Generalized Mercer theorem and its application to feature space related to indefinite kernels

Chen, Degang; Wang, Hengyou; Tsang, Eric W. K.

doi:10.1109/icmlc.2008.4620508

Cited by 12 publications

(5 citation statements)

References 11 publications

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“…where E[⋅] is the expectation, and 𝜅 𝜎 (⋅, ⋅) denotes a shift-invariant kernel function satisfying the Mercer's theory. 32 In this article, Gaussian kernel is used as the kernel function of the correntropy, which is given by. 19 𝜅 𝜎 (x, y) = G 𝜎 (𝜀) = exp…”

Section: Maximum Correntropy Criterionmentioning

confidence: 99%

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Improved maximum correntropy cubature Kalman and information filters with application to target tracking under non‐Gaussian noise

Lu,

Zhou,

Tong

2024

Adaptive Control & Signal

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SummaryThe cubature Kalman filter (CKF) based on the maximum correntropy criterion (MCC) has been widely used in the target tracking. However, numerical problems usually occur when there are outliers in the measurement noise. In order to solve the problems of state estimation under the non‐Gaussian measurement noise, a new combined cost function is defined based on the weighted least squares (WLS) method and MCC. In addition, a new method is also used to adaptively adjust the kernel size, then the improved maximum correntropy CKF (PMCCKF) and its corresponding improved maximum correntropy cubature information filter (PMCCIF) are proposed. Compared with the existing algorithms, the new method can not only obtain similar or even better estimation performance, but also avoid numerical problems. Moreover, when the kernel size is infinite, the performance of proposed algorithms will reduce to the standard CKF and corresponding cubature information filter (CIF) respectively, but the classical maximum correntropy CIF (MCCIF) will not, and even the performance is poor in this case. The advantages of the proposed algorithms are verified by four classical nonlinear models.

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Section: Maximum Correntropy Criterionmentioning

confidence: 99%

“…,then according to (32), Kk = K k is obtained, and Equation ( 39) is equal to Equation (30). Next, we consider the P k .…”

Section: Appendix Amentioning

confidence: 99%

Improved maximum correntropy cubature Kalman and information filters with application to target tracking under non‐Gaussian noise

Lu,

Zhou,

Tong

2024

Adaptive Control & Signal

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“…Lemma 1. (Chen et al, 2008). Mercer theorem demonstrates that any semi-positive definite symmetric function can be used as a kernel function.…”

Section: Preliminarymentioning

confidence: 99%

A novel twin-support vector machine for binary classification to imbalanced data

Chao²

2023

DTA

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PurposeBinary classification on imbalanced data is a challenge; due to the imbalance of the classes, the minority class is easily masked by the majority class. However, most existing classifiers are better at identifying the majority class, thereby ignoring the minority class, which leads to classifier degradation. To address this, this paper proposes a twin-support vector machines for binary classification on imbalanced data.Design/methodology/approachIn the proposed method, the authors construct two support vector machines to focus on majority classes and minority classes, respectively. In order to promote the learning ability of the two support vector machines, a new kernel is derived for them.Findings(1) A novel twin-support vector machine is proposed for binary classification on imbalanced data, and new kernels are derived. (2) For imbalanced data, the complexity of data distribution has negative effects on classification results; however, advanced classification results can be gained and desired boundaries are learned by using optimizing kernels. (3) Classifiers based on twin architectures have more advantages than those based on single architecture for binary classification on imbalanced data.Originality/valueFor imbalanced data, the complexity of data distribution has negative effects on classification results; however, advanced classification results can be gained and desired boundaries are learned through using optimizing kernels.

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“…To ensure the convexity of the optimization problem and introduce the Kernel mapping in which the calculation of scalar products is possible, you must use a kernel function that follows the conditions set by Mercers Theorem [12], [13].…”

Section: B Svm (Support Vector Machine)mentioning

confidence: 99%

Application of support vector machines and two dimensional discrete cosine transform in speech automatic recognition

Batista

Silva

2015

2015 SAI Intelligent Systems Conference (IntelliSys)

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This paper proposes the implementation of a Support Vector Machine (SVM) for automatic recognition of numerical speech commands. Besides the pre-processing of the speech signal with mel-ceptral coefficients, is used to Discrete Cosine Transform (DCT) to generate a two-dimensional matrix used as input to SVM algorithm for generating the pattern of words to be recognized. The Support Vector Machines represent a new approach to pattern classification. SVM is used to recognize speech patterns from the mean and variance of the speech signal input through the two-dimensional array aforementioned, the algorithm trains and tests those data showing the best response. Finally shows the experimental results in speech recognition applied to Brazilian Portuguese language process.

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Generalized Mercer theorem and its application to feature space related to indefinite kernels

Cited by 12 publications

References 11 publications

Improved maximum correntropy cubature Kalman and information filters with application to target tracking under non‐Gaussian noise

Improved maximum correntropy cubature Kalman and information filters with application to target tracking under non‐Gaussian noise

A novel twin-support vector machine for binary classification to imbalanced data

Application of support vector machines and two dimensional discrete cosine transform in speech automatic recognition

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