SVM Kernel Configuration and Optimization for the Handwritten Digit Recognition

Drewnik, Monika; Pasternak-Winiarski, Zbigniew

doi:10.1007/978-3-319-59105-6_8

Cited by 17 publications

(15 citation statements)

References 13 publications

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“…In fact, it is a realization of the general construction described in Theorem 2 with the function F : → l 2 (X ) defined as F( , z) := k( , z)δ r ( ,z) , where δ x : X → C denotes the Kronecker delta concentrated at x ∈ X . Moreover, the above kernel satisfies (9). Indeed, by (11,12) one has that, whenever r (χ ) = r (γ ),…”

Section: Examplementioning

confidence: 97%

“…The theory of reproducing kernel Hilbert spaces (RKHS) provides research tools in such domains as complex analysis, probability theory and statistics [2], stochastic (Gaussian) processes [15], quantum physics [16,17] or computer science (especially artificial intelligence [9,12]). Basic properties and definitions together with the detailed analysis of RKHS can be found in [19,25].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Reproducing Kernel Hilbert Space Associated with a Unitary Representation of a Groupoid

Drewnik¹,

Miller

Pasternak-Winiarski

2021

Complex Anal. Oper. Theory

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The aim of the paper is to create a link between the theory of reproducing kernel Hilbert spaces (RKHS) and the notion of a unitary representation of a group or of a groupoid. More specifically, it is demonstrated on one hand how to construct a positive definite kernel and an RKHS for a given unitary representation of a group(oid), and on the other hand how to retrieve the unitary representation of a group or a groupoid from a positive definite kernel defined on that group(oid) with the help of the Moore–Aronszajn theorem. The kernel constructed from the group(oid) representation is inspired by the kernel defined in terms of the convolution of functions on a locally compact group. Several illustrative examples of reproducing kernels related with unitary representations of groupoids are discussed in detail. The paper is concluded with the brief overview of the possible applications of the proposed constructions.

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Section: Examplementioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Reproducing Kernel Hilbert Space Associated with a Unitary Representation of a Groupoid

Drewnik¹,

Miller

Pasternak-Winiarski

2021

Complex Anal. Oper. Theory

Self Cite

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“…The second SVM classifier used polynomial as the kernel. Polynomial is suitable for normalized data (Drewnik and Pasternak-Winiarski, 2017). The equation of the polynomial kernel shown in equation 3.…”

Section: ) Phase 1: Data Preprocessing Using Nonlinear Scaler Of Data Standardizationmentioning

confidence: 99%

A Review of Support Vector Machine-based Intrusion Detection System for Wireless Sensor Network with Different Kernel Functions

Hamzah

Othman

2021

Int J Innov Comp

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Wireless sensor network (WSN) is among the popular communication technology which capable of self-configured and infrastructure-less wireless networks to monitor physical or environmental conditions. WSN also is the most standard services employed in commercial and industrial applications, because of its technical development in a processor, communication, and low-power usage of embedded computing devices. However, WSN is vulnerable due to the dynamic nature of wireless network. One of the best solutions to mitigate the risk is implementing Intrusion Detection System (IDS) to the network. Numerous researches were done to improve the efficiency of WSN-IDS because attacks in networks has been evolved due to the rapid growth of technology. Support Vector Machine (SVM) is one of the best algorithms for the enhancement of WSN-IDS. Nevertheless, the efficiency of classification in SVM is based on the kernel function used. Since dynamic environment of WSN consist of nonlinear data, linear classification of SVM has limitations in maximizing its margin during the classification. It is important to have the best kernel in classifying nonlinear data as the main goal of SVM to maximize the margin in the feature space during classification. In this research, kernel function of SVM such as Linear, RBF, Polynomial and Sigmoid were used separately in data classification. In addition, a modified version of KDD’99, NSL-KDD was used for the experiment of this research. Performance evaluation was made based on the experimental result obtained. Finally, this research found out that RBF kernel provides the best classification result with 91% accuracy.

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“…He considered equation with weight of reproducing kernel in it. On the other hand, M. Drewnik and Z. Pasternak-Winiarski used reproducing kernels to recognize handwritten digits ( [2]). In their paper they wanted to find the optimal weight (in some sense).…”

Section: Introductionmentioning

confidence: 99%