Research on Dimensionality Reduction Based on Neighborhood Preserving Embedding and Sparse Representation

2011 ◽  
Vol 58-60 ◽  
pp. 547-550
Author(s):  
Di Wu ◽  
Zhao Zheng
Keyword(s):  
Dimensionality Reduction ◽  
Linear Subspace ◽  
Rapid Development ◽  
Linear Method ◽  
High Dimensional ◽  
Data Sets ◽  
Artificial Data ◽  
Nonlinear Method ◽  
Nonlinear Methods ◽  
Data Dimensionality Reduction

In real world, high-dimensional data are everywhere, but the nature structure behind them is always featured by only a few parameters. With the rapid development of computer vision, more and more data dimensionality reduction problems are involved, this leads to the rapid development of dimensionality reduction algorithms. Linear method such as LPP [1], NPE [2], nonlinear method such as LLE [3] and improvement version kernel NPE. One particularly simple but effective assumption in face recognition is that the samples from the same class lie on a linear subspace, so lots of nonlinear methods only perform well on some artificial data sets. This paper emphasizes on NPE and SPP [4] come up with recently, and combines these methods, the experiments show the effect of new method outperform some classic unsupervised methods.

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.

Multi-Instance Dimensionality Reduction via Sparsity and Orthogonality

2018 ◽  
Vol 30 (12) ◽  
pp. 3281-3308
Author(s):  
Hong Zhu ◽  
Li-Zhi Liao ◽  
Michael K. Ng
Keyword(s):  
Dimensionality Reduction ◽  
Optimization Problem ◽  
Augmented Lagrangian ◽  
Main Idea ◽  
Real Data ◽  
Learning Performance ◽  
High Dimensional ◽  
Data Sets ◽  
Outer Loop ◽  
Orthogonality Constraints

We study a multi-instance (MI) learning dimensionality-reduction algorithm through sparsity and orthogonality, which is especially useful for high-dimensional MI data sets. We develop a novel algorithm to handle both sparsity and orthogonality constraints that existing methods do not handle well simultaneously. Our main idea is to formulate an optimization problem where the sparse term appears in the objective function and the orthogonality term is formed as a constraint. The resulting optimization problem can be solved by using approximate augmented Lagrangian iterations as the outer loop and inertial proximal alternating linearized minimization (iPALM) iterations as the inner loop. The main advantage of this method is that both sparsity and orthogonality can be satisfied in the proposed algorithm. We show the global convergence of the proposed iterative algorithm. We also demonstrate that the proposed algorithm can achieve high sparsity and orthogonality requirements, which are very important for dimensionality reduction. Experimental results on both synthetic and real data sets show that the proposed algorithm can obtain learning performance comparable to that of other tested MI learning algorithms.

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 DATA DIMENSIONALITY REDUCTION FOR NEURAL BASED CLASSIFICATION OF OPTICAL SURFACES DEFECTS

2014 ◽  
pp. 32-42
Author(s):  
Matthieu Voiry ◽  
Kurosh Madani ◽  
Véronique Véronique Amarger ◽  
Joël Bernier
Keyword(s):  
Dimensionality Reduction ◽  
Harmful Effect ◽  
Optical Devices ◽  
High Dimensional ◽  
Major Step ◽  
Optical Surfaces ◽  
Data Dimensionality Reduction ◽  
Classification Tasks ◽  
Faults Diagnosis

A major step for high-quality optical surfaces faults diagnosis concerns scratches and digs defects characterization in products. This challenging operation is very important since it is directly linked with the produced optical component’s quality. A classification phase is mandatory to complete optical devices diagnosis since a number of correctable defects are usually present beside the potential “abiding” ones. Unfortunately relevant data extracted from raw image during defects detection phase are high dimensional. This can have harmful effect on the behaviors of artificial neural networks which are suitable to perform such a challenging classification. Reducing data dimension to a smaller value can decrease the problems related to high dimensionality. In this paper we compare different techniques which permit dimensionality reduction and evaluate their impact on classification tasks performances.

Using Self-Similarity to Incorporate Dimensionality Reduction and Cluster Evolution Tracking

2013 ◽  
Vol 336-338 ◽  
pp. 2242-2247
Author(s):  
Guang Hui Yan ◽  
Yong Chen ◽  
Hong Yun Zhao ◽  
Ya Jin Ren ◽  
Zhi Cheng Ma
Keyword(s):  
Dimensionality Reduction ◽  
Synthetic Data ◽  
Fractal Dimensionality ◽  
High Dimensional ◽  
Data Sets ◽  
Stream Data ◽  
Self Similarity ◽  
Cluster Evolution ◽  
Dimensionality Reduction Technique ◽  
On Line

Cluster evolution tracking and dimensionality reduction have been studied intensively but separately in the time decayed and high dimensional stream data environment during the past decades. However, the interaction between the cluster evolution and the dimensionality reduction is the most common scenario in the time decayed stream data. Therefore, the dimensionality reduction should interact with cluster operation in the endless life cycle of stream data. In this paper, we first investigate the interaction between dimensionality reduction and cluster evolution in the high dimensional time decayed stream data. Then, we integrate the on-line sequential forward fractal dimensionality reduction technique with self-adaptive technique for cluster evolution tracking based on multi-fractal. Our performance experiments over a number of real and synthetic data sets illustrate the effectiveness and efficiency provided by our approach.

scholarly journals A SURVEY ON THE CURES FOR THE CURSE OF DIMENSIONALITY IN BIG DATA

2017 ◽  
Vol 10 (13) ◽  
pp. 355 ◽  
Author(s):  
Reshma Remesh ◽  
Pattabiraman. V
Keyword(s):  
Dimensionality Reduction ◽  
Input Data ◽  
Principal Component ◽  
Kernel Principal Component Analysis ◽  
High Dimensional ◽  
Data Sets ◽  
Learning Approaches ◽  
Data Set ◽  
Reduction Techniques ◽  
Dimensionality Reduction Techniques

Dimensionality reduction techniques are used to reduce the complexity for analysis of high dimensional data sets. The raw input data set may have large dimensions and it might consume time and lead to wrong predictions if unnecessary data attributes are been considered for analysis. So using dimensionality reduction techniques one can reduce the dimensions of input data towards accurate prediction with less cost. In this paper the different machine learning approaches used for dimensionality reductions such as PCA, SVD, LDA, Kernel Principal Component Analysis and Artificial Neural Network  have been studied.

LTSA Algorithm for Dimension Reduction of Microarray Data

2013 ◽  
Vol 645 ◽  
pp. 192-195 ◽  
Author(s):  
Xiao Zhou Chen
Keyword(s):  
Dimensionality Reduction ◽  
Dimension Reduction ◽  
Manifold Learning ◽  
Microarray Data ◽  
Learning Algorithm ◽  
Medical Applications ◽  
Data Sets ◽  
Learning Method ◽  
Data Dimensionality Reduction ◽  
Low Dimensional

Dimension reduction is an important issue to understand microarray data. In this study, we proposed a efficient approach for dimensionality reduction of microarray data. Our method allows to apply the manifold learning algorithm to analyses dimensionality reduction of microarray data. The intra-/inter-category distances were used as the criteria to quantitatively evaluate the effects of data dimensionality reduction. Colon cancer and leukaemia gene expression datasets are selected for our investigation. When the neighborhood parameter was effectivly set, all the intrinsic dimension numbers of data sets were low. Therefore, manifold learning is used to study microarray data in the low-dimensional projection space. Our results indicate that Manifold learning method possesses better effects than the linear methods in analysis of microarray data, which is suitable for clinical diagnosis and other medical applications.

scholarly journals Comparison of Approaches to Quantify Arterial Damping Capacity From Pressurization Tests on Mouse Conduit Arteries

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Lian Tian ◽  
Zhijie Wang ◽  
Roderic S. Lakes ◽  
Naomi C. Chesler
Keyword(s):  
Linear Method ◽  
Hysteresis Loops ◽  
Dissipated Energy ◽  
Damping Capacity ◽  
Outer Diameter ◽  
Cauchy Stress ◽  
Nonlinear Method ◽  
Stress Strain ◽  
Nonlinear Methods ◽  
Physiological Pressure

Large conduit arteries are not purely elastic, but viscoelastic, which affects not only the mechanical behavior but also the ventricular afterload. Different hysteresis loops such as pressure-diameter, pressure-luminal cross-sectional area (LCSA), and stress–strain have been used to estimate damping capacity, which is associated with the ratio of the dissipated energy to the stored energy. Typically, linearized methods are used to calculate the damping capacity of arteries despite the fact that arteries are nonlinearly viscoelastic. The differences in the calculated damping capacity between these hysteresis loops and the most common linear and correct nonlinear methods have not been fully examined. The purpose of this study was thus to examine these differences and to determine a preferred approach for arterial damping capacity estimation. Pressurization tests were performed on mouse extralobar pulmonary and carotid arteries in their physiological pressure ranges with pressure (P) and outer diameter (OD) measured. The P-inner diameter (ID), P-stretch, P-Almansi strain, P-Green strain, P-LCSA, and stress–strain loops (including the Cauchy and Piola-Kirchhoff stresses and Almansi and Green strains) were calculated using the P-OD data and arterial geometry. Then, the damping capacity was calculated from these loops with both linear and nonlinear methods. Our results demonstrate that the linear approach provides a reasonable approximation of damping capacity for all of the loops except the Cauchy stress-Almansi strain, for which the estimate of damping capacity was significantly smaller (22 ± 8% with the nonlinear method and 31 ± 10% with the linear method). Between healthy and diseased extralobar pulmonary arteries, both methods detected significant differences. However, the estimate of damping capacity provided by the linear method was significantly smaller (27 ± 11%) than that of the nonlinear method. We conclude that all loops except the Cauchy stress-Almansi strain loop can be used to estimate artery wall damping capacity in the physiological pressure range and the nonlinear method is recommended over the linear method.

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