A Weighted Error Distance Metrics (WEDM) for Performance Evaluation on Multiple Change-Point (MCP) Detection in Synthetic Time Series

Abstract

Change-point detection (CPD) is to find abrupt changes in time-series data. Various computational algorithms have been developed for CPD applications. To compare the different CPD models, many performance metrics have been introduced to evaluate the algorithms. Each of the previous evaluation methods measures the different aspects of the methods. Based on the existing weighted error distance (WED) method on single change-point (CP) detection, a novel WED metrics (WEDM) was proposed to evaluate the overall performance of a CPD model across not only repetitive tests on single CP detection, but also successive tests on multiple change-point (MCP) detection on synthetic time series under the random slide window (RSW) and fixed slide window (FSW) frameworks. In the proposed WEDM method, a concept of normalized error distance was introduced that allows comparisons of the distance between the estimated change-point (eCP) position and the target change point (tCP) in the synthetic time series. In the successive MCPs detection, the proposed WEDM method first divides the original time-series sample into a series of data segments in terms of the assigned tCPs set and then calculates a normalized error distance (NED) value for each segment. Next, our WEDM presents the frequency and WED distribution of the resultant eCPs from all data segments in the normalized positive-error distance (NPED) and the normalized negative-error distance (NNED) intervals in the same coordinates. Last, the mean WED (MWED) and MWTD (1-MWED) were obtained and then dealt with as important performance evaluation indexes. Based on the synthetic datasets in the Matlab platform, repetitive tests on single CP detection were executed by using different CPD models, including ternary search tree (TST), binary search tree (BST), Kolmogorov–Smirnov (KS) tests, t-tests (T), and singular spectrum analysis (SSA) algorithms. Meanwhile, successive tests on MCPs detection were implemented under the fixed slide window (FSW) and random slide window (RSW) frameworks. These CPD models mentioned above were evaluated in terms of our WED metrics, together with supplementary indexes for evaluating the convergence of different CPD models, including rates of hit, miss, error, and computing time, respectively. The experimental results showed the value of this WEDM method.