Unlock instant, AI-driven research and patent intelligence for your innovation.

A Quantum Laplace Eigenmapping Method

A feature mapping method, Laplace's technology, applied in instruments, complex mathematical operations, informatics, etc.

Active Publication Date: 2020-04-07
UNIV OF ELECTRONICS SCI & TECH OF CHINA
View PDF4 Cites 0 Cited by
  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

Still, there is no nonlinear quantum version of dimensionality reduction here

Method used

the structure of the environmentally friendly knitted fabric provided by the present invention; figure 2 Flow chart of the yarn wrapping machine for environmentally friendly knitted fabrics and storage devices; image 3 Is the parameter map of the yarn covering machine
View more

Image

Smart Image Click on the blue labels to locate them in the text.
Viewing Examples
Smart Image
  • A Quantum Laplace Eigenmapping Method
  • A Quantum Laplace Eigenmapping Method
  • A Quantum Laplace Eigenmapping Method

Examples

Experimental program
Comparison scheme
Effect test

Embodiment Construction

[0038] Further describe the technical scheme of the present invention in detail below:

[0039] For the classic Laplacian eigenmap algorithm: The Laplacian eigenmap algorithm assumes that data in a high-dimensional space has a corresponding low-dimensional structure. Use the location information of the data to build a graph G, the vertex V is the data, and the edge E is the similarity of data in different fields.

[0040] In order to reduce the dimensionality of the data, we want to minimize the objective function J(u), through the following equation:

[0041]

[0042] Among them, y i is the data point x i The low-dimensional representation of w ij corresponding to x i with x j The weight of , L represents the Laplacian matrix of graph G.

[0043] And for optimizing min(2Y T LY) problem can be transformed into a generalized eigenvalue problem:

[0044] Lv=λDv

[0045] where D is a diagonal matrix, D ii =∑ j W(i,j), W ij corresponds to x i with x j The weight o...

the structure of the environmentally friendly knitted fabric provided by the present invention; figure 2 Flow chart of the yarn wrapping machine for environmentally friendly knitted fabrics and storage devices; image 3 Is the parameter map of the yarn covering machine
Login to View More

PUM

No PUM Login to View More

Abstract

The invention discloses a quantum Laplacian eigenmapping method. Based on the existing Laplacian eigenmapping algorithm, the Laplacian matrix is ​​regarded as the covariance matrix of the data set, and a density can be easily obtained. At the same time, the existing eigenvector problem is converted accordingly, and the calculation is performed in a quantum way. The present invention proposes a quantum version of Laplacian Eigenmaps - QLE (Quantum Laplacian Eigenmaps), which uses conjugate chains and matrix operations to solve nonlinear dimensionality reduction problems. Compared to the polynomial time required by classical Laplacian eigenmaps, the present invention can provide an exponential speedup.

Description

technical field [0001] The invention relates to a quantum Laplace characteristic mapping method. Background technique [0002] Machine learning and data analysis play an increasingly important role in dimensionality reduction, prediction and classification. In many cases the original data is in a high-dimensional feature space, such as an image with n square pixels (each pixel serves as a feature). So in order to analyze these high-dimensional feature data, we need to reduce the dimensionality of the data by considering the natural structure as a low-dimensional manifold embedded in a high-dimensional space. [0003] In order to reduce the dimensionality of high-dimensional data, no matter which method we choose, we need to consider the time required. As we know, a well-designed quantum algorithm can greatly improve our classical algorithms. Lloyd and others proposed a quantum version of PCA, which can exponentially increase the speed of the algorithm. Cong et al general...

Claims

the structure of the environmentally friendly knitted fabric provided by the present invention; figure 2 Flow chart of the yarn wrapping machine for environmentally friendly knitted fabrics and storage devices; image 3 Is the parameter map of the yarn covering machine
Login to View More

Application Information

Patent Timeline
no application Login to View More
Patent Type & Authority Patents(China)
IPC IPC(8): G06F17/10
CPCG16Z99/00
Inventor 李晓瑜黄一鸣雷航郑德生
Owner UNIV OF ELECTRONICS SCI & TECH OF CHINA