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Quantum Laplacian Eigenmaps method

A feature mapping method, Laplace's technology, applied in special data processing applications, instruments, electrical digital data processing, etc.

Active Publication Date: 2017-07-04
UNIV OF ELECTRONIC SCI & TECH OF CHINA
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

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

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Embodiment Construction

[0038] The technical solution of the present invention is described in further detail below:

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

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

[0041]

[0042] Where y i Is 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] For optimization min(2Y T The problem of LY) 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 of λ represents t...

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Abstract

The invention discloses a Quantum Laplacian Eigenmaps method. Based on an existing Laplacian Eigenmaps algorithm, a Laplacian matrix is deemed as a covariance matrix of a dataset, so a density matrix can be obtained easily; current characteristic vector problems can be converted correspondingly; and computation can be conducted in a quantum manner. The invention discloses a QLE (Quantum Laplacian Eigenmaps) method of a quantum version, wherein a conjugated chain and matrix computation are used to solve nonlinear dimension-reduction problems. In comparison with polynomial time needed by classical Laplacian Eigenmaps, the method disclosed by the invention can provide acceleration of an exponential order.

Description

Technical field [0001] The invention relates to a quantum Laplacian feature mapping method. Background technique [0002] Machine learning and data analysis are playing 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 a picture with n square pixels (each pixel is used as a feature). Therefore, in order to analyze these high-dimensional feature data, we need to treat the natural structure as a low-dimensional manifold embedded in the high-dimensional space data dimensionality reduction. [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 algorithm. Lloyd and others proposed a quantum version of PCA, which can increase the speed of the algorithm exponentially. Cong et al. generalized the ...

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Application Information

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IPC IPC(8): G06F19/00
CPCG16Z99/00
Inventor 李晓瑜黄一鸣雷航郑德生
Owner UNIV OF ELECTRONIC SCI & TECH OF CHINA