A Classification Algorithm with Reject Option Based on Adaptive Minimum Spanning Tree Covering Model in High-dimensional Space

Hu, Zhengping; Xu, Chengqian; Jia, Qian-wen

doi:10.3724/sp.j.1146.2009.00021

Cited by 2 publications

(12 citation statements)

References 6 publications

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“…If m G (∅) = 0, the GBPA reduces to a traditional BPA. Definition 4: Given two GPBAs(m 1 and m 2 ), the generalized combination rule (GCR) is defined as follows [34]: The algorithm is very effective in solving the problem of rejected classification by accepting the idea of boundary cover and virtual sample [47], [48]. It describes the known class using Minimum Spanning Tree (MST) with the assumption that the edges of the graph are also basic elements of the classifier which offers additional virtual training data for a better coverage.…”

Section: B Generalized Evidence Theorymentioning

confidence: 99%

“…For the test sample x, whether it falls within the coverage area of each class is determined according to equation as follows [48]:…”

Section: B Generalized Evidence Theorymentioning

confidence: 99%

“…Assuming that the rejected samples belong to class w r and the accepted samples belong to class w a , the rejection rule is shown as follows [48]:…”

Section: B Generalized Evidence Theorymentioning

confidence: 99%

“…Definition 7: Define the distance d(x, X k tr ) between training sample x and class {w k } C k=1 as follows [48]:…”

Section: B Generalized Evidence Theorymentioning

confidence: 99%

“…(13), EMST represents the (n k − 1) edges of MST of class {w k } C k=1 . According to the geometry of higher dimensional space, the definition of projection Pr(x, e ij ) of x onto the edge e ij is shown as follows [48]:…”

Section: B Generalized Evidence Theorymentioning

confidence: 99%

See 4 more Smart Citations

A New Method to Identify Incomplete Frame of Discernment in Evidence Theory

Sun

Deng

2019

IEEE Access

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One assumption of Dempster-Shafer evidence theory (D-S theory) is the closed world. However, how to determine whether the frame of discernment is incomplete or not is still an open issue. In this paper, a new method is proposed based on a minimum spanning tree. For each new sample collected in the system, the mass function of the empty set is determined based on the proposed method. The value of the mass function of the empty set is used to determine whether the frame of discernment is incomplete or not. The experimental results on several benchmark datasets illustrate that the proposed method has a high accuracy in identifying the incomplete frame of discernment while the error rate is low. INDEX TERMS Dempster-Shafer evidence theory, generalized evidence theory, open world, incomplete frame of discernment, minimum spanning tree covering model, classification.

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Section: B Generalized Evidence Theorymentioning

confidence: 99%

“…For the test sample x, whether it falls within the coverage area of each class is determined according to equation as follows [48]:…”

Section: B Generalized Evidence Theorymentioning

confidence: 99%

“…Assuming that the rejected samples belong to class w r and the accepted samples belong to class w a , the rejection rule is shown as follows [48]:…”

Section: B Generalized Evidence Theorymentioning

confidence: 99%

“…Definition 7: Define the distance d(x, X k tr ) between training sample x and class {w k } C k=1 as follows [48]:…”

Section: B Generalized Evidence Theorymentioning

confidence: 99%

Section: B Generalized Evidence Theorymentioning

confidence: 99%

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A New Method to Identify Incomplete Frame of Discernment in Evidence Theory

Sun

Deng

2019

IEEE Access

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A New Method to Determine Generalized Basic Probability Assignment in the Open World

Sun

Deng

2019

IEEE Access

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Dempster-Shafer evidence theory (D-S theory) is a very useful tool to solve problems in the field of information fusion. But how to determine generalized basic probability assignment (GBPA) more accurately and efficiently in D-S theory is still a matter of debate, especially in the open world. In this paper, we put forward a new method to determine GBPA in the open world. First, a minimum spanning tree (MST) is established for samples in each known class. The covering radius of every edge in MST of each class will be generated based on the formula for generating improved radius. The MST coverage of every class will be established. Combine these coverages to form the MST covering model. Each new sample should be justified the MST coverages it belongs to. Then, we put forward a formula to generate GBPA of the sample. Finally, determine whether the sum of GBPA is smaller than 1. If so, m(∅) needs to be generated. Otherwise, GBPA needs to be standardized. The experimental results on Iris dataset prove the effectiveness of our method.INDEX TERMS Dempster-Shafer evidence theory, generalized evidence theory, basic probability assignment, open world, minimum spanning tree covering model.

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A Classification Algorithm with Reject Option Based on Adaptive Minimum Spanning Tree Covering Model in High-dimensional Space

Cited by 2 publications

References 6 publications

A New Method to Identify Incomplete Frame of Discernment in Evidence Theory

A New Method to Identify Incomplete Frame of Discernment in Evidence Theory

A New Method to Determine Generalized Basic Probability Assignment in the Open World

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