To offer an appropriate recommendation to customers in recommender systems, the issue of clustering and separating users with different tastes from the rest of people is of significant importance. The MkMeans + + algorithm is a technique for clustering and separating users in collaborative filtering systems. This algorithm utilizes a specific procedure for selecting the initial centroids of the clusters and has a better function compared with its similar algorithms such as kMeans + + . In this paper, MkMeans + + algorithm is combined with Firefly, Cuckoo, and Krill algorithms and new algorithms called FireflyMkMeans + + , CuckooMkMeans + + , and KrillMkMeans + + are introduced in order to specify the optimal centroid of the cluster, better separate users, and avoid local optimals. In the proposed hybrid clustering approach, the initial population of firefly, cuckoo, and krill algorithms is initialized through the solutions generated by MkMeans + + algorithm, and it makes use of the benefits of MkMeans + + as well as firefly, cuckoo, and krill algorithms. Results and implementations on both MovieLens and FilmTrust datasets indicate that the proposed algorithms can perform better than their similar algorithms in clustering and separating users with different tastes (graysheep users), and enhance the quality of clusters and the accuracy of recommendations for users with similar tastes (white users).

为了向推荐者系统中的客户提供适当的推荐，将具有不同品味的用户与其他人进行聚类和分离的问题非常重要。所述MkMeans  + +算法是用于聚类和在分离的用户的技术协同过滤系统。该算法利用特定的过程选择聚类的初始质心，并且与类似的算法（例如kMeans  ++）相比，具有更好的功能。本文将MkMeans  ++算法与Firefly，Cuckoo和Krill算法以及称为FireflyMkMeans  ++的新算法结合在一起，CuckooMkMeans  + +  ，和KrillMkMeans  + +是为了指定集群，更好的区分用户的最佳重心，并避免局部最优化中介绍。在提出的混合聚类方法中，通过MkMeans  ++算法生成的解决方案初始化了萤火虫，布谷鸟和磷虾算法的初始种群，并利用了MkMeans  ++以及萤火虫，杜鹃和磷虾的优势算法。MovieLens和FilmTrust的结果和实现数据集表明，在聚类和分离具有不同品味的用户（灰羊用户）方面，所提出的算法比同类算法具有更好的性能，并提高了聚类的质量和针对具有相似品味的用户（白人用户）的推荐准确性。