Optimization is used to find the maximum or minimum of a function. In this research, optimization is applied to the objective function of the FCM algorithm. FCM is an effective algorithm for grouping data, but it is often trapped in local optimum solutions. Therefore, the similarity measure in the clustering process using FCM is very important. This study uses a new method, which combines the Minkowski distance with the Chebyshev distance which is used as a measure of similarity in the clustering process on FCM. The amount of data that is quite large and complex becomes one of the difficulties in providing analysis of multivariate data. To overcome this, one of the techniques used is dimensional reduction using Principal Component Analysis (PCA). PCA is an algorithm of the dimensional reduction method based on the main components obtained from linear combinations, which can help stabilize cluster analysis measurements. The method used in this research is dimensional reduction using PCA, clustering using FCM with a combination of Minkowski and Chebyshev distances (FCMMC), and clustering evaluation using the Davies Bouldin Index (DBI). The purpose of this research is to minimize the objective function of FCM using new distances, namely, the combination of Minkowski and Chebyshev distances through the assistance of dimensional reduction by PCA. The results showed that the cluster accuracy of the combined application of the PCA and FCMMC algorithms was 1.6468. Besides, the minimum value of the combined objective function of the two methods is also obtained, namely, 0.0373 which is located in the 15th iteration, where this value is the smallest value of the 100 maximum iterations set.

优化用于查找函数的最大值或最小值。在这项研究中，将优化应用于FCM算法的目标函数。FCM是一种有效的数据分组算法，但通常会陷入局部最优解中。因此，在使用FCM的聚类过程中的相似性度量非常重要。这项研究使用了一种新方法，该方法将Minkowski距离与Chebyshev距离相结合，该距离被用作FCM聚类过程中的相似性度量。庞大而复杂的数据量成为提供多变量数据分析的困难之一。为了克服这个问题，使用的一种技术是使用主成分分析（PCA）进行尺寸缩减。PCA是基于线性组合获得的主要成分的降维方法算法，可以帮助稳定聚类分析测量。在这项研究中使用的方法是使用PCA进行尺寸缩减，使用结合了Minkowski和Chebyshev距离（FCMMC）的FCM进行聚类以及使用Davies Bouldin指数（DBI）进行聚类评估。这项研究的目的是通过PCA的降维，使用新的距离（即Minkowski和Chebyshev距离的组合）最小化FCM的目标函数。结果表明，PCA和FCMMC算法联合应用的聚类精度为1.6468。此外，还获得了两种方法的组合目标函数的最小值，即0。