Weighted extreme learning machine for imbalance learning
Citations
1,292 citations
Cites background from "Weighted extreme learning machine f..."
...These approaches can be categorized into two groups: the internal approaches that create new algorithms or modify existing ones to take the class-imbalance problem into consideration [7,41,82,129,152] and external approaches that preprocess the data in order to diminish the effect of their class imbalance [9,43]....
[...]
1,289 citations
678 citations
Cites background or methods from "Weighted extreme learning machine f..."
...for specific problems, such as ELMs for online sequential data [29]–[31], ELMs for noisy/missing data [32]–[34], ELMs for imbalanced data [35], and so on....
[...]
...Note that similar to the weighted ELM algorithm (W-ELM) introduced in [35], here, we associate different penalty coefficient Ci on the prediction errors with respect to patterns from different classes....
[...]
540 citations
358 citations
Cites background from "Weighted extreme learning machine f..."
...There are several other studies that have previously scrutinized ELM with fixed network architectures [30], [32]–[34]....
[...]
References
26,531 citations
"Weighted extreme learning machine f..." refers background in this paper
...From optimization point of view, connections between ELM and the popular support vector machines (SVMs) exist mainly in the aspects of problem formulation, network architecture except that solutions of SVMs are suboptimal compared to those of ELM [5,6]....
[...]
...Note that another popular machine learning technique support vector machine (SVM) [20,21], originally a binary classifier, fails to be applied to the multiclass problems directly without modification....
[...]
...Similar to SVMs which aim to minimize the training errors and maximize the marginal distance between two classes, the goal of ELM is the same: Minimize : JHb TJ2 and JbJ ð4Þ Similar to LS-SVM, the optimization problem is mathematically written as Minimize : LPELM ¼ 1 2 JbJ2þC 1 2 XN i ¼ 1 JniJ 2 Subject to : hðxiÞb¼ tTi n T i , i¼ 1, . . . ,N ð5Þ where ni ¼ ½xi,1, . . . ,xi,m T is the training error vector of the m output nodes with respect to the training sample xi....
[...]
...Usually the multiclass problem is decomposed into binary subproblems, implemented by multiple SVMs....
[...]
...To find out the predicted label of x, users just need to refer to a simple equation as below: labelðxÞ ¼ arg max f iðxÞ, iAf1, . . . ,mg ð16Þ Note that another popular machine learning technique support vector machine (SVM) [20,21], originally a binary classifier, fails to be applied to the multiclass problems directly without modification....
[...]
17,017 citations
"Weighted extreme learning machine f..." refers methods in this paper
...Another interesting tool, receiver operating characteristics (ROC) graph [16], provides a visual illustration of the performance of classifiers on binary datasets, where a classifier corresponds to a point....
[...]
10,217 citations
"Weighted extreme learning machine f..." refers background in this paper
...Extreme learning machine (ELM) [1,2,11] was originally proposed for the single-hidden layer feedforward neural networks and was then extended to the ‘‘generalized’’ single-hidden layer feedforward networks (SLFNs) where the hidden layer need not be neuron alike [3,4]....
[...]