Geodesic line preservation-based nonlinear data dimension reduction method

Abstract

The invention discloses a geodesic line preservation-based nonlinear data dimension reduction method. Firstly a random shortest path is obtained for an input sample point set, and a geodesic line set of the sample point set is found. Low-dimensional embedded global coordinates of each geodesic line are obtained by performing rotation transformation on local coordinates of the geodesic line in a high-dimensional manifold, so that centralized low-dimensional embedded global coordinates can be represented by using centralized local coordinates in the high-dimensional manifold. The global coordinates of each geodesic line can be represented by using low-dimensional embedded coordinates of a selection matrix and all sample points, and a square error sum of the low-dimensional embedded global coordinates and the local coordinates subjected to the rotation transformation is minimized according to a square error of an actual value and an estimated value, and a minimum principle, so that the low-dimensional embedded global coordinates of the sample points are obtained.

Description

technical field [0001] The invention belongs to the field of machine learning, and in particular relates to a non-linear data dimension reduction method based on geodesic preservation in manifold learning. Background technique [0002] Data dimensionality reduction refers to the process of mapping samples from a high-dimensional space to a low-dimensional space through a linear or nonlinear method, thereby obtaining a representation of the high-dimensional space in a lower-dimensional space. Through this operation, the redundancy of the original data can be reduced, and the efficiency and pertinence of data processing can be improved. Data dimensionality reduction methods are mainly divided into two categories: linear mapping and nonlinear mapping methods. Among them, the representative methods of the linear mapping method include principal component analysis (Principle Component Analysis, PCA for short) and linear decision analysis (Linear Discriminant Analysis, LDA for sh...

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Problems solved by technology

As a very good popular learning algorithm, LTSA can effectively learn the overall embedding coordinates that reflect the low-dimensional manifold structure of the data set, but it also has shortcomings: the order of the matrix used for eigenvalue decomposition in the algorithm is equal to the number of samples, When the sample set is large, it will not be able to handle

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