Local eigendimension estimation method based on Gaussian mixture function compression transformation

Abstract

The invention designs a method for estimating manifold local eigendimension at any sample point position according to sample data, and the method mainly comprises the following steps: at a measured point, superposing Gaussian functions of adjacent points of each sample, and then applying a special compression transformation to obtain a manifold local eigendimension; and then eigendecomposition of the second-order partial derivative matrix and the real symmetric matrix of the sample features is calculated, so the eigenvalue corresponding to the dimension above the manifold is close to 0, and the eigenvalue corresponding to the dimension outside the manifold is close to 1, and therefore, a reliable basis can be provided for extracting the local eigendimension and the dimension base vector of the manifold. According to the method, the distance and direction information between the measured points and the sample adjacent points is fully utilized in the calculation process, the method does not depend on the predefinition of the observation scale, the obtained eigenvalues continuously change between the continuous measured points and can be used for detecting the boundary, and the estimated value of the eigendimension is more accurate and is not sensitive to measurement errors and sampling density.

Description

technical field [0001] The invention relates to G06F electrical digital data processing, specifically a data processing method using differential and matrix calculation. Background technique [0002] Many tasks in the field of data processing require estimating the local intrinsic dimension (Local Intrinsic Dimensionality, referred to as intrinsic dimension) of the manifold based on the sampled data in the high-dimensional sample space. The local eigendimension of the manifold generally refers to the dimension of the local subspace spanned by the sample neighbor points of a measured point on the manifold. Among them, the sample neighbor point refers to: for a measured point (not necessarily a sample point), all the sample points within a certain observation scale near the point are called the sample neighbor points of the point. [0003] The eigendimension estimation methods in the prior art are as follows: [0004] 1. The method based on the simplex volume: construct a si...

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Problems solved by technology

The disadvantages of this method are: ① the process of constructing the simplex is relatively complicated; ② the structure of the simplex is easily affected by measurement errors; ③ only the eigendimension can be estimated, and the basis vectors of each dimension cannot be estimated;

The disadvantages of this method are: ①It is very sensitive to uneven sampling density; ②It can only estimate the intrinsic dimension, but cannot estimate the basis vector of each dimension;

The disadvantages of this method are: ① It is necessary to assume that the local subspace is a linear space; ② it is sensitive to the coordinates of the neighboring points of the samples farther away;

The disadvantage of this method is that the distance information between the measured point and the sample neighbor is completely ignored. If the distance between the measured point and the sample neighbor is very close, it is prone to ill-conditioned problems.

[0008] In addition, the common disadvantages of the above methods are: ① The number of sample neighbor points of the measured point is a step-like integer, which is easy to cause a jump in the intrinsic dimension; ② The measurement of the sample neighbor points near the boundary of the observation scale range Errors are likely to have a greater impact on the results

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