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

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 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 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

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 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.

scholarly journals Statistical Analysis of Nonlinear Processes Based on Penalty Factor

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yingwei Zhang ◽  
Chuanfang Zhang ◽  
Wei Zhang
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Feature Space ◽  
Component Analysis ◽  
Kernel Principal Component Analysis ◽  
Forgetting Factor ◽  
Analysis Algorithm ◽  
Penalty Factor ◽  
New Process ◽  
Principal Component Analysis Algorithm

A new process monitoring approach is proposed for handling the nonlinear monitoring problem in the electrofused magnesia furnace (EFMF). Compared to conventional method, the contributions are as follows: (1) a new kernel principal component analysis is proposed based on loss function in the feature space; (2) the model of kernel principal component analysis based on forgetting factor is updated; (3) a new iterative kernel principal component analysis algorithm is proposed based on penalty factor.

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.

scholarly journals Monitoring a Reverse Osmosis Process with Kernel Principal Component Analysis: A Preliminary Approach

2021 ◽  
Vol 11 (14) ◽  
pp. 6370
Author(s):  
Elena Quatrini ◽  
Francesco Costantino ◽  
David Mba ◽  
Xiaochuan Li ◽  
Tat-Hean Gan
Keyword(s):  
Principal Component Analysis ◽  
Fault Detection ◽  
Water Purification ◽  
Principal Component ◽  
Temporal Correlation ◽  
Component Analysis ◽  
Kernel Principal Component Analysis ◽  
Original Dataset ◽  
Monitoring Process ◽  
Machine Health

The water purification process is becoming increasingly important to ensure the continuity and quality of subsequent production processes, and it is particularly relevant in pharmaceutical contexts. However, in this context, the difficulties arising during the monitoring process are manifold. On the one hand, the monitoring process reveals various discontinuities due to different characteristics of the input water. On the other hand, the monitoring process is discontinuous and random itself, thus not guaranteeing continuity of the parameters and hindering a straightforward analysis. Consequently, further research on water purification processes is paramount to identify the most suitable techniques able to guarantee good performance. Against this background, this paper proposes an application of kernel principal component analysis for fault detection in a process with the above-mentioned characteristics. Based on the temporal variability of the process, the paper suggests the use of past and future matrices as input for fault detection as an alternative to the original dataset. In this manner, the temporal correlation between process parameters and machine health is accounted for. The proposed approach confirms the possibility of obtaining very good monitoring results in the analyzed context.

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