Interactive visual cluster analysis is the most intuitive way for finding clustering patterns, validating algorithmic clustering results, understanding data clusters with domain knowledge, and refining cluster definitions. The most challenging step is visualizing multidimensional data and allowing user to interactively explore the data to identify clustering structures. In this paper, we systematically study the star-coordinate based visualization models and propose the optimized design that presents the best visualization results and supports the most efficient interaction methods. We explain the intuition behind the models and their link with random projection, and then optimize the visual design in terms of the efficiency of visual presentation and interactive operations. We also discuss the randomized visualization generation method, which can be used to generate batches of meaningful visualization results in parallel for big data. Finally, we present the experimental evaluation for the optimal design of models. This study is critical to generating effective visualization and minimizing the computational cost for visualizing data clusters for big data in the cloud.