scholarly journals Nonlinear dimensionality reduction in climate data

2004 ◽  
Vol 11 (3) ◽  
pp. 393-398 ◽  
Author(s):  
A. J. Gámez ◽  
C. S. Zhou ◽  
A. Timmermann ◽  
J. Kurths
Keyword(s):  
Dimensionality Reduction ◽  
Southern Oscillation ◽  
Nonlinear Dimensionality Reduction ◽  
Climate Data ◽  
Nonlinear Method ◽  
Minimum Number ◽  
Low Dimensional ◽  
Selection Of ◽  
Variance Explained ◽  
The Tropical Pacific

Abstract. Linear methods of dimensionality reduction are useful tools for handling and interpreting high dimensional data. However, the cumulative variance explained by each of the subspaces in which the data space is decomposed may show a slow convergence that makes the selection of a proper minimum number of subspaces for successfully representing the variability of the process ambiguous. The use of nonlinear methods can improve the embedding of multivariate data into lower dimensional manifolds. In this article, a nonlinear method for dimensionality reduction, Isomap, is applied to the sea surface temperature and thermocline data in the tropical Pacific Ocean, where the El Niño-Southern Oscillation (ENSO) phenomenon and the annual cycle phenomena interact. Isomap gives a more accurate description of the manifold dimensionality of the physical system. The knowledge of the minimum number of dimensions is expected to improve the development of low dimensional models for understanding and predicting ENSO.

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.

Information Technology in an Improved Supervised Locally Linear Embedding for Recognizing Speech Emotion

2014 ◽  
Vol 1014 ◽  
pp. 375-378 ◽  
Author(s):  
Ri Sheng Huang
Keyword(s):  
Dimensionality Reduction ◽  
Speech Emotion Recognition ◽  
High Dimensional ◽  
Locally Linear Embedding ◽  
Nonlinear Dimensionality Reduction ◽  
Discriminating Power ◽  
Speech Feature ◽  
Linear Embedding ◽  
Acoustic Space ◽  
Low Dimensional

To improve effectively the performance on speech emotion recognition, it is needed to perform nonlinear dimensionality reduction for speech feature data lying on a nonlinear manifold embedded in high-dimensional acoustic space. This paper proposes an improved SLLE algorithm, which enhances the discriminating power of low-dimensional embedded data and possesses the optimal generalization ability. The proposed algorithm is used to conduct nonlinear dimensionality reduction for 48-dimensional speech emotional feature data including prosody so as to recognize three emotions including anger, joy and neutral. Experimental results on the natural speech emotional database demonstrate that the proposed algorithm obtains the highest accuracy of 90.97% with only less 9 embedded features, making 11.64% improvement over SLLE algorithm.

scholarly journals Learning Neural Representations and Local Embedding for Nonlinear Dimensionality Reduction Mapping

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1017
Author(s):  
Sheng-Shiung Wu ◽  
Sing-Jie Jong ◽  
Kai Hu ◽  
Jiann-Ming Wu
Keyword(s):  
Dimensionality Reduction ◽  
Dimensional Space ◽  
Nonlinear Dimensionality Reduction ◽  
Distributed Data ◽  
Dimensional Manifold ◽  
Distance Constraints ◽  
Internal Representations ◽  
Data Clusters ◽  
Low Dimensional ◽  
Output Space

This work explores neural approximation for nonlinear dimensionality reduction mapping based on internal representations of graph-organized regular data supports. Given training observations are assumed as a sample from a high-dimensional space with an embedding low-dimensional manifold. An approximating function consisting of adaptable built-in parameters is optimized subject to given training observations by the proposed learning process, and verified for transformation of novel testing observations to images in the low-dimensional output space. Optimized internal representations sketch graph-organized supports of distributed data clusters and their representative images in the output space. On the basis, the approximating function is able to operate for testing without reserving original massive training observations. The neural approximating model contains multiple modules. Each activates a non-zero output for mapping in response to an input inside its correspondent local support. Graph-organized data supports have lateral interconnections for representing neighboring relations, inferring the minimal path between centroids of any two data supports, and proposing distance constraints for mapping all centroids to images in the output space. Following the distance-preserving principle, this work proposes Levenberg-Marquardt learning for optimizing images of centroids in the output space subject to given distance constraints, and further develops local embedding constraints for mapping during execution phase. Numerical simulations show the proposed neural approximation effective and reliable for nonlinear dimensionality reduction mapping.

Discriminating complex networks through supervised NDR and Bayesian classifier

2016 ◽  
Vol 27 (05) ◽  
pp. 1650051
Author(s):  
Ke-Sheng Yan ◽  
Li-Li Rong ◽  
Kai Yu
Keyword(s):  
Dimensionality Reduction ◽  
Complex Networks ◽  
Systematic Study ◽  
Discrimination Task ◽  
Bayesian Classifier ◽  
Nonlinear Dimensionality Reduction ◽  
Large Set ◽  
Network Properties ◽  
Low Dimensional ◽  
Projection Score

Discriminating complex networks is a particularly important task for the purpose of the systematic study of networks. In order to discriminate unknown networks exactly, a large set of network measurements are needed to be taken into account for comprehensively considering network properties. However, as we demonstrate in this paper, these measurements are nonlinear correlated with each other in general, resulting in a wide variety of redundant measurements which unintentionally explain the same aspects of network properties. To solve this problem, we adopt supervised nonlinear dimensionality reduction (NDR) to eliminate the nonlinear redundancy and visualize networks in a low-dimensional projection space. Though unsupervised NDR can achieve the same aim, we illustrate that supervised NDR is more appropriate than unsupervised NDR for discrimination task. After that, we perform Bayesian classifier (BC) in the projection space to discriminate the unknown network by considering the projection score vectors as the input of the classifier. We also demonstrate the feasibility and effectivity of this proposed method in six extensive research real networks, ranging from technological to social or biological. Moreover, the effectiveness and advantage of the proposed method is proved by the contrast experiments with the existing method.

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.

scholarly journals Intuitive Graphical Visualization of Transcriptomes by Nonlinear Dimensionality Reduction Exposes Relatedness between Human Placenta Tissues

2020 ◽  
Author(s):  
Liu Yajun ◽  
Zhang Yi ◽  
Jinquan Cui
Keyword(s):  
Dimensionality Reduction ◽  
Linear Method ◽  
Chorionic Villus ◽  
Placental Tissue ◽  
Scale Model ◽  
Nonlinear Dimensionality Reduction ◽  
Data Sets ◽  
Nonlinear Method ◽  
In Vitro Cell Lines

The establishment of a complex multi-scale model of biological tissue is of great significance for the study of related diseases, and the integration of relevant quantitative data is the premise to achieve this goal. Whereas, the systematic collation of data sets related to placental tissue is relatively lacking. In this study, 18 published transcriptomes (a total of 425 samples) datasets of human pregnancy-related tissues (including chorionic villus and decidua, term placenta, endometrium, in vitro cell lines, etc.) from public databases were collected and analyzed. We compared the most widely used dimensionality reduction (DR) methods to generate a 2D-map for visualization of these data. We also compared the effects of different parameter settings and commonly used manifold learning methods on the results. The result indicates that the nonlinear method can better preserve the small differences between different subtypes of placental tissue than linear method. It led the foundation for the study on accurate computational modeling of placental tissue development in the future. The datasets and analysis provide a useful source for the researchers in the field of the maternal-fetal interface and the establishment of pregnancy.

Determination of the minimum number of technological bases of a part

2020 ◽  
pp. 73-75
Author(s):  
B.M. Bazrov ◽  
T.M. Gaynutdinov
Keyword(s):  
Cost Price ◽  
Labor Input ◽  
Part Surface ◽  
Technological Base ◽  
Size Accuracy ◽  
Minimum Number ◽  
The Cost ◽  
Input Cost ◽  
Selection Of

The selection of technological bases is considered before the choice of the type of billet and the development of the route of the technological process. A technique is proposed for selecting the minimum number of sets of technological bases according to the criterion of equality in the cost price of manufacturing the part according to the principle of unity and combination of bases at this stage. Keywords: part, surface, coordinating size, accuracy, design and technological base, labor input, cost price. [email protected]

Nonlinear Dimensionality Reduction for Data on Manifold with Rings

2009 ◽  
Vol 19 (11) ◽  
pp. 2908-2920
Author(s):  
De-Yu MENG ◽  
Nan-Nan GU ◽  
Zong-Ben XU ◽  
Yee LEUNG
Keyword(s):  
Dimensionality Reduction ◽  
Nonlinear Dimensionality Reduction
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