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.

Wavelet Transform for Face Recognition Based on Improved Fuzzy C-Means

2014 ◽  
Vol 602-605 ◽  
pp. 2170-2173
Author(s):  
Xiao Fei Li
Keyword(s):  
Face Recognition ◽  
Wavelet Transform ◽  
Wavelet Analysis ◽  
Dimensional Space ◽  
Training Data ◽  
High Dimensional ◽  
Analysis Method ◽  
Running Time ◽  
Fuzzy C Means ◽  
Low Dimensional

The popular approaches for face recognition are PCA and LDA methods. But PCA could not capture the simplest invariance unless information is explicitly provided in the training data and LDA approach suffers from a small size problem. 2DPCA could reduce high dimensional data to a low-dimensional space.2DLDA could extract the proper features from image matrices based on LDA. Ensemble incomplete wavelet analysis method for face recognition is proposed based on improved fuzzy C-Means in this paper. The method proposed shows that it improves the accuracy and reduces the running time.

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.

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.

Cost-Sensitive Sparsity Preserving Projections for Face Recognition

2013 ◽  
Vol 760-762 ◽  
pp. 1615-1620 ◽  
Author(s):  
Xiao Yuan Jing ◽  
Wen Qian Li ◽  
Hao Gao ◽  
Yong Fang Yao ◽  
Jiang Yue Man
Keyword(s):  
Face Recognition ◽  
Sparse Representation ◽  
Dimensional Space ◽  
Recognition Rate ◽  
Recognition Task ◽  
Cost Information ◽  
The Public ◽  
Sparsity Preserving Projection ◽  
Low Dimensional ◽  
The Cost

As one of the most popular research topics, sparse representation (SR) technique has been successfully employed to solve face recognition task. Though current SR based methods prove to achieve high classification accuracy, they implicitly assume that the losses of all misclassifications are the same. However, in many real-world face recognition applications, this assumption may not hold as different misclassifications could lead to different losses. Driven by this concern, in this paper, we propose a cost-sensitive sparsity preserving projections (CSSPP) for face recognition. CSSPP considers the cost information of sparse representation while calculating the sparse structure of the training set. Then, CSSPP employs the sparsity preserving projection method to achieve the projection transform and keeps the sparse structure in the low-dimensional space. Experimental results on the public AR and FRGC face databases are presented to demonstrate that both of the proposed approaches can achieve high recognition rate and low misclassification loss, which validate the efficacy of the proposed approach.

scholarly journals Laplacian Eigenmaps for Dimensionality Reduction and Data Representation

2003 ◽  
Vol 15 (6) ◽  
pp. 1373-1396 ◽  
Author(s):  
Mikhail Belkin ◽  
Partha Niyogi
Keyword(s):  
Dimensionality Reduction ◽  
Dimensional Space ◽  
Graph Laplacian ◽  
Data Representation ◽  
Beltrami Operator ◽  
High Dimensional ◽  
Nonlinear Dimensionality Reduction ◽  
Complex Data ◽  
Dimensional Manifold ◽  
Natural Connection

One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a low-dimensional manifold embedded in a high-dimensional space. Drawing on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for representing the high-dimensional data. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality-preserving properties and a natural connection to clustering. Some potential applications and illustrative examples are discussed.

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.

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.

scholarly journals Prediction of Disease-related microRNAs through Integrating Attributes of microRNA Nodes and Multiple Kinds of Connecting Edges

Molecules ◽  
2019 ◽  
Vol 24 (17) ◽  
pp. 3099 ◽  
Author(s):  
Xuan ◽  
Li ◽  
Zhang ◽  
Zhang ◽  
Song
Keyword(s):  
State Of The Art ◽  
Dimensional Space ◽  
Nonnegative Matrix ◽  
Superior Performance ◽  
Pancreatic Cancers ◽  
Node Attribute ◽  
Disease Associations ◽  
Node Attributes ◽  
Novel Method ◽  
Low Dimensional

Identifying disease-associated microRNAs (disease miRNAs) contributes to the understanding of disease pathogenesis. Most previous computational biology studies focused on multiple kinds of connecting edges of miRNAs and diseases, including miRNA–miRNA similarities, disease–disease similarities, and miRNA–disease associations. Few methods exploited the node attribute information related to miRNA family and cluster. The previous methods do not completely consider the sparsity of node attributes. Additionally, it is challenging to deeply integrate the node attributes of miRNAs and the similarities and associations related to miRNAs and diseases. In the present study, we propose a novel method, known as MDAPred, based on nonnegative matrix factorization to predict candidate disease miRNAs. MDAPred integrates the node attributes of miRNAs and the related similarities and associations of miRNAs and diseases. Since a miRNA is typically subordinate to a family or a cluster, the node attributes of miRNAs are sparse. Similarly, the data for miRNA and disease similarities are sparse. Projecting the miRNA and disease similarities and miRNA node attributes into a common low-dimensional space contributes to estimating miRNA-disease associations. Simultaneously, the possibility that a miRNA is associated with a disease depends on the miRNA’s neighbour information. Therefore, MDAPred deeply integrates projections of multiple kinds of connecting edges, projections of miRNAs node attributes, and neighbour information of miRNAs. The cross-validation results showed that MDAPred achieved superior performance compared to other state-of-the-art methods for predicting disease-miRNA associations. MDAPred can also retrieve more actual miRNA-disease associations at the top of prediction results, which is very important for biologists. Additionally, case studies of breast, lung, and pancreatic cancers further confirmed the ability of MDAPred to discover potential miRNA–disease associations.

A nonlinear method for monitoring industrial process

2020 ◽  
pp. 014233122095923
Author(s):  
Yuan Li ◽  
Chengcheng Feng
Keyword(s):  
Fault Detection ◽  
Objective Function ◽  
Dimensional Space ◽  
Detection Methods ◽  
High Dimensional ◽  
Locally Linear Embedding ◽  
Industrial Case Study ◽  
Laplacian Eigenmaps ◽  
Linear Embedding ◽  
Locally Linear

Aiming at fault detection in industrial processes with nonlinear or high dimensions, a novel method based on locally linear embedding preserve neighborhood for fault detection is proposed in this paper. Locally linear embedding preserve neighborhood is a feature-mapping method that combines Locally linear embedding and Laplacian eigenmaps algorithms. First, two weight matrices are obtained by the Locally linear embedding and Laplacian eigenmaps, respectively. Subsequently, the two weight matrices are combined by a balance factor to obtain the objective function. Locally linear embedding preserve neighborhood method can effectively maintain the characteristics of data in high-dimensional space. The purpose of dimension reduction is to map the high-dimensional data to low-dimensional space by optimizing the objective function. Process monitoring is performed by constructing T2 and Q statistics. To demonstrate its effectiveness and superiority, the proposed locally linear embedding preserve neighborhood for fault detection method is tested under the Swiss Roll dataset and an industrial case study. Compared with traditional fault detection methods, the proposed method in this paper effectively improves the detection rate and reduces the false alarm rate.

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.

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