Thanks to the recent advances in microarray technology, simultaneously expressing different levels of genes is possible. Although the representation of confidential information in genes simplifies to analyze them; both high number of genes and high amount of noise in the data sets make difficult to identify the gene data. In order to identify genes various clustering methods are generally used. Microarray data is one of the best examples of multidimensional data. In this study, in order to cluster multidimensional data, new methods for selecting initial cluster centers are proposed for the standard K-means and Particle Swarm Optimization (PSO)-based clustering algorithms. Also, coreset approach is adapted for PSO algorithm. The correctness of the developed methods is examined on datasets which are frequently used in the literature, and also these proposed approaches are run on Colon Cancer microarray data set. The performance of the proposed approaches is compared with the standard K-means and PSO-based clustering methods by means of average iteration number, Rand, and Silhouette index metrics. In experimental studies, we observe that proposed methods give superior results on the normalized datasets in which feature selection process is performed.