We propose a dynamic programming algorithm for the one-dimensional Fused Lasso Signal Approximator (FLSA). The proposed algorithm has a linear running time in the worst case. A similar approach is developed for the task of least squares segmentation, and simulations indicate substantial performance improvement over existing algorithms. Examples of R and C implementations are provided in the online Supplementary materials, posted on the journal web site.
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Nicholas A. Johnson (2013) studied this question.
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