Nonlinear data dimensionality reduction method based on local nonlinear alignment

Abstract

The invention discloses a nonlinear data dimensionality reduction method based on local nonlinear alignment. The method comprises steps of: first obtaining the neighbor points of each sample point ina high-dimensional space by using a KNN algorithm and forming the corresponding blocks; reducing the data point blocks from the high-dimensional space to a low-dimensional space plane by a PCA algorithm; perfectly splicing the blocks reduced by the PCA in the low-dimensional space by respective translational rotation, wherein a splicing criterion is that each point may be contained in different blocks, then the points contained in all blocks belong to the same point, and the low-dimensional representation of the pints should be coincident in theory; thus, the position of an average point of the points in the blocks can be obtained, the sum of the two norm of the distance from the points that should be represented as the same point in different blocks to its average point should be the lowest, so as to ensure the same point in different blocks are coincident as much as possible. After the translational rotation of all blocks, the sum of the errors produced by respective points is minimum, so that the different blocks can be perfectly spliced in a low-dimensional plane. Therefore, the global coordinates of the sample points embedded in the low-dimensional are solved, and the nonlinear data dimensionality reduction of the local nonlinear alignment is realized.

Description

technical field [0001] The invention belongs to the field of machine learning, and in particular relates to a nonlinear data dimensionality reduction method based on local nonlinear alignment 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 the 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. 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 shor...

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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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