| 초록 |
There are various real world datasets which can be effectively modeled by piecewise linear functions. The problem of piecewise linear fitting is to simultaneously identify 1) optimal number of break points, 2) optimal locations of break points, and 3) slopes and intercepts of fitted lines. Due to the combinatorial nature of such problem, brute-force-based approach is computationally prohibitive for large size problems. To efficiently solve such problem, there have been several attempts to formulate such problem into an optimization problem. However, a potential disadvantage of this approach is that it still requires much time especially when the number of lines increases. To address such a disadvantage, in this study, we propose a gradient descent with momentum approach for piecewise linear fitting. Specifically, starting from an initial point, the locations of break points are iteratively updated on the basis of local gradients. To calculate local gradients, piecewise linear regression problem is iteratively solved using the current breakpoints and the adjacent ones. We demonstrate the effectiveness of the proposed method through several illustrative examples. |
