Possibility measure based fuzzy support function machine for set-based fuzzy classifications

Chen, Jiqiang; Hu, Qinghua; Xue, Xiaoping; Ha, Ming-Hu; Ma, Li; Zhang, Xuchang; Yu, Zhipeng

doi:10.1016/j.ins.2019.01.022

Cited by 7 publications

(2 citation statements)

References 35 publications

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“…The task of classifying these types of datasets is known as class-imbalanced classification. For example, in the context of water quality assessment [2], the data related to water quality tend to remain relatively stable over a short period of time. This results in one category, known as the majority class, having significantly more samples than the other categories, referred to as the minority class.…”

Section: Introductionmentioning

confidence: 99%

Regularized Discrete Optimal Transport for Class-Imbalanced Classifications

Chen,

Wan,

2024

Mathematics

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Imbalanced class data are commonly observed in pattern analysis, machine learning, and various real-world applications. Conventional approaches often resort to resampling techniques in order to address the imbalance, which inevitably alter the original data distribution. This paper proposes a novel classification method that leverages optimal transport for handling imbalanced data. Specifically, we establish a transport plan between training and testing data without modifying the original data distribution, drawing upon the principles of optimal transport theory. Additionally, we introduce a non-convex interclass regularization term to establish connections between testing samples and training samples with the same class labels. This regularization term forms the basis of a regularized discrete optimal transport model, which is employed to address imbalanced classification scenarios. Subsequently, in line with the concept of maximum minimization, a maximum minimization algorithm is introduced for regularized discrete optimal transport. Subsequent experiments on 17 Keel datasets with varying levels of imbalance demonstrate the superior performance of the proposed approach compared to 11 other widely used techniques for class-imbalanced classification. Additionally, the application of the proposed approach to water quality evaluation confirms its effectiveness.

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Section: Introductionmentioning

confidence: 99%

Regularized Discrete Optimal Transport for Class-Imbalanced Classifications

Chen,

Wan,

2024

Mathematics

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“…This difficulty appears in case where the size of two land cover classes may be larger than the pixel size, but some parts of their boundaries are localized within a single pixel [2]. As the traditional hard classification algorithms cannot be applied to solve mixed pixels problem [3,4], the best solution consists in using spectral unmixing [5,6] and fuzzy classification [7] in order to specify the endmembers (classes) and their presence ratio, while their precise spatial localization cannot be determined. In 1997, sub-pixel mapping methods were first proposed by Atkinson [8] to approximate the spatial locations at a sub-pixel scale from coarse spatial resolution hyperspectral data.…”

Section: Introductionmentioning

confidence: 99%

Sub-Pixel Mapping Model Based on Total Variation Regularization and Learned Spatial Dictionary

et al. 2021

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In this research study, we deal with remote sensing data analysis over high dimensional space formed by hyperspectral images. This task is generally complex due to the large spectral, spatial richness, and mixed pixels. Thus, several spectral un-mixing methods have been proposed to discriminate mixing spectra by estimating the classes and their presence rates. However, information related to mixed pixel composition is very interesting for some applications, but it is insufficient for many others. Thus, it is necessary to have much more data about the spatial localization of the classes detected during the spectral un-mixing process. To solve the above-mentioned problem and specify the spatial location of the different land cover classes in the mixed pixel, sub-pixel mapping techniques were introduced. This manuscript presents a novel sub-pixel mapping process relying on K-SVD (K-singular value decomposition) learning and total variation as a spatial regularization parameter (SMKSVD-TV: Sub-pixel Mapping based on K-SVD dictionary learning and Total Variation). The proposed approach adopts total variation as a spatial regularization parameter, to make edges smooth, and a pre-constructed spatial dictionary with the K-SVD dictionary training algorithm to have more spatial configurations at the sub-pixel level. It was tested and validated with three real hyperspectral data. The experimental results reveal that the attributes obtained by utilizing a learned spatial dictionary with isotropic total variation allowed improving the classes sub-pixel spatial localization, while taking into account pre-learned spatial patterns. It is also clear that the K-SVD dictionary learning algorithm can be applied to construct a spatial dictionary, particularly for each data set.

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On the conjunction of possibility measures under intuitionistic evidence sets

Xue

Deng

2020

J Ambient Intell Human Comput

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Possibility measure based fuzzy support function machine for set-based fuzzy classifications

Cited by 7 publications

References 35 publications

Regularized Discrete Optimal Transport for Class-Imbalanced Classifications

Regularized Discrete Optimal Transport for Class-Imbalanced Classifications

Sub-Pixel Mapping Model Based on Total Variation Regularization and Learned Spatial Dictionary

On the conjunction of possibility measures under intuitionistic evidence sets

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