An algorithm for optimal partitioning of data on an interval

Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large space of partitions of N data points in time O(N-2). The algorithm is guaranteed to find the exact global optimum, automatically determines the model order (the number of segments), has a convenient realtime mode, can be extended to higher dimensional data spaces, and solves a surprising variety of problems in signal detection and characterization, density estimation, cluster analysis, and classification.