Fractal dimension calculating method based on density peak clustering

A fractal dimension and density peak technology, applied in the field of signal processing, to achieve the effect of easy implementation, effective and accurate weather prediction, and accurate calculation results

Inactive Publication Date: 2018-11-30
CHONGQING NORMAL UNIVERSITY
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Problems solved by technology

[0004] In view of this, the object of the present invention is to provide a method for calculating the correlation dimension based on density peak clustering, which is used to solve the problem of calculating the fractal dimension in the actual chaotic system, and adopts th...

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  • Fractal dimension calculating method based on density peak clustering
  • Fractal dimension calculating method based on density peak clustering
  • Fractal dimension calculating method based on density peak clustering

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Embodiment Construction

[0035] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0036] Henon is a classic chaotic system. The chaotic time series generated by it is often used to verify the validity of some encryption algorithms or chaotic characteristic indices. Its equation can be written as:

[0037]

[0038] The advantages of the present invention are illustrated below with specific implementation examples. The details are as follows: figure 1 Shown:

[0039] Step 1: For the Henon equation, the initial value is [00], the number of iterations is 18,000, and the previous transient point is removed to obtain time series data {x(i),i=1,2,...,10000}.

[0040] Step 2: If figure 2 As shown, the GP algorithm optimized by the k-d tree is used to preprocess the sampled time series data to obtain the logarithmic set of associated integrals, which are specifically divided into the following five steps:

[0041] Step 20...

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Abstract

The invention relates to a fractal dimension calculating method based on a density peak clustering algorithm, and belongs to the field of signal processing. The fractal dimension calculating method comprises the following steps that S1, one-dimensional chaotic time series signals are obtained from practical engineering; S2, sampled time series data are subjected to pre-treatment to obtain an associative integral logarithmic set by using a k-d tree optimized GP algorithm; S3, second order difference is applied to obtained data, and zero fluctuation data are extracted by using the density peak clustering algorithm; S4, the interval of continuous natural numbers in the zero fluctuation data is selected to conduct statistical analysis, and effective zero fluctuation data are maintained; and S5, the reserved data are fitted by using the least square method, and the correlation dimension is calculated. A scale-free interval can be automatically recognized objectively and accurately, calculation results are more precise, the procedure is simple, achievement is easy, and great significance to nonlinear application is achieved.

Description

technical field [0001] The invention belongs to the field of signal processing and relates to a method for calculating fractal dimension based on density peak clustering. Background technique [0002] Fractal dimension is an important index to quantitatively describe the degree of irregularity of nonlinear dynamics, referred to as fractal dimension. At present, the common fractal dimensions mainly include: box dimension, information dimension, Hausdorff dimension, Lyapunov dimension, correlation dimension, etc. Among them, the correlation dimension is relatively simple and easy to implement, and has been widely used in astrophysics, fault diagnosis, signal processing, hydrological prediction, etc. [0003] In the process of calculating the correlation dimension, it is necessary to artificially select a scale-free interval to calculate the correlation dimension, and the scale-free interval is an important guarantee for accurately calculating the fractal dimension, but subjec...

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Application Information

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IPC IPC(8): G06K9/62
CPCG06F18/2321
Inventor 周双吴至友杨志春赵克全
Owner CHONGQING NORMAL UNIVERSITY
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