A new piecewise linear representation method based on the R-squared statistic

In recent years, different piecewise linear representation (PLR) methods have been proposed to segment time series. This paper proposes a new PLR method based on the R-squared statistic. The main principle is that the R-squared statistic is inversely proportional to the fitting error and directly proportional to the amplitude change of a segment. A rule is formulated that introducing an extra PLR segment is not worthwhile unless the R-squared statistic becomes larger. By comparing the R-squared statistic between newly added segments and original segments, the best PLR segments can be selected in a transparent manner. Simulation and industrial examples illustrate the effectiveness of the proposed method.