scholarly journals Fault Identification Based on Local Feature Correlation

2022 ◽  
pp. 119-146
Author(s):  
Jing Wang ◽  
Jinglin Zhou ◽  
Xiaolu Chen
Keyword(s):  
Data Processing ◽  
High Dimension ◽  
Dimensional Space ◽  
Original Data ◽  
Mapping Method ◽  
Kernel Functions ◽  
High Dimensional ◽  
Monitoring Methods ◽  
Multivariate Statistical ◽  
Low Dimensional

AbstractIndustrial data variables show obvious high dimension and strong nonlinear correlation. Traditional multivariate statistical monitoring methods, such as PCA, PLS, CCA, and FDA, are only suitable for solving the high-dimensional data processing with linear correlation. The kernel mapping method is the most common technique to deal with the nonlinearity, which projects the original data in the low-dimensional space to the high-dimensional space through appropriate kernel functions so as to achieve the goal of linear separability in the new space. However, the space projection from the low dimension to the high dimension is contradictory to the actual requirement of dimensionality reduction of the data. So kernel-based method inevitably increases the complexity of data processing.

A COMPUTATIONAL AND THEORETICAL ANALYSIS OF LOCAL NULL SPACE DISCRIMINANT METHOD FOR PATTERN CLASSIFICATION

2011 ◽  
Vol 25 (01) ◽  
pp. 117-134 ◽  
Author(s):  
MIAO CHENG ◽  
BIN FANG ◽  
YUAN YAN TANG ◽  
HENGXIN CHEN
Keyword(s):  
Pattern Classification ◽  
Null Space ◽  
Traditional Approach ◽  
Dimensional Space ◽  
Original Data ◽  
High Dimensional ◽  
Dimensional Manifold ◽  
Low Dimensional ◽  
Low Dimensional Manifold ◽  
Discriminant Power

Many problems in pattern classification and feature extraction involve dimensionality reduction as a necessary processing. Traditional manifold learning algorithms, such as ISOMAP, LLE, and Laplacian Eigenmap, seek the low-dimensional manifold in an unsupervised way, while the local discriminant analysis methods identify the underlying supervised submanifold structures. In addition, it has been well-known that the intraclass null subspace contains the most discriminative information if the original data exist in a high-dimensional space. In this paper, we seek for the local null space in accordance with the null space LDA (NLDA) approach and reveal that its computational expense mainly depends on the quantity of connected edges in graphs, which may be still unacceptable if a great deal of samples are involved. To address this limitation, an improved local null space algorithm is proposed to employ the penalty subspace to approximate the local discriminant subspace. Compared with the traditional approach, the proposed method can achieve more efficiency so that the overload problem is avoided, while slight discriminant power is lost theoretically. A comparative study on classification shows that the performance of the approximative algorithm is quite close to the genuine one.

STRING theorem from one dimension to high dimension

2021 ◽  
pp. 002072092098351
Author(s):  
Minchuan Qin
Keyword(s):  
String Theory ◽  
Energy Density ◽  
High Dimension ◽  
Dimensional Space ◽  
Energy System ◽  
One Dimension ◽  
High Dimensional ◽  
Quantum Energy ◽  
Change Trend ◽  
Low Dimensional

STRING is an important concept in geometry and physics, and is closely related to the distribution of energy system. This paper finds a geometric phenomenon that some properties of two-dimension STRING also exists in multiple-dimension STRING and proposes a STRING theorem from a dimension to high dimension. On this basis, an algorithm is designed to demonstrate the theorem and verify it. The concept of quantum energy density function is established to reveal the energy density conversion rule, and change trend between low-dimensional space and high-dimensional space in the framework of string theory.

Affinity Propagation Clustering Algorithm Based on PCA

2014 ◽  
Vol 590 ◽  
pp. 688-692
Author(s):  
Bei Chen ◽  
Kun Song
Keyword(s):  
Clustering Algorithm ◽  
Dimensional Space ◽  
Original Data ◽  
New Method ◽  
Affinity Propagation ◽  
High Dimensional ◽  
Redundant Information ◽  
Affinity Propagation Clustering ◽  
Components Analysis ◽  
Low Dimensional

Overlap information usually exits in the high-dimensional data. Misclassified points may be more when affinity propagation clustering is applied to these data. Concerning this problem, a new method combining principal components analysis and affinity propagation clustering is proposed. In this method, dimensionality of the original data is reduced on the premise of reserving most information of the variables. Then, affinity propagation clustering is implemented in the low-dimensional space. Thus, because the redundant information is deleted, the classification is accurate. Experiment is done by using this new method, the results of the experiment explain that this method is effective.

scholarly journals Unsupervised Text Feature Learning via Deep Variational Auto-encoder

2020 ◽  
Vol 49 (3) ◽  
pp. 421-437
Author(s):  
Genggeng Liu ◽  
Lin Xie ◽  
Chi-Hua Chen
Keyword(s):  
Dimensionality Reduction ◽  
High Dimensional Data ◽  
Image Data ◽  
Original Data ◽  
Feature Representation ◽  
High Dimensional ◽  
Learning To Learn ◽  
Text Feature ◽  
Reduction Methods ◽  
Low Dimensional

Dimensionality reduction plays an important role in the data processing of machine learning and data mining, which makes the processing of high-dimensional data more efficient. Dimensionality reduction can extract the low-dimensional feature representation of high-dimensional data, and an effective dimensionality reduction method can not only extract most of the useful information of the original data, but also realize the function of removing useless noise. The dimensionality reduction methods can be applied to all types of data, especially image data. Although the supervised learning method has achieved good results in the application of dimensionality reduction, its performance depends on the number of labeled training samples. With the growing of information from internet, marking the data requires more resources and is more difficult. Therefore, using unsupervised learning to learn the feature of data has extremely important research value. In this paper, an unsupervised multilayered variational auto-encoder model is studied in the text data, so that the high-dimensional feature to the low-dimensional feature becomes efficient and the low-dimensional feature can retain mainly information as much as possible. Low-dimensional feature obtained by different dimensionality reduction methods are used to compare with the dimensionality reduction results of variational auto-encoder (VAE), and the method can be significantly improved over other comparison methods.

scholarly journals Discovering a sparse set of pairwise discriminating features in high-dimensional data

2020 ◽  
Author(s):  
Samuel Melton ◽  
Sharad Ramanathan
Keyword(s):  
Single Cell ◽  
Dimensional Space ◽  
Cell Types ◽  
Dimensional Subspace ◽  
Supplementary Information ◽  
High Dimensional ◽  
Technological Advances ◽  
Data Points ◽  
Low Dimensional ◽  
Sparse Set

Abstract Motivation Recent technological advances produce a wealth of high-dimensional descriptions of biological processes, yet extracting meaningful insight and mechanistic understanding from these data remains challenging. For example, in developmental biology, the dynamics of differentiation can now be mapped quantitatively using single-cell RNA sequencing, yet it is difficult to infer molecular regulators of developmental transitions. Here, we show that discovering informative features in the data is crucial for statistical analysis as well as making experimental predictions. Results We identify features based on their ability to discriminate between clusters of the data points. We define a class of problems in which linear separability of clusters is hidden in a low-dimensional space. We propose an unsupervised method to identify the subset of features that define a low-dimensional subspace in which clustering can be conducted. This is achieved by averaging over discriminators trained on an ensemble of proposed cluster configurations. We then apply our method to single-cell RNA-seq data from mouse gastrulation, and identify 27 key transcription factors (out of 409 total), 18 of which are known to define cell states through their expression levels. In this inferred subspace, we find clear signatures of known cell types that eluded classification prior to discovery of the correct low-dimensional subspace. Availability and implementation https://github.com/smelton/SMD. Supplementary information Supplementary data are available at Bioinformatics online.

Head Pose Recognition Based on 2-D KPCA

2013 ◽  
Vol 373-375 ◽  
pp. 468-472
Author(s):  
Chun Ling Li ◽  
Yu Feng Lu
Keyword(s):  
Interpolation Method ◽  
Dimensional Space ◽  
Linear Method ◽  
Principal Component ◽  
Kernel Functions ◽  
Kernel Principal Component Analysis ◽  
Estimation Accuracy ◽  
High Dimensional ◽  
Head Pose ◽  
Face Images

One’s head pose can be estimated using face images. The hidden manifold of head pose in the high dimensional space can be successfully embedded into a 2 dimensional space using Kernel Principal Component Analysis (KPCA). A pose curve is gotten using KPCA train samples and new pose image is projected onto this curve. The pose angle can be estimated using interpolation method. The disadvantage of traditional linear method is conquered by using 2-D KPCA and the experimental results that the method is effective to estimate head poses. The kernel functions effects on estimation accuracy are also discussed.

scholarly journals Complex Moment-Based Supervised Eigenmap for Dimensionality Reduction

2019 ◽  
Vol 33 ◽  
pp. 3910-3918 ◽  
Author(s):  
Akira Imakura ◽  
Momo Matsuda ◽  
Xiucai Ye ◽  
Tetsuya Sakurai
Keyword(s):  
Dimensionality Reduction ◽  
Parallel Implementation ◽  
Dimensional Space ◽  
Recognition Performance ◽  
Optimization Methods ◽  
Original Data ◽  
Dimensional Subspace ◽  
Reduction Methods ◽  
Low Dimensional ◽  
Matrix Trace

Dimensionality reduction methods that project highdimensional data to a low-dimensional space by matrix trace optimization are widely used for clustering and classification. The matrix trace optimization problem leads to an eigenvalue problem for a low-dimensional subspace construction, preserving certain properties of the original data. However, most of the existing methods use only a few eigenvectors to construct the low-dimensional space, which may lead to a loss of useful information for achieving successful classification. Herein, to overcome the deficiency of the information loss, we propose a novel complex moment-based supervised eigenmap including multiple eigenvectors for dimensionality reduction. Furthermore, the proposed method provides a general formulation for matrix trace optimization methods to incorporate with ridge regression, which models the linear dependency between covariate variables and univariate labels. To reduce the computational complexity, we also propose an efficient and parallel implementation of the proposed method. Numerical experiments indicate that the proposed method is competitive compared with the existing dimensionality reduction methods for the recognition performance. Additionally, the proposed method exhibits high parallel efficiency.

Extracting principal parameters of complex networks

2015 ◽  
Vol 26 (09) ◽  
pp. 1550103
Author(s):  
Yifang Ma ◽  
Zhiming Zheng
Keyword(s):  
Dynamic Systems ◽  
Growth Process ◽  
Dimensional Space ◽  
High Dimensional ◽  
Scale Function ◽  
Control Parameters ◽  
Diffusion Matrix ◽  
Similarity Relations ◽  
Low Dimensional ◽  
Network Ensembles

The evolution of networks or dynamic systems is controlled by many parameters in high-dimensional space, and it is crucial to extract the reduced and dominant ones in low-dimensional space. Here we consider the network ensemble, introduce a matrix resolvent scale function and apply it to a spectral approach to get the similarity relations between each pair of networks. The concept of Diffusion Maps is used to get the principal parameters, and we point out that the reduced dimensional principal parameters are captured by the low order eigenvectors of the diffusion matrix of the network ensemble. We validate our results by using two classical network ensembles and one dynamical network sequence via a cooperative Achlioptas growth process where an abrupt transition of the structures has been captured by our method. Our method provides a potential access to the pursuit of invisible control parameters of complex systems.

scholarly journals Locally Linear Discriminate Embedding for Face Recognition

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Eimad E. Abusham ◽  
E. K. Wong
Keyword(s):  
Face Recognition ◽  
Dimensional Space ◽  
Linear Structure ◽  
Data Representation ◽  
High Dimensional ◽  
Fast Processing ◽  
Novel Method ◽  
Computational Simplicity ◽  
Low Dimensional ◽  
Locally Linear

A novel method based on the local nonlinear mapping is presented in this research. The method is called Locally Linear Discriminate Embedding (LLDE). LLDE preserves a local linear structure of a high-dimensional space and obtains a compact data representation as accurately as possible in embedding space (low dimensional) before recognition. For computational simplicity and fast processing, Radial Basis Function (RBF) classifier is integrated with the LLDE. RBF classifier is carried out onto low-dimensional embedding with reference to the variance of the data. To validate the proposed method, CMU-PIE database has been used and experiments conducted in this research revealed the efficiency of the proposed methods in face recognition, as compared to the linear and non-linear approaches.

scholarly journals SCDRHA: A scRNA-Seq Data Dimensionality Reduction Algorithm Based on Hierarchical Autoencoder

2021 ◽  
Vol 12 ◽  
Author(s):  
Jianping Zhao ◽  
Na Wang ◽  
Haiyun Wang ◽  
Chunhou Zheng ◽  
Yansen Su
Keyword(s):  
Dimensionality Reduction ◽  
Data Visualization ◽  
State Of The Art ◽  
Dimensional Space ◽  
High Dimensional ◽  
Reduction Algorithm ◽  
Cell Clustering ◽  
Data Dimensionality Reduction ◽  
Single Cell Rna Sequencing ◽  
Low Dimensional

Dimensionality reduction of high-dimensional data is crucial for single-cell RNA sequencing (scRNA-seq) visualization and clustering. One prominent challenge in scRNA-seq studies comes from the dropout events, which lead to zero-inflated data. To address this issue, in this paper, we propose a scRNA-seq data dimensionality reduction algorithm based on a hierarchical autoencoder, termed SCDRHA. The proposed SCDRHA consists of two core modules, where the first module is a deep count autoencoder (DCA) that is used to denoise data, and the second module is a graph autoencoder that projects the data into a low-dimensional space. Experimental results demonstrate that SCDRHA has better performance than existing state-of-the-art algorithms on dimension reduction and noise reduction in five real scRNA-seq datasets. Besides, SCDRHA can also dramatically improve the performance of data visualization and cell clustering.

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