Visualization can largely improve biomedical data analysis. It plays a crucial role in explorative data analysis and may support various data mining tasks. The paper presents FreeViz, an optimization method that finds linear projection and associated scatterplot that best separates instances of different class. In a single graph, the resulting FreeViz visualization can provide a global view of the classification problem being studied, reveal interesting relations between classes and features, uncover feature interactions, and provide information about intra-class similarities. The paper gives mathematical foundations of FreeViz, and presents its utility on various biomedical data sets.