A Genetic Algorithm Based Piecewise Linear Representation of Time Series

Abstract

Line Segment Representation (LSR) refers to represents a time series by a few of line segments, such that the original time series and the piecewise line segment series have shapes as similar as possible. Because of its simple expression, LSR based time series are often easier to be understood and computed for some time series datamining tasks than the original raw data. Two kinds of continuous LSR methods, namely, 11 trend filtering and mix-integer programming (MILP) method, are discussed in this paper. To overcome the poor representation ability of l1 trend filtering, and the high computational complexity of MILP, this paper proposes a hybrid method combining GA and linear programming (GA-LP) to find the optimal LSR time series efficiently. In GA-LP, locations of the breakpoints of the piecewise linear segment are fixed by GA, and values on these locations are fixed by a LP method. Numerical experiments reveal that GA-LP can reduce representation error by comparisons with l1 trend filtering and MILP method, and its computing time is much less than that of MILP.