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.

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.

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 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.

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

Network Embedding on Hierarchical Community Structure Network

2021 ◽  
Vol 15 (4) ◽  
pp. 1-23
Author(s):  
Guojie Song ◽  
Yun Wang ◽  
Lun Du ◽  
Yi Li ◽  
Junshan Wang
Keyword(s):  
Community Structure ◽  
Structural Information ◽  
Spherical Surface ◽  
Network Embedding ◽  
The Galaxy ◽  
Community Information ◽  
The Hierarchical Structure ◽  
Network Properties ◽  
Multi Class Classification ◽  
Low Dimensional

Network embedding is a method of learning a low-dimensional vector representation of network vertices under the condition of preserving different types of network properties. Previous studies mainly focus on preserving structural information of vertices at a particular scale, like neighbor information or community information, but cannot preserve the hierarchical community structure, which would enable the network to be easily analyzed at various scales. Inspired by the hierarchical structure of galaxies, we propose the Galaxy Network Embedding (GNE) model, which formulates an optimization problem with spherical constraints to describe the hierarchical community structure preserving network embedding. More specifically, we present an approach of embedding communities into a low-dimensional spherical surface, the center of which represents the parent community they belong to. Our experiments reveal that the representations from GNE preserve the hierarchical community structure and show advantages in several applications such as vertex multi-class classification, network visualization, and link prediction. The source code of GNE is available online.

scholarly journals Supervised dimensionality reduction for big data

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Joshua T. Vogelstein ◽  
Eric W. Bridgeford ◽  
Minh Tang ◽  
Da Zheng ◽  
Christopher Douville ◽  
...  
Keyword(s):  
Dimensionality Reduction ◽  
Data Science ◽  
Real Data ◽  
Low Rank ◽  
Conditional Moment ◽  
Desktop Computer ◽  
Reduction Techniques ◽  
Reduction Methods ◽  
The Individual ◽  
Low Dimensional

AbstractTo solve key biomedical problems, experimentalists now routinely measure millions or billions of features (dimensions) per sample, with the hope that data science techniques will be able to build accurate data-driven inferences. Because sample sizes are typically orders of magnitude smaller than the dimensionality of these data, valid inferences require finding a low-dimensional representation that preserves the discriminating information (e.g., whether the individual suffers from a particular disease). There is a lack of interpretable supervised dimensionality reduction methods that scale to millions of dimensions with strong statistical theoretical guarantees. We introduce an approach to extending principal components analysis by incorporating class-conditional moment estimates into the low-dimensional projection. The simplest version, Linear Optimal Low-rank projection, incorporates the class-conditional means. We prove, and substantiate with both synthetic and real data benchmarks, that Linear Optimal Low-Rank Projection and its generalizations lead to improved data representations for subsequent classification, while maintaining computational efficiency and scalability. Using multiple brain imaging datasets consisting of more than 150 million features, and several genomics datasets with more than 500,000 features, Linear Optimal Low-Rank Projection outperforms other scalable linear dimensionality reduction techniques in terms of accuracy, while only requiring a few minutes on a standard desktop computer.

scholarly journals Artifacts in Simultaneous hdEEG/fMRI Imaging: A Nonlinear Dimensionality Reduction Approach

Sensors ◽  
2019 ◽  
Vol 19 (20) ◽  
pp. 4454 ◽  
Author(s):  
Marek Piorecky ◽  
Vlastimil Koudelka ◽  
Jan Strobl ◽  
Martin Brunovsky ◽  
Vladimir Krajca
Keyword(s):  
Data Structure ◽  
Spatial Clustering ◽  
Dimensional Space ◽  
Head Movements ◽  
Nonlinear Dimensionality Reduction ◽  
Space Resolution ◽  
Additional Information ◽  
Nonlinear Dimension ◽  
The Time Domain ◽  
Low Dimensional

Simultaneous recordings of electroencephalogram (EEG) and functional magnetic resonance imaging (fMRI) are at the forefront of technologies of interest to physicians and scientists because they combine the benefits of both modalities—better time resolution (hdEEG) and space resolution (fMRI). However, EEG measurements in the scanner contain an electromagnetic field that is induced in leads as a result of gradient switching slight head movements and vibrations, and it is corrupted by changes in the measured potential because of the Hall phenomenon. The aim of this study is to design and test a methodology for inspecting hidden EEG structures with respect to artifacts. We propose a top-down strategy to obtain additional information that is not visible in a single recording. The time-domain independent component analysis algorithm was employed to obtain independent components and spatial weights. A nonlinear dimension reduction technique t-distributed stochastic neighbor embedding was used to create low-dimensional space, which was then partitioned using the density-based spatial clustering of applications with noise (DBSCAN). The relationships between the found data structure and the used criteria were investigated. As a result, we were able to extract information from the data structure regarding electrooculographic, electrocardiographic, electromyographic and gradient artifacts. This new methodology could facilitate the identification of artifacts and their residues from simultaneous EEG in fMRI.

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