Background: Multidimensional scaling (MDS) is a widely used approach to dimensionality reduction. It has been applied to feature selection and visualization in various areas. Among diverse MDS methods, the classical MDS is a simple and theoretically sound solution for projecting data objects onto a low dimensional space while preserving the original distances among them as much as possible. However, it is not trivial to apply it to genome-scale data (e.g., microarray gene expression profiles) on regular desktop computers, because of its high computational complexity.
Results: We implemented a highly-efficient software application, called CFMDS (CUDA-based Fast MultiDimensional Scaling), which produces an approximate solution of the classical MDS based on CUDA (compute unified device architecture) and the divide-and-conquer principle. CUDA is a parallel computing architecture exploiting the power of the GPU (graphics processing unit). The principle of divide-and-conquer was adopted for circumventing the small memory problem of usual graphics cards. Our application software has been tested on various benchmark datasets including microarrays and compared with the classical MDS algorithms implemented using C# and MATLAB. In our experiments, CFMDS was more than a hundred times faster for large data than such general solutions. Regarding the quality of dimensionality reduction, our approximate solutions were as good as those from the general solutions, as the Pearson's correlation coefficients between them were larger than 0.9.
Conclusions: CFMDS is an expeditious solution for the data dimensionality reduction problem. It is especially useful for efficient processing of genome-scale data consisting of several thousands of objects in several minutes.