scholarly journals A Construction of an Averaged Representation of Human Cortical Gyri Using Non-linear Principal Component Analysis

2005 ◽  
pp. 749-756
Author(s):  
G. Lohmann ◽  
D. Y. von Cramon ◽  
A. C. F. Colchester
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Non Linear

scholarly journals Non-linear complex principal component analysis of nearshore bathymetry

2005 ◽  
Vol 12 (5) ◽  
pp. 661-670 ◽  
Author(s):  
S. S. P. Rattan ◽  
B. G. Ruessink ◽  
W. W. Hsieh
Keyword(s):  
Principal Component Analysis ◽  
Data Structure ◽  
Linear Method ◽  
Principal Component ◽  
Component Analysis ◽  
Dimensional Structure ◽  
Linear Phase ◽  
Linear Complex ◽  
Amplitude Variability ◽  
Non Linear

Abstract. Complex principal component analysis (CPCA) is a useful linear method for dimensionality reduction of data sets characterized by propagating patterns, where the CPCA modes are linear functions of the complex principal component (CPC), consisting of an amplitude and a phase. The use of non-linear methods, such as the neural-network based circular non-linear principal component analysis (NLPCA.cir) and the recently developed non-linear complex principal component analysis (NLCPCA), may provide a more accurate description of data in case the lower-dimensional structure is non-linear. NLPCA.cir extracts non-linear phase information without amplitude variability, while NLCPCA is capable of extracting both. NLCPCA can thus be viewed as a non-linear generalization of CPCA. In this article, NLCPCA is applied to bathymetry data from the sandy barred beaches at Egmond aan Zee (Netherlands), the Hasaki coast (Japan) and Duck (North Carolina, USA) to examine how effective this new method is in comparison to CPCA and NLPCA.cir in representing propagating phenomena. At Duck, the underlying low-dimensional data structure is found to have linear phase and amplitude variability only and, accordingly, CPCA performs as well as NLCPCA. At Egmond, the reduced data structure contains non-linear spatial patterns (asymmetric bar/trough shapes) without much temporal amplitude variability and, consequently, is about equally well modelled by NLCPCA and NLPCA.cir. Finally, at Hasaki, the data structure displays not only non-linear spatial variability but also considerably temporal amplitude variability, and NLCPCA outperforms both CPCA and NLPCA.cir. Because it is difficult to know the structure of data in advance as to which one of the three models should be used, the generalized NLCPCA model can be used in each situation.

scholarly journals Performance Analysis of Classifiers in Identifying NREM Sleep and Awaken Stages from EEG Signals

2020 ◽  
Vol 8 (6) ◽  
pp. 4321-4326
Keyword(s):  
Principal Component Analysis ◽  
Logistic Regression ◽  
Linear Regression ◽  
Expectation Maximization ◽  
Principal Component ◽  
Nrem Sleep ◽  
Component Analysis ◽  
Medical Procedure ◽  
Eeg Signals ◽  
Non Linear

Electroencephalogram is a medical procedure which helps in analyzing the activities of the brain through electrical signals. In this paper a simple classification technique of EEG signal into two stages as NREM sleep and awaken stages had been undertaken. Classifying these stages helps the physician to understand the patient's sleep disorder by knowing whether the person's brain is in NREM sleep or awaken stages. Physionet EEG signals are samples of 256 signals per second for 10 seconds duration is used in this work. Then the EEG samples properties are analyzed through various parameters like statistical features, entropy Pearson correlation coefficient, Power spectral density, scatter plots and Hilbert transform plots. The classification of NREM sleep and awaken stage is performed by the ten different classifiers broadly grouped into non linear and hybrid one. The classifiers used include Linear Regression, Non Linear Regression, Logistic Regression, Principal Component Analysis, Kernel Principal Component Analysis, Expectation Maximization, Compensatory Expectation Maximization, Expectation Maximization with Logistic Regression Compensatory Expectation Maximization with Logistic Regression, and Firefly. The performances of the classifiers are analyzed using regular parameters like sensitivity, accuracy, specificity, performance index. The highest accuracy of 95.575% is achieved with linear regression for awaken signal and an accuracy of 95.315% is achieved using kernel PCA for sleep signal.

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