Generation and Nonlinear Mapping of Reducts—Nearest Neighbor Classification

Ishii, Naohiro; Torii, Ippei; Iwata, Kazunori; Nakashima, Toyoshiro

doi:10.1007/978-3-319-46200-4_5

Cited by 6 publications

(2 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…,where , , 0     hold by convex condition. In the vectors in equation ( 8), By removing the reference point data, from vectors in equation ( 8), the following equation holds in the linear subspace, By applying the equation ( 8) removing reference point data, 4 X does not satisfy the equation (9) in the linear subspace, that is, Figure 9: Convex cone by data with nearest neighbor relation generated on the hyperplane 4 3 5 7…”

Section: Reduction Of Variables Through Nearest Neighbor Relations In Threshold Networkmentioning

confidence: 99%

“…A new consistent method for the generation of reduced variables and their classification in threshold networks is expected from the point of the efficient processing of data. In this paper, we have developed a method of reduction of data variables and the classification using the nearest neighbor relations [9], which are proposed to be relations with minimal distance between different classes. First, it is shown that the nearest neighbor relations are useful to derive minimal Boolean function in threshold function [6,13,14].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Reduction of Variables through Nearest Neighbor Relations in Threshold Networks

Ishii

Iwata

Odagiri

et al. 2020

International Journal of Smart Computing and Artificial Intelligence

Self Cite

View full text Add to dashboard Cite

Threshold networks are useful as a fundamental technology in the recent learning and AI domains. Reduction of data variables in threshold networks is an important issue and it is needed for the processing of higher dimensional data in the application domains and AI. Boolean and rough set is fundamental and useful to reduce higher dimensional data to lower one for the classification. We develop a reduction of data variables and classification method based on geometrical reasoning, which is characterized by nearest neighbor relations. In this paper, the nearest neighbor relations are shown to be useful for the reduction of variables and their classification in threshold networks. The Boolean operation and convex cones generated by the nearest neighbor relations derive the reduced variables of data and the classifications using them. Then, the edges of convex cones are compared for the reduction of variables. Further, hyperplanes with reduced variables are generated on the same convex cones for data classification.

show abstract

Section: Reduction Of Variables Through Nearest Neighbor Relations In Threshold Networkmentioning

confidence: 99%