article · International Transactions in Operational Research · 1994
Best L1 piecewise monotonic data modelling
Cited by 15Abstract and details only
Abstract
Abstract Let us consider n data measurements of a univariate process that have been altered by random errors. We assume that an underlying model function has a substantially smaller number of turning points than the observed ones. We propose algorithms that make least the sum of the moduli of the errors by requiring k monotonic sections, altered increasing and decreasing, in the sequence of the smoothed values. The main difficulty in this calculation is that the optimal positions of the joins of the monotonic sections have to be found automatically among so many combinations that it is impossible to test each one separately. Moreover, the calculation seems to be very intractable to general optimization techniques because O ( n k ) local minima can occur. It is shown that dynamic programming can be used for separating the data into optimal disjoint sections of adjacent data, where each section requires a single L 1 monotonic calculation. This procedure is highly efficient, requiring at most O ( k n ) computer operations and O ( n ) bes L 1 monotonic calculations to subranges of data for a global minimum.
Cite this paper
Δημητρίου, Ι. (1994). Best L1 piecewise monotonic data modelling. International Transactions in Operational Research, 1(1), 85–94. https://doi.org/10.1016/0969-6016(94)90048-5
Δημητρίου, Ιωάννης. “Best L1 piecewise monotonic data modelling.” International Transactions in Operational Research, vol. 1, no. 1, 1994, pp. 85–94, https://doi.org/10.1016/0969-6016(94)90048-5.
Δημητρίου, Ιωάννης. 1994. “Best L1 piecewise monotonic data modelling.” International Transactions in Operational Research 1 (1): 85–94. https://doi.org/10.1016/0969-6016(94)90048-5.
Δημητρίου, Ι. (1994) ‘Best L1 piecewise monotonic data modelling’, International Transactions in Operational Research, 1(1), pp. 85–94. Available at: https://doi.org/10.1016/0969-6016(94)90048-5.
@article{anon1994best,
title = {{Best L1 piecewise monotonic data modelling}},
author = {Δημητρίου, Ιωάννης},
journal = {International Transactions in Operational Research},
volume = {1},
number = {1},
pages = {85--94},
year = {1994},
doi = {10.1016/0969-6016(94)90048-5}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.