High-Dimensional Data Dimension Reduction Based on KECA

2013 ◽  
Vol 303-306 ◽  
pp. 1101-1104 ◽  
Author(s):  
Yong De Hu ◽  
Jing Chang Pan ◽  
Xin Tan
Keyword(s):  
Principal Component Analysis ◽  
Dimension Reduction ◽  
High Dimensional Data ◽  
Principal Component ◽  
Good Method ◽  
Component Analysis ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Kernel Principal Component Analysis ◽  
High Dimensional

Kernel entropy component analysis (KECA) reveals the original data’s structure by kernel matrix. This structure is related to the Renyi entropy of the data. KECA maintains the invariance of the original data’s structure by keeping the data’s Renyi entropy unchanged. This paper described the original data by several components on the purpose of dimension reduction. Then the KECA was applied in celestial spectra reduction and was compared with Principal Component Analysis (PCA) and Kernel Principal Component Analysis (KPCA) by experiments. Experimental results show that the KECA is a good method in high-dimensional data reduction.

scholarly journals Comprehensive evaluation of robotic global performance based on modified principal component analysis

2020 ◽  
Vol 17 (4) ◽  
pp. 172988141989688
Author(s):  
Liming Li ◽  
Jing Zhao ◽  
Chunrong Wang ◽  
Chaojie Yan
Keyword(s):  
Principal Component Analysis ◽  
Dimension Reduction ◽  
Kernel Function ◽  
Principal Component ◽  
Component Analysis ◽  
Kernel Principal Component Analysis ◽  
Polynomial Kernel ◽  
Analysis Method ◽  
Principal Component Analysis Method ◽  
Global Performance

The multivariate statistical method such as principal component analysis based on linear dimension reduction and kernel principal component analysis based on nonlinear dimension reduction as the modified principal component analysis method are commonly used. Because of the diversity and correlation of robotic global performance indexes, the two multivariate statistical methods principal component analysis and kernel principal component analysis methods can be used, respectively, to comprehensively evaluate the global performance of PUMA560 robot with different dimensions. When using the kernel principal component analysis method, the kernel function and parameters directly have an effect on the result of comprehensive performance evaluation. Because kernel principal component analysis with polynomial kernel function is time-consuming and inefficient, a new kernel function based on similarity degree is proposed for the big sample data. The new kernel function is proved according to Mercer’s theorem. By comparing different dimension reduction effects of principal component analysis method, the kernel principal component analysis method with polynomial kernel function, and the kernel principal component analysis method with the new kernel function, the kernel principal component analysis method with the new kernel function could deal more effectively with the nonlinear relationship among indexes, and its calculation result is more reasonable for containing more comprehensive information. The simulation shows that the kernel principal component analysis method with the new kernel function has the advantage of low time consuming, good real-time performance, and good ability of generalization.

scholarly journals Multilevel Functional Principal Component Analysis for High-Dimensional Data

2011 ◽  
Vol 20 (4) ◽  
pp. 852-873 ◽  
Author(s):  
Vadim Zipunnikov ◽  
Brian Caffo ◽  
David M. Yousem ◽  
Christos Davatzikos ◽  
Brian S. Schwartz ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
High Dimensional Data ◽  
Principal Component ◽  
Component Analysis ◽  
Functional Principal Component Analysis ◽  
High Dimensional ◽  
Functional Principal Component

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 Performance Analysis of Dimensionality Reduction Techniques in the Context of Clustering

2019 ◽  
Vol 8 (S3) ◽  
pp. 66-71
Author(s):  
T. Sudha ◽  
P. Nagendra Kumar
Keyword(s):  
Principal Component Analysis ◽  
Dimensionality Reduction ◽  
High Dimensional Data ◽  
Principal Component ◽  
Component Analysis ◽  
High Dimensional ◽  
Reduction Techniques ◽  
Dimensionality Reduction Techniques ◽  
Low Dimensional ◽  
Probabilistic Principal Component Analysis

Data mining is one of the major areas of research. Clustering is one of the main functionalities of datamining. High dimensionality is one of the main issues of clustering and Dimensionality reduction can be used as a solution to this problem. The present work makes a comparative study of dimensionality reduction techniques such as t-distributed stochastic neighbour embedding and probabilistic principal component analysis in the context of clustering. High dimensional data have been reduced to low dimensional data using dimensionality reduction techniques such as t-distributed stochastic neighbour embedding and probabilistic principal component analysis. Cluster analysis has been performed on the high dimensional data as well as the low dimensional data sets obtained through t-distributed stochastic neighbour embedding and Probabilistic principal component analysis with varying number of clusters. Mean squared error; time and space have been considered as parameters for comparison. The results obtained show that time taken to convert the high dimensional data into low dimensional data using probabilistic principal component analysis is higher than the time taken to convert the high dimensional data into low dimensional data using t-distributed stochastic neighbour embedding.The space required by the data set reduced through Probabilistic principal component analysis is less than the storage space required by the data set reduced through t-distributed stochastic neighbour embedding.

Comprehensive Evaluation of Parallel Mechanism and Robot Performance Based on Principal Component Analysis and Kernel Principal Component Analysis

2015 ◽  
Author(s):  
Liming Li ◽  
Jing Zhao
Keyword(s):  
Principal Component Analysis ◽  
Dimension Reduction ◽  
Topological Structure ◽  
Parallel Mechanism ◽  
Principal Component ◽  
Component Analysis ◽  
Kernel Principal Component Analysis ◽  
Parallel Mechanisms ◽  
Performance Indexes ◽  
Comprehensive Performance

Revealing the relations among parallel mechanism and robot comprehensive performance, topological structure and dimension is the basis to optimize mechanism. Due to the correlation and diversity of the single performance indexes, statistical principles of linear dimension reduction and nonlinear dimension reduction were introduced into comprehensive performance analysis and evaluation for typical parallel mechanisms and robots. Then the mechanism’s topological structure and dimension with the best comprehensive performance could be selected based on principal component analysis (PCA) and kernel principal component analysis (KPCA) respectively. Through comparing the results, KPCA could reveal the nonlinear relationship among different single performance indexes to provide more comprehensive performance evaluation information than PCA, and indicate the numerical calculation relations among comprehensive performance, topological structure and dimension validly.

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