Piecewise Trend Approximation: A Ratio-Based Time Series Representation

Jingpei Dan,Kaoru Hirota,Weiren Shi,Fangyan Dong

doi:10.1155/2013/603629

Abstract

A time series representation, piecewise trend approximation (PTA), is proposed to improve efficiency of time series data mining in high dimensional large databases. PTA represents time series in concise form while retaining main trends in original time series; the dimensionality of original data is therefore reduced, and the key features are maintained. Different from the representations that based on original data space, PTA transforms original data space into the feature space of ratio between any two consecutive data points in original time series, of which sign and magnitude indicate changing direction and degree of local trend, respectively. Based on the ratio-based feature space, segmentation is performed such that each two conjoint segments have different trends, and then the piecewise segments are approximated by the ratios between the first and last points within the segments. To validate the proposed PTA, it is compared with classical time series representations PAA and APCA on two classical datasets by applying the commonly used K-NN classification algorithm. For ControlChart dataset, PTA outperforms them by 3.55% and 2.33% higher classification accuracy and 8.94% and 7.07% higher for Mixed-BagShapes dataset, respectively. It is indicated that the proposed PTA is effective for high dimensional time series data mining.

Highlights

Time series representation is one of the key issues in time series data mining, since the suitable choice of representation greatly affects the ease and efficiency of time series data mining
This study focuses on the first dimensionality reduction method, and the time series representations based on piecewise discontinuous functions are reviewed as follows
To validate the performance of the proposed piecewise trend approximation (PTA) representation for similarity search in time series data, we design a classification experiment based on two classical datasets ControlChart and Mixed-BagShapes [27] by applying the most common classification algorithm, K-nearest neighbor (K-NN) classification

Summary

Introduction

Time series representation is one of the key issues in time series data mining, since the suitable choice of representation greatly affects the ease and efficiency of time series data mining. Dimensionality reduction methods help to compare time series efficiently by modeling time series into a more compact form, whereas significant information about main trends in a time series, which are essential to effective similarity search, may be lost. To support accurate and fast similarity detection in time series, a number of special requirements that should be satisfied by any representation model are summarized as follows [1]. Time series should be modeled into a form that can be naturally mapped to the time domain. This will make it feasible to benefit from using dynamic time warping (DTW) that can compare time series with local time shifting and different lengths for similarity detection

Methods

Results

Conclusion