scholarly journals Visualization of classified data with kernel principal component analysis

2018 ◽  
Author(s):  
Toni Bakhtiar
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Feature Space ◽  
Original Data ◽  
Component Analysis ◽  
Kernel Functions ◽  
Kernel Principal Component Analysis ◽  
Gaussian Kernel ◽  
Kernel Pca ◽  
Study Results

Kernel Principal Component Analysis (Kernel PCA) is a generalization of the ordinary PCA which allows mapping the original data into a high-dimensional feature space. The mapping is expected to address the issues of nonlinearity among variables and separation among classes in the original data space. The key problem in the use of kernel PCA is the parameter estimation used in kernel functions that so far has not had quite obvious guidance, where the parameter selection mainly depends on the objectivity of the research. This study exploited the use of Gaussian kernel function and focused on the ability of kernel PCA in visualizing the separation of the classified data. Assessments were undertaken based on misclassification obtained by Fisher Discriminant Linear Analysis of the first two principal components. This study results suggest for the visualization of kernel PCA by selecting the parameter in the interval between the closest and the furthest distances among the objects of original data is better than that of ordinary PCA.

scholarly journals Plot Multivariate Menggunakan Kernel Principal Component Analysis (KPCA) dengan Fungsi Power Kernel

d'CARTESIAN ◽  
2015 ◽  
Vol 4 (1) ◽  
pp. 95
Author(s):  
Vitawati Bawotong ◽  
Hanny Komalig ◽  
Nelson Nainggolan
Keyword(s):  
Principal Component Analysis ◽  
Input Data ◽  
Principal Component ◽  
Feature Space ◽  
Component Analysis ◽  
Kernel Principal Component Analysis ◽  
Kernel Pca

Kernel PCA merupakan PCA yang diaplikasikan pada input data yang telah ditransformasikan ke feature space. Misalkan F: Rn®F fungsi yang memetakan semua input data xiÎRn, berlaku F(xi)ÎF. Salah satu dari banyak fungsi kernel adalah power kernel. Fungsi power kernel K(xi, xj) = –|| xi – xj ||b dengan 0 < b ≤ 1. Tujuan dari penelitian ini yaitu mempelajari penggunaan Kernel PCA (KPCA) dengan fungsi Power Kernel untuk membantu menyelesaikan masalah plot multivariate nonlinier terutama yang berhubungan dalam pengelompokan. Hasil menunjukkan bahwa Penggunaan KPCA dengan fungsi Power Kernel sangat membantu dalam menyelesaikan masalah plot multivariate yang belum dapat dikelompokan dengan garis pemisah yang linier. Kata kunci : Kernel Principal Component Analysis (KPCA), Plot Multivariate, Power Kernel

scholarly journals Kernel principal component analysis for multimedia retrieval

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Guang-Ho Cha
Keyword(s):  
Principal Component Analysis ◽  
Dimensionality Reduction ◽  
Principal Components ◽  
Principal Component ◽  
Feature Space ◽  
Component Analysis ◽  
Multimedia Retrieval ◽  
Kernel Principal Component Analysis ◽  
Kernel Pca ◽  
Data Set

Principal component analysis (PCA) is an important tool in many areas including data reduction and interpretation, information retrieval, image processing, and so on. Kernel PCA has recently been proposed as a nonlinear extension of the popular PCA. The basic idea is to first map the input space into a feature space via a nonlinear map and then compute the principal components in that feature space. This paper illustrates the potential of kernel PCA for dimensionality reduction and feature extraction in multimedia retrieval. By the use of Gaussian kernels, the principal components were computed in the feature space of an image data set and they are used as new dimensions to approximate image features. Extensive experimental results show that kernel PCA performs better than linear PCA with respect to the retrieval quality as well as the retrieval precision in content-based image retrievals.Keywords: Principal component analysis, kernel principal component analysis, multimedia retrieval, dimensionality reduction, image retrieval

scholarly journals Penggunaan Kernel Principal Component Analysis Fungsi Polinomial Dalam Menyelesaikan Masalah Pengelompokan Plot Peubah Ganda

d'CARTESIAN ◽  
2015 ◽  
Vol 4 (1) ◽  
pp. 76
Author(s):  
Sueharti Maatuil ◽  
Hanny Komalig ◽  
Charles Mongi
Keyword(s):  
Principal Component Analysis ◽  
Input Data ◽  
Principal Component ◽  
Feature Space ◽  
Component Analysis ◽  
Kernel Principal Component Analysis ◽  
Kernel Pca

Tujuan dari penelitian ini yaitu mempelajari penggunaan kernel PCA fungsi polinomial untuk membantu menyelesaikan masalah plot peubah ganda terutama yang berhubungan dalam pengelompokan. Data yang digunakan dalam penelitian ini adalah data sekunder yang berupa plot peubah ganda. Metode kernel adalah salah satu cara untuk mengatasi kasus-kasus yang tidak linier. Kernel PCA merupakan PCA yang diaplikasikan pada input data yang telah ditransformasikan ke feature space. Misalkan F: Rn®F fungsi yang memetakan semua input data xiÎRn, berlaku F(xi)ÎF. Salah satu kernel yang banyak digunakan adalah kernel polinomial. Dimana h0 adalah parameter skala yang akan dipilih. Fungsi kernel polynomial  K(xi, xj‘) = (xiT, xj‘ + h0)d. Hasil dari penelitian ini menunjukkan bahwa penggunaan Kernel Principal Component Analysis (KPCA) dengan fungsi kernel polinomial sangat membantu dalam menyelesaikan masalah plot peubah ganda yang belum dapat dikelompokan dengan garis pemisah yang linier. Kata kunci : Kernel PCA, Kernel PCA Fungsi Polinomial, Plot Peubah Ganda

Fault Diagnosis of Bearing Based on KPCA and KNN Method

2014 ◽  
Vol 986-987 ◽  
pp. 1491-1496 ◽  
Author(s):  
Qiang Wang ◽  
Yong Bao Liu ◽  
Xing He ◽  
Shu Yong Liu ◽  
Jian Hua Liu
Keyword(s):  
Principal Component Analysis ◽  
Fault Diagnosis ◽  
Nearest Neighbor ◽  
Feature Vector ◽  
Principal Component ◽  
Feature Space ◽  
Component Analysis ◽  
Kernel Functions ◽  
Kernel Principal Component Analysis ◽  
K Nearest Neighbor

Selection of secondary variables is an effective way to reduce redundant information and to improve efficiency in nonlinear system modeling. The combination of Kernel Principal Component Analysis (KPCA) and K-Nearest Neighbor (KNN) is applied to fault diagnosis of bearing. In this approach, the integral operator kernel functions is used to realize the nonlinear map from the raw feature space of vibration signals to high dimensional feature space, and structure and statistics in the feature space to extract the feature vector from the fault signal with the principal component analytic method. Assessment method using the feature vector of the Kernel Principal Component Analysis, and then enter the sensitive features to K-Nearest Neighbor classification. The experimental results indicated that this method has good accuracy.

Uncertain Nonlinear Process Monitoring Using Interval Ensemble Kernel Principal Component Analysis

2021 ◽  
Vol 25 (1) ◽  
pp. 101-109
Author(s):  
Xianrui Wang ◽  
Guoxin Zhao ◽  
Yu Liu ◽  
Shujie Yang ◽  
◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Process Monitoring ◽  
Principal Component ◽  
Nonlinear Process ◽  
Component Analysis ◽  
Kernel Principal Component Analysis ◽  
Gaussian Kernel ◽  
Bayesian Decision ◽  
Symbolic Data ◽  
Nonlinear Process Monitoring

To solve uncertainties in industrial processes, interval kernel principal component analysis (IKPCA) has been proposed based on symbolic data analysis. However, it is experimentally discovered that the performance of IKPCA is worse than that of other algorithms. To improve the IKPCA algorithm, interval ensemble kernel principal component analysis (IEKPCA) is proposed. By optimizing the width parameters of the Gaussian kernel function, IEKPCA yields better performances. Ensemble learning is incorporated in the IEKPCA algorithm to build submodels with different width parameters. However, the multiple submodels will yield a large number of results, which will complicate the algorithm. To simplify the algorithm, a Bayesian decision is used to convert the result into fault probability. The final result is obtained via a weighting strategy. To verify the method, IEKPCA is applied to the Tennessee Eastman (TE) process. The false alarm rate, fault detection rate, accuracy, and other indicators used in the IEKPCA are compared with those of other algorithms. The results show that the IEKPCA improves the accuracy of uncertain nonlinear process monitoring.

Damage detection in nonlinear civil structures using kernel principal component analysis

2020 ◽  
Vol 23 (11) ◽  
pp. 2414-2430
Author(s):  
Khaoula Ghoulem ◽  
Tarek Kormi ◽  
Nizar Bel Hadj Ali
Keyword(s):  
Principal Component Analysis ◽  
Damage Detection ◽  
Structural Model ◽  
Principal Component ◽  
Original Data ◽  
Component Analysis ◽  
Correlated Data ◽  
Data Driven ◽  
Kernel Principal Component Analysis ◽  
Structural Systems

In the general framework of data-driven structural health monitoring, principal component analysis has been applied successfully in continuous monitoring of complex civil infrastructures. In the case of linear or polynomial relationship between monitored variables, principal component analysis allows generation of structured residuals from measurement outputs without a priori structural model. The principal component analysis has been widely used for system monitoring based on its ability to handle high-dimensional, noisy, and highly correlated data by projecting the data onto a lower dimensional subspace that contains most of the variance of the original data. However, for nonlinear systems, it could be easily demonstrated that linear principal component analysis is unable to disclose nonlinear relationships between variables. This has naturally motivated various developments of nonlinear principal component analysis to tackle damage diagnosis of complex structural systems, especially those characterized by a nonlinear behavior. In this article, a data-driven technique for damage detection in nonlinear structural systems is presented. The proposed method is based on kernel principal component analysis. Two case studies involving nonlinear cable structures are presented to show the effectiveness of the proposed methodology. The validity of the kernel principal component analysis–based monitoring technique is shown in terms of the ability to damage detection. Robustness to environmental effects and disturbances are also studied.

CORRIDOR-SCENE CLASSIFYING METHODS FOR MOBILE ROBOT BASED ON MULTI-SONAR-SENSOR INFORMATION FUSION

2007 ◽  
Vol 04 (01) ◽  
pp. 15-26 ◽  
Author(s):  
XIUQING WANG ◽  
ZENG-GUANG HOU ◽  
LONG CHENG ◽  
MIN TAN ◽  
FEI ZHU
Keyword(s):  
Principal Component Analysis ◽  
Mobile Robot ◽  
Principal Component ◽  
Component Analysis ◽  
Experimental Results ◽  
Scene Analysis ◽  
Kernel Principal Component Analysis ◽  
Kernel Pca ◽  
Sonar Sensor ◽  
Pca Method

The ability of cognition and recognition for complex environment is very important for a real autonomous robot. A new scene analysis method using kernel principal component analysis (kernel-PCA) for mobile robot based on multi-sonar-ranger data fusion is put forward. The principle of classification by principal component analysis (PCA), kernel-PCA, and the BP neural network (NN) approach to extract the eigenvectors which have the largest k eigenvalues are introduced briefly. Next the details of PCA, kernel-PCA and the BP NN method applied in the corridor scene analysis and classification for the mobile robots based on sonar data are discussed and the experimental results of those methods are given. In addition, a corridor-scene-classifier based on BP NN is discussed. The experimental results using PCA, kernel-PCA and the methods based on BP neural networks (NNs) are compared and the robustness of those methods are also analyzed. Such conclusions are drawn: in corridor scene classification, the kernel-PCA method has advantage over the ordinary PCA, and the approaches based on BP NNs can also get satisfactory results. The robustness of kernel-PCA is better than that of the methods based on BP NNs.

scholarly journals Kernel Principal Component Analysis Allowing Sparse Representation and Sample Selection

2019 ◽  
Vol 13 (1) ◽  
pp. 9-20 ◽  
Author(s):  
Duo Wang ◽  
Toshihisa Tanaka
Keyword(s):  
Principal Component Analysis ◽  
Sparse Representation ◽  
Sample Selection ◽  
Principal Component ◽  
Real Data ◽  
Component Analysis ◽  
Kernel Functions ◽  
Kernel Principal Component Analysis ◽  
Alternating Direction ◽  
Sparse Kernel

Kernel principal component analysis (KPCA) is a kernelized version of principal component analysis (PCA). A kernel principal component is a superposition of kernel functions. Due to the number of kernel functions equals the number of samples, each component is not a sparse representation. Our purpose is to sparsify coefficients expressing in linear combination of kernel functions, two types of sparse kernel principal component are proposed in this paper. The method for solving sparse problem comprises two steps: (a) we start with the Pythagorean theorem and derive an explicit regression expression of KPCA and (b) two types of regularization $l_1$-norm or $l_{2,1}$-norm are added into the regression expression in order to obtain two different sparsity form, respectively. As the proposed objective function is different from elastic net-based sparse PCA (SPCA), the SPCA method cannot be directly applied to the proposed cost function. We show that the sparse representations are obtained in its iterative optimization by conducting an alternating direction method of multipliers. Experiments on toy examples and real data confirm the performance and effectiveness of the proposed method.

Multi-channel Raman Spectral Reconstruction Based on Gaussian Kernel Principal Component Analysis

2020 ◽  
Vol 49 (3) ◽  
pp. 330001-330001
Author(s):  
王昕 Xin WANG ◽  
康哲铭 Zhe-ming KANG ◽  
刘龙 Long LIU ◽  
范贤光 Xian-guang FAN
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Kernel Principal Component Analysis ◽  
Gaussian Kernel ◽  
Spectral Reconstruction ◽  
Raman Spectral

scholarly journals Ensemble Learning Based Multiple Kernel Principal Component Analysis for Dimensionality Reduction and Classification of Hyperspectral Imagery

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Hamidullah Binol
Keyword(s):  
Principal Component Analysis ◽  
Dimension Reduction ◽  
Ensemble Learning ◽  
Principal Component ◽  
Component Analysis ◽  
Hyperspectral Data ◽  
Feature Representation ◽  
Kernel Principal Component Analysis ◽  
Kernel Pca ◽  
Multiple Kernel

Classification is one of the most challenging tasks of remotely sensed data processing, particularly for hyperspectral imaging (HSI). Dimension reduction is widely applied as a preprocessing step for classification; however the reduction of dimension using conventional methods may not always guarantee high classification rate. Principal component analysis (PCA) and its nonlinear version kernel PCA (KPCA) are known as traditional dimension reduction algorithms. In a previous work, a variant of KPCA, denoted as Adaptive KPCA (A-KPCA), is suggested to get robust unsupervised feature representation for HSI. The specified technique employs several KPCAs simultaneously to obtain better feature points from each applied KPCA which includes different candidate kernels. Nevertheless, A-KPCA neglects the influence of subkernels employing an unweighted combination. Furthermore, if there is at least one weak kernel in the set of kernels, the classification performance may be reduced significantly. To address these problems, in this paper we propose an Ensemble Learning (EL) based multiple kernel PCA (M-KPCA) strategy. M-KPCA constructs a weighted combination of kernels with high discriminative ability from a predetermined set of base kernels and then extracts features in an unsupervised fashion. The experiments on two different AVIRIS hyperspectral data sets show that the proposed algorithm can achieve a satisfactory feature extraction performance on real data.

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