Survey: Dimension reduction by pattern decomposition

Pattern processing exists in various fields like image processing and expert systems. Focus has been put on to high dimensional pattern processing, where there is a big concern of the system performance due to the high dimensionality. In the field of fuzzy inference systems, an exponential explosion in the required computational time complexity is caused by the multi variables in the input pattern. The key point of system design is an efficient approach to deal with the high dimensional input patterns. Decomposing high dimensional patterns into low dimensional patterns is an approach to solving this problem. In decomposing, an issue we confront with is: how to achieve global optimality while we are dealing with the components individually. The approach depends on the definition of optimality. Usually two aspects are considered: stability and time complexity. This survey is to summarize the recent research works related to the idea of decomposing high dimensional patterns into low dimensional patterns and approaches to achieve global optimality concerning stability and time complexity.