647-660. |
[14] | Liu Y., Yao X. (1999) Simultaneous training of negatively correlated neural networks in an ensemble. IEEE Transactions on Systems Man & Cybernetics Part B Cybernetics A Publication of the IEEE Systems Man & Cybernetics Society 29: 716-725. |
[15] |
Minku F. L., Inoue H., Yao X. (2009) Negative correlation in incremental learning. Natural Computing 8: 289-320. doi: 10.1007/s11047-007-9063-7
![]() |
[16] |
Muhlbaier M., Topalis A., Polikar R. (2004) Incremental learning from unbalanced data. In
Neural Networks, 2004. Proceedings. 2004 IEEE International Joint Conference on, IEEE 2: 1057-1062. doi: 10.1109/IJCNN.2004.1380080
![]() |
[17] |
Muhlbaier M., Topalis A., Polikar R. (2004) Learn++.mt: A new approach to incremental learning. Lecture Notes in Computer Science 3077: 52-61. doi: 10.1007/978-3-540-25966-4_5
![]() |
[18] | M. D. Muhlbaier, A. Topalis and R. Polikar, Learn ++. nc: combining ensemble of classifiers with dynamically weighted consult-and-vote for efficient incremental learning of new classes, IEEE Transactions on Neural Networks 20 (2009), p152. |
[19] |
Ozawa S., Pang S., Kasabov N. (2008) Incremental learning of chunk data for online pattern classification systems. IEEE Trans Neural Netw 19: 1061-1074. doi: 10.1109/TNN.2007.2000059
![]() |
[20] |
Polikar R., Byorick J., Krause S., Marino A. (2002) Learn++: A classifier independent incremental learning algorithm for supervised neural networks. International Joint Conference on Neural Networks 1742-1747. doi: 10.1109/IJCNN.2002.1007781
![]() |
[21] |
Polikar R., Upda L., Upda S. S., Honavar V. (2001) Learn++: an incremental learning algorithm for supervised neural networks. IEEE Transactions on Systems Man & Cybernetics Part C 31: 497-508. doi: 10.1109/5326.983933
![]() |
[22] |
Salganicoff M. (1997) Tolerating concept and sampling shift in lazy learning using prediction error context switching. Artificial Intelligence Review 11: 133-155. doi: 10.1007/978-94-017-2053-3_5
![]() |
[23] |
Su M. C., Lee J., Hsieh K. L. (2006) A new artmap-based neural network for incremental learning. Neurocomputing 69: 2284-2300. doi: 10.1016/j.neucom.2005.06.020
![]() |
[24] |
Sun Y., Kamel M. S., Wang Y. (2006) Boosting for learning multiple classes with imbalanced class distribution. In Data Mining, 2006. ICDM'06. Sixth International Conference on, IEEE 592-602. doi: 10.1109/ICDM.2006.29
![]() |
[25] |
Tang E. K., Suganthan P. N., Yao X. (2006) An analysis of diversity measures. Machine Learning 65: 247-271. doi: 10.1007/s10994-006-9449-2
![]() |
[26] |
Tang K., Lin M., Minku F. L., Yao X. (2009) Selective negative correlation learning approach to incremental learning. Neurocomputing 72: 2796-2805. doi: 10.1016/j.neucom.2008.09.022
![]() |
[27] | Wen W. X., Liu H., Jennings A. (2002) Self-generating neural networks. International Joint Conference on Neural Networks 4: 850-855. |
[28] |
Widmer G., Kubat M. (1993) Effective learning in dynamic environments by explicit context tracking. In Machine learning: ECML-93, Springer 667: 227-243. doi: 10.1007/3-540-56602-3_139
![]() |
[29] |
Williamson J. R. (1996) Gaussian artmap: A neural network for fast incremental learning of noisy multidimensional maps. Neural Networks 9: 881-897. doi: 10.1016/0893-6080(95)00115-8
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