﻿ 基于变值测量对三项式组合系数的多维可视化探索 Multidimensional Visualization Exploration of Trinomial Combination Coef-ficient Based on Variant Measurement

Statistics and Application
Vol. 08  No. 04 ( 2019 ), Article ID: 31883 , 7 pages
10.12677/SA.2019.84080

Multidimensional Visualization Exploration of Trinomial Combination Coefficient Based on Variant Measurement

Feng Deng, Zhijie Zheng

Yunnan University, Kunming Yunnan

Received: Aug. 6th, 2019; accepted: Aug. 16th, 2019; published: Aug. 26th, 2019

ABSTRACT

The binomial and trinomial combination counting calculation mode plays a core role in data description and data analysis of probability statistics, artificial intelligence, and big data. In this paper, the variable measurement is used to calculate and project the multi-dimensional distribution of the trinomial combination counting coefficient. Based on the binomial combination equation and the quaternary variable metric, the binomial combination coefficients are decomposed and transformed to form a trinomial combination coefficient equation, and the two-dimensional quantization counting matrix is obtained by the combination number calculation method. The relevant numerical calculation results are converted into statistical two-dimensional histograms and displayed in a two-dimensional color map. In this paper, the results of spatial symmetry and distribution diversity of the trinomial coefficients are exhibited by using multiple graphical results. From the variation and invariant characteristics of the trinomial combination coefficient distribution, the clustering distribution characteristics of various combined transformations are systematically explored.

Keywords:Variable Measurement, Combination Number, Visualization, Trinomial Coefficient

1. 引言

2. 基本理论

2.1. 二项式系数

$\left(\begin{array}{c}n\\ i\end{array}\right)=\frac{n!}{i!\left(n-i\right)!}$ (1)

2.2. 范德蒙德综合式

(范德蒙德综合式)对所有整数n，有

${\sum }_{k}\left(\begin{array}{c}r\\ k\end{array}\right)\left(\begin{array}{c}s\\ n-k\end{array}\right)=\left(\begin{array}{c}r+s\\ n\end{array}\right)$ (2)

2.3. 基本测量公式

$\left(\begin{array}{c}m\\ p\end{array}\right)={\sum }_{p}\left(\begin{array}{c}m-2q\\ p-k\end{array}\right)\left(\begin{array}{c}2q\\ k\end{array}\right)$ (3)

3. 计算模型

Figure 1. Curve: Trinomial coefficient solution processing model

4. 结果展示

4.1. 计数矩阵

· 当m = 10，m = 11，q = 0时有：

Table 1. Resulting data of trinomial coefficients

*注：表中只显示有数据的列，未显示的数据列，其列值均为0。

· 当m = 10，m = 11，q = 2时有：

Table 2. Resulting data of trinomial coefficients

*注：表中只显示有数据的列，未显示的数据列，其列值均为0。

· 当m = 10，m = 11，q = 4时有：

Table 3. Resulting data of trinomial coefficients

*注：表中只显示有数据的列，未显示的数据列，其列值均为0。

4.2. 图示

4.2.1. m = 10, q值变换

Figure 2. Curve: q value conversion result icon

4.2.2. m = 11, q值变换

Figure 3. Curve: q value conversion result icon

5. 结果分析

6. 总结

Multidimensional Visualization Exploration of Trinomial Combination Coef-ficient Based on Variant Measurement[J]. 统计学与应用, 2019, 08(04): 704-710. https://doi.org/10.12677/SA.2019.84080

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