# A Novel Hybrid High-Dimensional PSO Clustering Algorithm Based on the Cloud Model and Entropy
## 2 Multi-Dimensional Cloud Model
From the conditional probability density formula, it can be inferred that the probability density function can be expressed as follows. \[f_{x}(x)=f_{En^{\prime}}(x)\times f_{x}(x\big{|}En^{\prime})=\int\limits_{- \infty}^{+\infty}\frac{1}{2\pi He\big{|}y\big{|}}e^{\frac{(x-Ex)^{2}}{2y^{2}}- \frac{(y-En)^{2}}{2 He^{2}}}dy \tag{7}\]  
For any variable, the corresponding function value can be obtained through numerical integration. When the number of cloud drops is cloud drops, the time parzen method can be used to estimate the probability density function. Consequently, the probability density function of the cloud model at that time \(He=0\) can be expressed as follows. \[f(x)=\frac{1}{\sqrt{2\pi En}}e^{\frac{(x-Ex)^{2}}{2 Et^{2}}} \tag{8}\]  
Because all cloud droplets come from the expectation that they are normal random variables, the expectation and variance have the conclusions \(EX=Ex\) and \(DX=En^{2}+He^{2}\). It is widely known that the traditional algorithms are easy to fall into local optimum and the convergence speed is slow. In order to overcome these shortcomings, a particle swarm optimization algorithm based on the cloud model is proposed. Simultaneously, we can assume that the two-dimensional cloud is represented by \(C_{i1}=(Ex_{i1},En_{i1},He_{i1})\) and \(C_{i2}=(Ex_{i2},En_{i2},He_{i2})\). Through the above analysis, the shape similarity calculation based on normal two-dimensional cloud is shown as follows. \[Sim_{si}(C_{i1},C_{i2})=\frac{\min\Bigl{(}\sqrt{En_{i1}^{2}+He_{i1}^{2}},\sqrt{ En_{i2}^{2}+He_{i2}^{2}}\Bigr{)}}{\max\Bigl{(}\sqrt{En_{i1}^{2}+He_{i1}^{2}}, \sqrt{En_{i2}^{2}+He_{i2}^{2}}\Bigr{)}} \tag{9}\]  
Through the above analysis, the distance similarity based on the normal cloud model can be calculated as follows. \[\Delta C\approx\mu_{A}(x)*\Delta x/(\sqrt{2\pi}En) \tag{2}\]0  
Therefore, the comprehensive similarity calculation of two-dimensional cloud model can be expressed as follows. \[\Delta C\approx\mu_{A}(x)*\Delta x/(\sqrt{2\pi}En) \tag{2}\]1  
Multi-dimensional data refers to a data set composed of a large number of samples with multi-dimensional attributes. Concurrently, the multi-dimensional cloud model is a cloud model generated according to various characteristics of data to establish an integrated cloud. Furthermore, the system can be evaluated by calculating the similarity between the multi-dimensional cloud model composed of new data and the integrated cloud. As a result, the multi-dimensional cloud model can effectively solve the problem of low clustering accuracy caused by the fuzziness and uncertainty of multi-sample, multi-dimensional data. In the meantime, the simulation results of the multi-dimensional cloud model can be represented in Figure 2 as follows. Due to the uncertainty and multidimensional attributes of complex data, it is difficult to obtain high clustering accuracy by directly using existing machine learning algorithms and statistical analysis methods. At the same time, it can be found, through experiments, that this clustering should have computational efficiency and be completed in the shortest time. In order to solve the two problems of similarity and attribute reduction, we propose a high-dimensional, multi-objective particle swarm optimization hybrid clustering algorithm based on the cloud model and entropy. HybridHigh-Dimensional, Multi-Objective PSO Clustering Algorithm Based on the Cloud Model and Entropy  
Clustering is a critical technology and method in data mining, machine learning, pattern recognition, and artificial intelligence. Through a clustering algorithm, we can find the global distribution pattern and the relationship between data attributes. In particular, the clustering algorithm has the ability of scalability, processing different types of data, and processing high-dimensional data. Therefore, the emergence of large-scale unbalanced data sets poses special challenges to clustering analysis technology.