scholarly journals Wavelet Kernel Principal Component Analysis in Noisy Multiscale Data Classification

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Shengkun Xie ◽  
Anna T. Lawniczak ◽  
Sridhar Krishnan ◽  
Pietro Lio
Keyword(s):  
Principal Component Analysis ◽  
Feature Extraction ◽  
Principal Component ◽  
Real Data ◽  
Component Analysis ◽  
Multiscale Methods ◽  
Kernel Principal Component Analysis ◽  
Simulation Data ◽  
Translation Invariant ◽  
Feature Extraction Method

We introduce multiscale wavelet kernels to kernel principal component analysis (KPCA) to narrow down the search of parameters required in the calculation of a kernel matrix. This new methodology incorporates multiscale methods into KPCA for transforming multiscale data. In order to illustrate application of our proposed method and to investigate the robustness of the wavelet kernel in KPCA under different levels of the signal to noise ratio and different types of wavelet kernel, we study a set of two-class clustered simulation data. We show that WKPCA is an effective feature extraction method for transforming a variety of multidimensional clustered data into data with a higher level of linearity among the data attributes. That brings an improvement in the accuracy of simple linear classifiers. Based on the analysis of the simulation data sets, we observe that multiscale translation invariant wavelet kernels for KPCA has an enhanced performance in feature extraction. The application of the proposed method to real data is also addressed.

Hot Rolling State Analysis Based on Kernel Principal Component Analysis and Information Entropy

2012 ◽  
Vol 572 ◽  
pp. 7-12
Author(s):  
Fei He ◽  
Quan Yang ◽  
Bao Jian Wang
Keyword(s):  
Principal Component Analysis ◽  
Feature Extraction ◽  
Information Entropy ◽  
Hot Rolling ◽  
Principal Component ◽  
Component Analysis ◽  
Kernel Principal Component Analysis ◽  
Process Data ◽  
Feature Extraction Method ◽  
Information Metric

With more and more process data acquired from manufacturing process, extracting useful information to build empirical models of past successful operations is urgently required to get higher product quality. Clustering is the important data mining methods, where feature extraction is a significant factor to ensure the accurate rate of clustering and classification. As a common non-linear feature extraction method, kernel principal component analysis (KPCA) uses the variance as the information metric, but the variance is not always effective in some cases. Since information entropy is nonlinear and can effectively represent the dependencies of features, the Renyi entropy is used as the information metric to extract the feature in this paper. Simulation data, Tennessee Eastman and hot rolling process data are used for model validation. As a result the proposed method has better performance on feature extraction, compared with traditional KPCA.

Training Data Reduction and Classification Based on Greedy Kernel Principal Component Analysis and Fuzzy C-Means Algorithm

2013 ◽  
Vol 347-350 ◽  
pp. 2390-2394
Author(s):  
Xiao Fang Liu ◽  
Chun Yang
Keyword(s):  
Principal Component Analysis ◽  
Feature Extraction ◽  
Computational Complexity ◽  
Principal Component ◽  
Large Data ◽  
Component Analysis ◽  
Training Data ◽  
Kernel Principal Component Analysis ◽  
Nonlinear Feature Extraction ◽  
Nonlinear Feature

Nonlinear feature extraction used standard Kernel Principal Component Analysis (KPCA) method has large memories and high computational complexity in large datasets. A Greedy Kernel Principal Component Analysis (GKPCA) method is applied to reduce training data and deal with the nonlinear feature extraction problem for training data of large data in classification. First, a subset, which approximates to the original training data, is selected from the full training data using the greedy technique of the GKPCA method. Then, the feature extraction model is trained by the subset instead of the full training data. Finally, FCM algorithm classifies feature extraction data of the GKPCA, KPCA and PCA methods, respectively. The simulation results indicate that the feature extraction performance of both the GKPCA, and KPCA methods outperform the PCA method. In addition of retaining the performance of the KPCA method, the GKPCA method reduces computational complexity due to the reduced training set in classification.

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.

scholarly journals Wavelet Power Spectral Domain Functional Principal Component Analysis for Feature Extraction of Epileptic EEGs

Computation ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 78
Author(s):  
Shengkun Xie
Keyword(s):  
Principal Component Analysis ◽  
Feature Extraction ◽  
Power Spectra ◽  
Principal Component ◽  
Component Analysis ◽  
Functional Principal Component Analysis ◽  
Eeg Signals ◽  
Feature Extraction Method ◽  
Functional Principal Component ◽  
Low Dimensional

Feature extraction plays an important role in machine learning for signal processing, particularly for low-dimensional data visualization and predictive analytics. Data from real-world complex systems are often high-dimensional, multi-scale, and non-stationary. Extracting key features of this type of data is challenging. This work proposes a novel approach to analyze Epileptic EEG signals using both wavelet power spectra and functional principal component analysis. We focus on how the feature extraction method can help improve the separation of signals in a low-dimensional feature subspace. By transforming EEG signals into wavelet power spectra, the functionality of signals is significantly enhanced. Furthermore, the power spectra transformation makes functional principal component analysis suitable for extracting key signal features. Therefore, we refer to this approach as a double feature extraction method since both wavelet transform and functional PCA are feature extractors. To demonstrate the applicability of the proposed method, we have tested it using a set of publicly available epileptic EEGs and patient-specific, multi-channel EEG signals, for both ictal signals and pre-ictal signals. The obtained results demonstrate that combining wavelet power spectra and functional principal component analysis is promising for feature extraction of epileptic EEGs. Therefore, they can be useful in computer-based medical systems for epilepsy diagnosis and epileptic seizure detection problems.

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