scholarly journals ENSO dynamics in current climate models: an investigation using nonlinear dimensionality reduction

2008 ◽  
Vol 15 (2) ◽  
pp. 339-363 ◽  
Author(s):  
I. Ross ◽  
P. J. Valdes ◽  
S. Wiggins
Keyword(s):  
Principal Component Analysis ◽  
Data Analysis ◽  
Dimensionality Reduction ◽  
El Niño ◽  
El Nino ◽  
Southern Oscillation ◽  
Principal Component ◽  
Component Analysis ◽  
Nonlinear Dimensionality Reduction ◽  
Climate Data

Abstract. Linear dimensionality reduction techniques, notably principal component analysis, are widely used in climate data analysis as a means to aid in the interpretation of datasets of high dimensionality. These linear methods may not be appropriate for the analysis of data arising from nonlinear processes occurring in the climate system. Numerous techniques for nonlinear dimensionality reduction have been developed recently that may provide a potentially useful tool for the identification of low-dimensional manifolds in climate data sets arising from nonlinear dynamics. Here, we apply Isomap, one such technique, to the study of El Niño/Southern Oscillation variability in tropical Pacific sea surface temperatures, comparing observational data with simulations from a number of current coupled atmosphere-ocean general circulation models. We use Isomap to examine El Niño variability in the different datasets and assess the suitability of the Isomap approach for climate data analysis. We conclude that, for the application presented here, analysis using Isomap does not provide additional information beyond that already provided by principal component analysis.

scholarly journals A kernel Principal Component Analysis (kPCA) Digest with a New Backward Mapping (pre-image reconstruction) Strategy

2020 ◽  
Author(s):  
Alberto García-González ◽  
Antonio Huerta ◽  
Sergio Zlotnik ◽  
Pedro Díez
Keyword(s):  
Principal Component Analysis ◽  
Dimensionality Reduction ◽  
Dimensional Space ◽  
Principal Component ◽  
Linear Structure ◽  
Component Analysis ◽  
Kernel Principal Component Analysis ◽  
Nonlinear Dimensionality Reduction ◽  
Dimensional Manifold ◽  
Low Dimensional

Abstract Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible dimensionality reduction if data belong to a nonlinear low-dimensional manifold. For nonlinear dimensionality reduction, kernel Principal Component Analysis (kPCA) is appreciated because of its simplicity and ease implementation. The paper provides a concise review of PCA and kPCA main ideas, trying to collect in a single document aspects that are often dispersed. Moreover, a strategy to map back the reduced dimension into the original high dimensional space is also devised, based on the minimization of a discrepancy functional.

Reaction Monitoring in Explorative Organic Synthesis Using Fiber-Optical NIR Spectroscopy and Principal Component Analysis

1996 ◽  
Vol 50 (12) ◽  
pp. 1541-1544 ◽  
Author(s):  
Hans-René Bjørsvik
Keyword(s):  
Principal Component Analysis ◽  
Data Analysis ◽  
Latent Variables ◽  
Near Infrared ◽  
Nir Spectroscopy ◽  
Principal Component ◽  
Component Analysis ◽  
Quantitative Information ◽  
Chemistry Laboratory ◽  
Reaction Profile

A method of combining spectroscopy and multivariate data analysis for obtaining quantitative information on how a reaction proceeds is presented. The method is an approach for the explorative synthetic organic laboratory rather than the analytical chemistry laboratory. The method implements near-infrared spectroscopy with an optical fiber transreflectance probe as instrumentation. The data analysis consists of decomposition of the spectral data, which are recorded during the course of a reaction by using principal component analysis to obtain latent variables, scores, and loading. From the scores and the corresponding reaction time, it is possible to obtain a reaction profile. This reaction profile can easily be recalculated to obtain the concentration profile over time. This calculation is based on only two quantitative measurements, which can be (1) measurement from the work-up of the reaction or (2) chromatographic analysis from two withdrawn samples during the reaction. The method is applied to the synthesis of 3-amino-propan-1,2-diol.

Physical-oriented and machine learning-based emission modeling in a diesel compression ignition engine: Dimensionality reduction and regression

2022 ◽  
pp. 146808742110707
Author(s):  
Aran Mohammad ◽  
Reza Rezaei ◽  
Christopher Hayduk ◽  
Thaddaeus Delebinski ◽  
Saeid Shahpouri ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Support Vector Machine ◽  
Factor Analysis ◽  
Dimensionality Reduction ◽  
Principal Component ◽  
Component Analysis ◽  
Data Driven ◽  
Support Vector ◽  
Emission Models ◽  
Emission Modeling

The development of internal combustion engines is affected by the exhaust gas emissions legislation and the striving to increase performance. This demands for engine-out emission models that can be used for engine optimization for real driving emission controls. The prediction capability of physically and data-driven engine-out emission models is influenced by the system inputs, which are specified by the user and can lead to an improved accuracy with increasing number of inputs. Thereby the occurrence of irrelevant inputs becomes more probable, which have a low functional relation to the emissions and can lead to overfitting. Alternatively, data-driven methods can be used to detect irrelevant and redundant inputs. In this work, thermodynamic states are modeled based on 772 stationary measured test bench data from a commercial vehicle diesel engine. Afterward, 37 measured and modeled variables are led into a data-driven dimensionality reduction. For this purpose, approaches of supervised learning, such as lasso regression and linear support vector machine, and unsupervised learning methods like principal component analysis and factor analysis are applied to select and extract the relevant features. The selected and extracted features are used for regression by the support vector machine and the feedforward neural network to model the NOx, CO, HC, and soot emissions. This enables an evaluation of the modeling accuracy as a result of the dimensionality reduction. Using the methods in this work, the 37 variables are reduced to 25, 22, 11, and 16 inputs for NOx, CO, HC, and soot emission modeling while maintaining the accuracy. The features selected using the lasso algorithm provide more accurate learning of the regression models than the extracted features through principal component analysis and factor analysis. This results in test errors RMSETe for modeling NOx, CO, HC, and soot emissions 19.22 ppm, 6.46 ppm, 1.29 ppm, and 0.06 FSN, respectively.

scholarly journals Dimensionality Reduction using PCA and K-Means Clustering for Breast Cancer Prediction

2018 ◽  
pp. 192 ◽  
Author(s):  
Ade Jamal ◽  
Annisa Handayani ◽  
Ali Akbar Septiandri ◽  
Endang Ripmiatin ◽  
Yunus Effendi
Keyword(s):  
Breast Cancer ◽  
Principal Component Analysis ◽  
Dimensionality Reduction ◽  
Principal Component ◽  
Component Analysis ◽  
Gradient Boosting ◽  
Support Vector ◽  
Breast Cancer Dataset ◽  
Cancer Prediction ◽  
Extreme Gradient Boosting

Breast cancer is the most important cause of death among women. A prediction of breast cancer in early stage provides a greater possibility of its cure. It needs a breast cancer prediction tool that can classify a breast tumor whether it was a harmful malignant tumor or un-harmful benign tumor. In this paper, two algorithms of machine learning, namely Support Vector Machine and Extreme Gradient Boosting technique will be compared for classification purpose. Prior to the classification, the number of data attribute will be reduced from the raw data by extracting features using Principal Component Analysis. A clustering method, namely K-Means is also used for dimensionality reduction besides the Principal Component Analysis. This paper will present a comparison among four models based on two dimensionality reduction methods combined with two classifiers which applied on Wisconsin Breast Cancer Dataset. The comparison will be measured by using accuracy, sensitivity and specificity metrics evaluated from the confusion matrices. The experimental results have indicated that the K-Means method, which is not usually used for dimensionality reduction can perform well compared to the popular Principal Component Analysis.

scholarly journals Hyperspectral Dimensionality Reduction Based on Multiscale Superpixelwise Kernel Principal Component Analysis

2019 ◽  
Vol 11 (10) ◽  
pp. 1219 ◽  
Author(s):  
Lan Zhang ◽  
Hongjun Su ◽  
Jingwei Shen
Keyword(s):  
Principal Component Analysis ◽  
Dimensionality Reduction ◽  
Principal Components ◽  
Classification Accuracy ◽  
Hyperspectral Image ◽  
Principal Component ◽  
Component Analysis ◽  
Homogeneous Region ◽  
Kernel Principal Component Analysis ◽  
Nonlinear Features

Dimensionality reduction (DR) is an important preprocessing step in hyperspectral image applications. In this paper, a superpixelwise kernel principal component analysis (SuperKPCA) method for DR that performs kernel principal component analysis (KPCA) on each homogeneous region is proposed to fully utilize the KPCA’s ability to acquire nonlinear features. Moreover, for the proposed method, the differences in the DR results obtained based on different fundamental images (the first principal components obtained by principal component analysis (PCA), KPCA, and minimum noise fraction (MNF)) are compared. Extensive experiments show that when 5, 10, 20, and 30 samples from each class are selected, for the Indian Pines, Pavia University, and Salinas datasets: (1) when the most suitable fundamental image is selected, the classification accuracy obtained by SuperKPCA can be increased by 0.06%–0.74%, 3.88%–4.37%, and 0.39%–4.85%, respectively, when compared with SuperPCA, which performs PCA on each homogeneous region; (2) the DR results obtained based on different first principal components are different and complementary. By fusing the multiscale classification results obtained based on different first principal components, the classification accuracy can be increased by 0.54%–2.68%, 0.12%–1.10%, and 0.01%–0.08%, respectively, when compared with the method based only on the most suitable fundamental image.

Sign in / Sign up

Export Citation Format

Share Document