scholarly journals Commodity Price Recognition and Simulation of Image Recognition Technology Based on the Nonlinear Dimensionality Reduction Method

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yongbin Liu ◽  
Jingjie Wang ◽  
Wei Bai
Keyword(s):  
Dimensionality Reduction ◽  
Image Recognition ◽  
Reduction Method ◽  
Dimensional Space ◽  
Recognition Rate ◽  
Commodity Price ◽  
High Dimensional ◽  
Nonlinear Dimensionality Reduction ◽  
Nonlinear Structure ◽  
Dimensionality Reduction Method

Dimensionality reduction of images with high-dimensional nonlinear structure is the key to improving the recognition rate. Although some traditional algorithms have achieved some results in the process of dimensionality reduction, they also expose their respective defects. In order to achieve the ideal effect of high-dimensional nonlinear image recognition, based on the analysis of the traditional dimensionality reduction algorithm and refining its advantages, an image recognition technology based on the nonlinear dimensionality reduction method is proposed. As an effective nonlinear feature extraction method, the nonlinear dimensionality reduction method can find the nonlinear structure of datasets and maintain the intrinsic structure of data. Applying the nonlinear dimensionality reduction method to image recognition is to divide the input image into blocks, take it as a dataset in high-dimensional space, reduce the dimension of its structure, and obtain the low-dimensional expression vector of its eigenstructure so that the problem of image recognition can be carried out in a lower dimension. Thus, the computational complexity can be reduced, the recognition accuracy can be improved, and it is convenient for further processing such as image recognition and search. The defects of traditional algorithms are solved, and the commodity price recognition and simulation experiments are carried out, which verifies the feasibility of image recognition technology based on the nonlinear dimensionality reduction method in commodity price recognition.

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 A topology-preserving dimensionality reduction method for single-cell RNA-seq data using graph autoencoder

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Zixiang Luo ◽  
Chenyu Xu ◽  
Zhen Zhang ◽  
Wenfei Jin
Keyword(s):  
Dimensionality Reduction ◽  
Single Cell ◽  
Topological Structure ◽  
Reduction Method ◽  
Dimensional Space ◽  
Oriented Graph ◽  
Developmental Trajectory ◽  
Structure Information ◽  
Dimensionality Reduction Method ◽  
Cell Graph

AbstractDimensionality reduction is crucial for the visualization and interpretation of the high-dimensional single-cell RNA sequencing (scRNA-seq) data. However, preserving topological structure among cells to low dimensional space remains a challenge. Here, we present the single-cell graph autoencoder (scGAE), a dimensionality reduction method that preserves topological structure in scRNA-seq data. scGAE builds a cell graph and uses a multitask-oriented graph autoencoder to preserve topological structure information and feature information in scRNA-seq data simultaneously. We further extended scGAE for scRNA-seq data visualization, clustering, and trajectory inference. Analyses of simulated data showed that scGAE accurately reconstructs developmental trajectory and separates discrete cell clusters under different scenarios, outperforming recently developed deep learning methods. Furthermore, implementation of scGAE on empirical data showed scGAE provided novel insights into cell developmental lineages and preserved inter-cluster distances.

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