Determining the number of segments for piece-wise linear representation of discrete-time signals

Abstract

Abstract Piece-wise linear representation (PLR) separates a discrete-time continuous-valued signal into a few short data segments, each of which is represented by a straight line. One prerequisite parameter in the PLR is the number of data segments. This paper proposes a new method to determine the number of data segments. The method is based on a key observation on two balancing effects of the number of data segments on the confidence intervals of line approximations. The confidence intervals define parallelogram-shaped spaces, and an index is formulated as the weighted percentage of these spaces occupied by data points in data segments. The number of data segments is determined as the one achieving the maximum value of the formulated index. Numerical and industrial examples are provided to illustrate the effectiveness of the proposed method.