Reduced Support Vector Machines: A Statistical Theory

Lee, Yuh-Jye; Huang, Su‐Yun

doi:10.1109/tnn.2006.883722

Cited by 205 publications

(73 citation statements)

References 28 publications

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“…The random choice of B holds the key to our privacy-preserving approximation and has been used effectively in SVM classification problems [14]. Computational results have shown that there is no essential difference between using a random B or a random submatrix ofĀ of the rows of A in reduced SVMs [9,8].…”

Section: Privacy-preserving Linear Kernel Approximationmentioning

confidence: 99%

“…For a given data matrix A ∈ R m×n , instead of using the usual kernel function K(A, A ′ ) : R m×n × R n×m −→ R m×m for constructing a linear or nonlinear approximation of a given y ∈ R m corresponding to the m rows of A, we use a random kernel [9,8] K(A, B ′ ) : R m×n × R n×m −→ R m×m ,m < n, where B is a completely random matrix that is publicly disclosed. Such a random kernel will be shown to completely hide the data matrix A.…”

Section: Introductionmentioning

confidence: 99%

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Privacy-preserving linear and nonlinear approximation via linear programming

Fung¹,

Mangasarian

2013

Optimization Methods and Software

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We propose a novel privacy-preserving random kernel approximation based on a data matrix A ∈ R m×n whose rows are divided into privately owned blocks. Each block of rows belongs to a different entity that is unwilling to share its rows or make them public. We wish to obtain an accurate function approximation for a given y ∈ R m corresponding to each of the m rows of A. Our approximation of y is a real function on R n evaluated at each row of A and is based on the concept of a reduced kernel K(A, B ′ ) where B ′ is the transpose of a completely random matrix B. The proposed linear-programming-based approximation, which is public but does not reveal the privately-held data matrix A, has accuracy comparable to that of an ordinary kernel approximation based on a publicly disclosed data matrix A.Keywords: privacy-preserving approximation, random kernels, support vector machines, linear programming INTRODUCTIONThe problem addressed in this work is that of obtaining an approximation to a given vector y ∈ R m of function values corresponding to the m rows of a data matrix A ∈ R m×n that represents m points in the n-dimensional real space R n . The matrix A is partitioned into q blocks of rows belonging to q entities that are unwilling to share their data or make them public. The motivation for this work arises from similar problems arising in classification theory where the data, corresponding to rows of a data matrix, is also held by various private entities and hence referred to as horizontally partitioned data. Thus in [19,15] privacy-preserving support vector machine (SVM) classifiers were obtained for such data, while in [20] induction tree classifiers were generated for similar problems. Other privacypreserving classifying techniques include cryptographically private SVMs [7], wavelet-based distortion [10] and rotation perturbation [3]. There is also a substantial body of research on privacy preservation in linear programming such as [1,12,13]. However, there does not appear to be any privacy-preserving applications to approximation problems in the literature. This is the problem we wish to address here as follows.In this work we propose an efficient privacy-preserving approximation (PPA) for horizontally partitioned data that is based on the following two ideas. For a given data matrix A ∈ R m×n , instead of using the usual kernel function K(A, A ′ ) : R m×n × R n×m −→ R m×m for constructing a linear or nonlinear approximation of a given y ∈ R m corresponding to the m rows of A, we use a random kernel [9, 8] K(A, B ′ ) : R m×n × R n×m −→ R m×m ,m < n, where B is a completely random matrix that is publicly disclosed. Such a random kernel will be shown to completely hide the data matrix A. The second idea is that each entity i ∈ {1, . . . , q} makes public only the kernel function K(A i , B ′ ) of its

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Section: Privacy-preserving Linear Kernel Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Privacy-preserving linear and nonlinear approximation via linear programming

Fung¹,

Mangasarian

2013

Optimization Methods and Software

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“…Method of searching for the optimal solutions formed by imitating the process of natural evolution, genetic algorithm (GA) has strong robustness and global search ability of [14] in the optimization problem. In order to give full play to the unique advantages of genetic algorithm in encoding operation, this paper selected in the individual, in accordance with the appropriate standards to the classifier parameters and feature subset combination form of the proper characterization, also need to meet the maximum two optimization criteria are the authentication function classifiers have, so this paper using genetic algorithm to realize the joint optimization of feature selection and classifier parameter.…”

Section: Classifier Parameter Optimization and Featurementioning

confidence: 99%

On-line Signature Verification Based on GA-SVM

Dong¹,

Gao²

2015

Int. J. Onl. Eng.

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Abstract-With the development of pen-based mobile device, on-line signature verification is gradually becoming a kind of important biometrics verification. This thesis proposes a method of verification of on-line handwritten signatures using both Support Vector Data Description (SVM) and Genetic Algorithm (GA). A 27-parameter feature set including shape and dynamic features is extracted from the on-line signatures data. The genuine signatures of each subject are treated as target data to train the SVM classifier. As a kernel based one-class classifier, SVM can accurately describe the feature distribution of the genuine signatures and detect the forgeries. To improving the performance of the authentication method, genetic algorithm (GA) is used to optimise classifier parameters and feature subset selection. Signature data form the SVC2013 database is used to carry out verification experiments. The proposed method can achieve an average Equal Error Rate (EER) of 4.93% of the skill forgery database.

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“…Basically RSVM is used from the view point of sampling design, its robustness, and the spectral analysis of the reduced kernel [2].…”

Section: Rsvmmentioning

confidence: 99%

“…We call it weight parameter. We note that the nonnegative constraint ϵ≥0 can be removed because of the term ∥ ∥ 2 2 in the objective function. We use an m×m diagonal matrix D, where D ii =y i ϵ {-1, 1}, to specify the corresponding class membership of each input point.…”

Section: Rsvm Formulationmentioning

confidence: 99%

Solving Classification Problem using Reduced Dimension and Eigen Structure in RSVM

Pal¹,

Bhati²,

Kaushik³

et al. 2015

IJCA

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Support vector machine (SVM) is a recent method to classify the data. SVM has been proved as a powerful tool for solving classification problem. The problem with complex dataset incurs significant complexity while classifying and its efficiency also cost very much. We propose a reduced set support vector machine based on Eigen structure, to classify dataset having multiple features. In this paper, Eigen vectors use to present the whole data in reduced dimensions. This minimize the task of classification by propose method and cost is reduced while efficiency is improved with the increase complexity of data. The proposed method takes a random chunk of data followed by Eigen structure use to reduce the dimension of the data. So as classification problem solve efficiently. We have compared the proposed method with SVM and RSVM. The result signifies that the proposed method gives better result in comparison to SVM and RSVM.

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Reduced Support Vector Machines: A Statistical Theory

Cited by 205 publications

References 28 publications

Privacy-preserving linear and nonlinear approximation via linear programming

Privacy-preserving linear and nonlinear approximation via linear programming

On-line Signature Verification Based on GA-SVM

Solving Classification Problem using Reduced Dimension and Eigen Structure in RSVM

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