An Improvement of PAA on Trend-Based Approximation for Time Series

Abstract

Piecewise Aggregate Approximation (PAA) is a competitive basic dimension reduction method for high-dimensional time series mining. When deployed, however, the limitations are obvious that some important information will be missed, especially the trend. In this paper, we propose two new approaches for time series that utilize approximate trend feature information. Our first method is based on relative mean value of each segment to record the trend, which divide each segment into two parts and use the numerical average respectively to represent the trend. We proved that this method satisfies lower bound which guarantee no false dismissals. Our second method uses a binary string to record the trend which is also relative to mean in each segment. Our methods are applied on similarity measurement in classification and anomaly detection, the experimental results show the improvement of accuracy and effectiveness by extracting the trend feature suitably.

Anomaly Detection Algorithm for Urban Infrastructure Construction Equipment based on Multidimensional Time Series

“…Formula (6) shows the Euclidean distance between two single-dimensional vectors. a ,a (6) Due to the symmetry of the Euclidean distance, the calculations were not repeated during traversal. Formula (7) shows the distance value of t A .…”

“…At present, time-series anomaly detection methods predominate single-dimensional problems [6]. Multidimensional problems are often transformed into single-dimensional problems through dimension reduction (such as by principal component analysis (PCA) [7], kernel PCA (KPCA) [8], and locally linear embedding (LLE) [9]) or independent analysis of each dimension [10].…”