scholarly journals Minimum Eigenvector Collaborative Representation Discriminant Projection for Feature Extraction

Sensors ◽  
2020 ◽  
Vol 20 (17) ◽  
pp. 4778
Author(s):  
Haoshuang Hu ◽  
Da-Zheng Feng
Keyword(s):  
Feature Extraction ◽  
Training Sample ◽  
Dimensional Subspace ◽  
Collaborative Representation ◽  
High Dimensional ◽  
Dimensional Manifold ◽  
Zero Eigenvalue ◽  
Sample Covariance ◽  
Low Dimensional ◽  
Discriminant Projection

High-dimensional signals, such as image signals and audio signals, usually have a sparse or low-dimensional manifold structure, which can be projected into a low-dimensional subspace to improve the efficiency and effectiveness of data processing. In this paper, we propose a linear dimensionality reduction method—minimum eigenvector collaborative representation discriminant projection—to address high-dimensional feature extraction problems. On the one hand, unlike the existing collaborative representation method, we use the eigenvector corresponding to the smallest non-zero eigenvalue of the sample covariance matrix to reduce the error of collaborative representation. On the other hand, we maintain the collaborative representation relationship of samples in the projection subspace to enhance the discriminability of the extracted features. Also, the between-class scatter of the reconstructed samples is used to improve the robustness of the projection space. The experimental results on the COIL-20 image object database, ORL, and FERET face databases, as well as Isolet database demonstrate the effectiveness of the proposed method, especially in low dimensions and small training sample size.

scholarly journals Modified Kernel Marginal Fisher Analysis for Feature Extraction and Its Application to Bearing Fault Diagnosis

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Li Jiang ◽  
Shunsheng Guo
Keyword(s):  
Feature Extraction ◽  
Fault Diagnosis ◽  
Nearest Neighbor ◽  
Feature Space ◽  
High Dimensional ◽  
Dimensional Manifold ◽  
Bearing Fault ◽  
Bearing Fault Diagnosis ◽  
Low Dimensional ◽  
Low Dimensional Manifold

The high-dimensional features of defective bearings usually include redundant and irrelevant information, which will degrade the diagnosis performance. Thus, it is critical to extract the sensitive low-dimensional characteristics for improving diagnosis performance. This paper proposes modified kernel marginal Fisher analysis (MKMFA) for feature extraction with dimensionality reduction. Due to its outstanding performance in enhancing the intraclass compactness and interclass dispersibility, MKMFA is capable of effectively extracting the sensitive low-dimensional manifold characteristics beneficial to subsequent pattern classification even for few training samples. A MKMFA- based fault diagnosis model is presented and applied to identify different bearing faults. It firstly utilizes MKMFA to directly extract the low-dimensional manifold characteristics from the raw time-series signal samples in high-dimensional ambient space. Subsequently, the sensitive low-dimensional characteristics in feature space are inputted into K-nearest neighbor classifier so as to distinguish various fault patterns. The four-fault-type and ten-fault-severity bearing fault diagnosis experiment results show the feasibility and superiority of the proposed scheme in comparison with the other five methods.

scholarly journals Neural Excursions from Low-Dimensional Manifold Structure Explain Intersubject Variation in Human Motor Learning

2021 ◽  
Author(s):  
Corson N Areshenkoff ◽  
Daniel J Gale ◽  
Joe Y Nashed ◽  
Dominic Standage ◽  
John Randall Flanagan ◽  
...  
Keyword(s):  
Motor Learning ◽  
Large Scale ◽  
Brain Activity ◽  
Dimensional Subspace ◽  
Learning Performance ◽  
Dimensional Manifold ◽  
Learning Abilities ◽  
Manifold Structure ◽  
Electrophysiological Studies ◽  
Low Dimensional

Humans vary greatly in their motor learning abilities, yet little is known about the neural mechanisms that underlie this variability. Recent neuroimaging and electrophysiological studies demonstrate that large-scale neural dynamics inhabit a low-dimensional subspace or manifold, and that learning is constrained by this intrinsic manifold architecture. Here we asked, using functional MRI, whether subject-level differences in neural excursion from manifold structure can explain differences in learning across participants. We had subjects perform a sensorimotor adaptation task in the MRI scanner on two consecutive days, allowing us to assess their learning performance across days, as well as continuously measure brain activity. We find that the overall neural excursion from manifold activity in both cognitive and sensorimotor brain networks is associated with differences in subjects' patterns of learning and relearning across days. These findings suggest that off-manifold activity provides an index of the relative engagement of different neural systems during learning, and that intersubject differences in patterns of learning and relearning across days are related to reconfiguration processes in cognitive and sensorimotor networks during learning.

scholarly journals An Incremental Version of L-MVU for the Feature Extraction of MI-EEG

2019 ◽  
Vol 2019 ◽  
pp. 1-19
Author(s):  
Mingai Li ◽  
Hongwei Xi ◽  
Xiaoqing Zhu
Keyword(s):  
Feature Extraction ◽  
Extraction Method ◽  
Average Energy ◽  
High Dimensional ◽  
Dimensional Representation ◽  
Feature Extraction Method ◽  
Sample Data ◽  
Out Of Sample ◽  
Nonlinear Features ◽  
Low Dimensional

Due to the nonlinear and high-dimensional characteristics of motor imagery electroencephalography (MI-EEG), it can be challenging to get high online accuracy. As a nonlinear dimension reduction method, landmark maximum variance unfolding (L-MVU) can completely retain the nonlinear features of MI-EEG. However, L-MVU still requires considerable computation costs for out-of-sample data. An incremental version of L-MVU (denoted as IL-MVU) is proposed in this paper. The low-dimensional representation of the training data is generated by L-MVU. For each out-of-sample data, its nearest neighbors will be found in the high-dimensional training samples and the corresponding reconstruction weight matrix be calculated to generate its low-dimensional representation as well. IL-MVU is further combined with the dual-tree complex wavelet transform (DTCWT), which develops a hybrid feature extraction method (named as IL-MD). IL-MVU is applied to extract the nonlinear features of the specific subband signals, which are reconstructed by DTCWT and have the obvious event-related synchronization/event-related desynchronization phenomenon. The average energy features of α and β waves are calculated simultaneously. The two types of features are fused and are evaluated by a linear discriminant analysis classifier. Based on the two public datasets with 12 subjects, extensive experiments were conducted. The average recognition accuracies of 10-fold cross-validation are 92.50% on Dataset 3b and 88.13% on Dataset 2b, and they gain at least 1.43% and 3.45% improvement, respectively, compared to existing methods. The experimental results show that IL-MD can extract more accurate features with relatively lower consumption cost, and it also has better feature visualization and self-adaptive characteristics to subjects. The t-test results and Kappa values suggest the proposed feature extraction method reaches statistical significance and has high consistency in classification.

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.

scholarly journals Bootstrapping spectral statistics in high dimensions

Biometrika ◽  
2019 ◽  
Vol 106 (4) ◽  
pp. 781-801 ◽  
Author(s):  
Miles E Lopes ◽  
Andrew Blandino ◽  
Alexander Aue
Keyword(s):  
Parametric Bootstrap ◽  
Covariance Matrices ◽  
Asymptotic Formulas ◽  
High Dimensional ◽  
High Dimensions ◽  
Full Data ◽  
Sample Covariance ◽  
Practical Standpoint ◽  
Spectral Statistics ◽  
Low Dimensional

Summary Statistics derived from the eigenvalues of sample covariance matrices are called spectral statistics, and they play a central role in multivariate testing. Although bootstrap methods are an established approach to approximating the laws of spectral statistics in low-dimensional problems, such methods are relatively unexplored in the high-dimensional setting. The aim of this article is to focus on linear spectral statistics as a class of prototypes for developing a new bootstrap in high dimensions, a method we refer to as the spectral bootstrap. In essence, the proposed method originates from the parametric bootstrap and is motivated by the fact that in high dimensions it is difficult to obtain a nonparametric approximation to the full data-generating distribution. From a practical standpoint, the method is easy to use and allows the user to circumvent the difficulties of complex asymptotic formulas for linear spectral statistics. In addition to proving the consistency of the proposed method, we present encouraging empirical results in a variety of settings. Lastly, and perhaps most interestingly, we show through simulations that the method can be applied successfully to statistics outside the class of linear spectral statistics, such as the largest sample eigenvalue and others.

Self-Organizing Map Learning Nonlinearly Embedded Manifolds

2005 ◽  
Vol 4 (1) ◽  
pp. 22-31 ◽  
Author(s):  
Timo Similä
Keyword(s):  
Learning Algorithm ◽  
Image Data ◽  
High Dimensional ◽  
Locally Linear Embedding ◽  
Complex Data ◽  
Dimensional Manifold ◽  
Self Organizing Map ◽  
Training Strategy ◽  
Low Dimensional ◽  
Self Organizing

One of the main tasks in exploratory data analysis is to create an appropriate representation for complex data. In this paper, the problem of creating a representation for observations lying on a low-dimensional manifold embedded in high-dimensional coordinates is considered. We propose a modification of the Self-organizing map (SOM) algorithm that is able to learn the manifold structure in the high-dimensional observation coordinates. Any manifold learning algorithm may be incorporated to the proposed training strategy to guide the map onto the manifold surface instead of becoming trapped in local minima. In this paper, the Locally linear embedding algorithm is adopted. We use the proposed method successfully on several data sets with manifold geometry including an illustrative example of a surface as well as image data. We also show with other experiments that the advantage of the method over the basic SOM is restricted to this specific type of data.

Equation-Free Continuation of Maximal Vibration Amplitudes in a Nonlinear Rotor-Bearing Model of a Turbocharger

2009 ◽  
Author(s):  
Michael Elmegaard ◽  
Jan Ru¨bel ◽  
Mizuho Inagaki ◽  
Atsushi Kawamoto ◽  
Jens Starke
Keyword(s):  
Dimensional Space ◽  
Dynamical Behaviour ◽  
Numerical Continuation ◽  
High Dimensional ◽  
Dimensional Manifold ◽  
Rotor Design ◽  
Investigation Methods ◽  
Rotor Bearing ◽  
Low Dimensional ◽  
Low Dimensional Manifold

Mechanical systems are typically described with finite element models resulting in high-dimensional dynamical systems. The high-dimensional space excludes the application of certain investigation methods like numerical continuation and bifurcation analysis to investigate the dynamical behaviour and its parameter dependence. Nevertheless, the dynamical behaviour usually lives on a low-dimensional manifold but typically no closed equations are available for the macroscopic quantities of interest. Therefore, an equation-free approach is suggested here to analyse and investigate the vibration behaviour of nonlinear rotating machinery. This allows then in the next step to optimize the rotor design specifications to reduce unbalance vibrations of a rotor-bearing system with nonlinear factors like the oil film dynamics. As an example we provide a simple model of a passenger car turbocharger where we investigate how the maximal vibration amplitude of the rotor depends on the viscosity of the oil used in the bearings.

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.

scholarly journals A real negative selection algorithm with evolutionary preference for anomaly detection

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 121-134 ◽  
Author(s):  
Tao Yang ◽  
Wen Chen ◽  
Tao Li
Keyword(s):  
Negative Selection ◽  
Feature Space ◽  
Dimensional Subspace ◽  
Experimental Result ◽  
High Dimensional ◽  
Selection Algorithm ◽  
Negative Selection Algorithm ◽  
Preference Theory ◽  
Low Dimensional ◽  
Selection Algorithms

AbstractTraditional real negative selection algorithms (RNSAs) adopt the estimated coverage (c0) as the algorithm termination threshold, and generate detectors randomly. With increasing dimensions, the data samples could reside in the low-dimensional subspace, so that the traditional detectors cannot effectively distinguish these samples. Furthermore, in high-dimensional feature space,c0cannot exactly reflect the detectors set coverage rate for the nonself space, and it could lead the algorithm to be terminated unexpectedly when the number of detectors is insufficient. These shortcomings make the traditional RNSAs to perform poorly in high-dimensional feature space. Based upon “evolutionary preference” theory in immunology, this paper presents a real negative selection algorithm with evolutionary preference (RNSAP). RNSAP utilizes the “unknown nonself space”, “low-dimensional target subspace” and “known nonself feature” as the evolutionary preference to guide the generation of detectors, thus ensuring the detectors can cover the nonself space more effectively. Besides, RNSAP uses redundancy to replacec0as the termination threshold, in this way RNSAP can generate adequate detectors under a proper convergence rate. The theoretical analysis and experimental result demonstrate that, compared to the classical RNSA (V-detector), RNSAP can achieve a higher detection rate, but with less detectors and computing cost.

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