# A Novel Hybrid High-Dimensional PSO Clustering Algorithm Based on the Cloud Model and Entropy
## 2 Multi-Dimensional Cloud Model  
The cloud model is a kind of uncertainty artificial intelligence theory and method from qualitative to quantitative transformation. At the same time, the cloud model has the characteristics of the fuzzy theory and membership function. Moreover, the cloud model can completely unify the fuzziness and uncertainty of things' cognitive concepts into qualitative and quantitative processing and apply them to data mining, intelligent control, and other fields. In practical applications, we consider that events obey or nearly obey the normal distribution, so we usually use the normal cloud model to analyze problems. Furthermore, we will use \(Ex\) to express the expectation of the cloud model because the expectation best represents the average degree and level of all sample points in the cloud model. In addition, we will use \(En\) to describe the entropy of the cloud model because the measurement of \(En\) is determined by the randomness and fuzziness of the sample points of the cloud model, which can describe the dispersion of cloud droplets in the cloud model. Subsequently, we will use \(He\) to represent the super entropy of the cloud model, which can measure the uncertainty measure of the cloud model. The larger \(He\) is, the greater the cloud droplet dispersion of the sample point and the larger the range of cloud droplet membership of the cloud model, thus the thicker the sample cloud generated. At the same time, we can find that the application of specific cloud models can be realized through cloud reasoning, cloud computing, cloud clustering, and other methods. Subsequently, the cloud models are transformed from abstract to specific by the cloud digital feature generation cloud droplet process. Through the above analysis, the specific relationship can be defined as follows. \[\mu(x)=e^{\frac{(x-Ex)^{2}}{2 Ex^{2}}} \tag{1}\]In the normal cloud model, cloud droplet groups have different contributions to qualitative concepts. In this paper, we use multi-dimensional normal clouds to illustrate the contribution of cloud droplet groups to the concept. It can be concluded that the contribution of all elements of the normal cloud model to the qualitative concept is determined as follows. \[\Delta C\approx\mu_{A}(x)*\Delta x/(\sqrt{2\pi}En) \tag{2}\]  
Through the above analysis of the normal cloud model, it can be concluded that the total contribution of all elements of the normal cloud model to the qualitative concept is expressed as follows. \[C=\frac{\int\limits_{-\infty}^{+\infty}\mu_{A}(x)dx}{\sqrt{2\pi}En}=\frac{ \int\limits_{-\infty}^{+\infty}e^{-(x-Ex)^{2}/(2 Ex^{2})}dx}{\sqrt{2\pi}En}=1 \tag{3}\]  
The total contribution of all elements in the universe \(Ex-3 En,Ex+3 En\) to the concept can be expressed as follows. \[C_{Ex\pm 3 En}=\frac{1}{\sqrt{2\pi}En}\int_{Ex-3 En}^{Ex+3 En}\mu_{A}(x)dx=99.74\% \tag{4}\]  
The sample cloud drops of cloud model in the interval \([Ex-2 En,Ex+2 En]\) and \([Ex-3 En,Ex+3 En]\) account for about 33.34%. At the same time, the contribution of cloud model sample points to qualitative concepts is about 4.40%. Through the above analysis of the cloud model, the contribution of cloud droplet groups in different cloud model sample areas to qualitative concepts can be described in Figure 1 as follows. The cloud model is actually a model that transforms qualitative concepts and quantitative data into each other. Positive cloud realizes the transformation from qualitative concept to quantitative data. Through the above analysis, the probability density function expected by the cloud model can be expressed as follows. \[f_{En^{\prime}}(x)=\frac{1}{\sqrt{2\pi}He}e^{\frac{(x-Ex)^{2}}{2 Et^{2}}} \tag{5}\]  
The probability density function of the variable can be determined as follows. \[f_{x}(x\big{|}En^{\prime})=\frac{1}{\sqrt{2\pi}En^{\prime}}e^{\frac{(x-Ex)^{2 }}{2 Et^{\prime 2}}} \tag{6}\]  
Figure 1: The qualitative concept map of the cloud model. where the expectation of variables is \(Ex\) and the normal distribution of variance is \(En^{\prime}\).