Piecewise Trend Approximation: A Ratio-Based Time Series Representation

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.

A Survey on Dimensionality Reduction Techniques for Time-Series Data

“…In recent times, multiple dimensionality reduction techniques data have been proposed, however, none of them is effective for time-series data. For instance, (1) Piecewise Trend Approximation which only focuses on the local trend of the data [8], (2) Piecewise Vector Quantized Approximation which performs poorly for non-stationary datasets [9], (3) Piecewise Constant Approximation that estimates every time-series only with constant value segments [10], (4) Piecewise Aggregate Approximation where choosing the number of segments as a parameter is challenging and highly data dependent [11], (5) Sliced Inverse Regression which suffers from the presence of outliers [12], (6) Factor Analysis has become less popular as it is quite similar to Principal Component Analysis (PCA) [13], (7) Independent Component analysis where the order of the independent components is ambiguous [14]. Due to these issues, we did not consider these algorithms for time series data in our work.…”

A Review on Time Series Dimensionality Reduction

“…inflection points detection in time series [31] which represents the movement shape of the time series more exactly than SAX, with fixed number of deflection points, this method can perform clustering of time series based on movement shape of time series. Piecewise Trend Approximation (PTA) method for time series representation [22], allows dimensionality reduction by retaining the main trends in time series using ratio between two consecutive points, segmentation is performed only if the two Sequential segments have diverse trend and each segment is approximated by the fraction of first and last points inside the segment. Piecewise Cloud Approximation (PWCA) is a cloud model based technique for dimensionality reduction [23], where each cloud reflects the distribution of data points within the "frame".…”

Distance- and Momentum-Based Symbolic Aggregate Approximation for Highly Imbalanced Classification

“…The most widely employed approach for time-series representation is dimensionality reduction [ 1 , 2 , 3 , 4 , 5 , 6 ]. One of the initially used dimensionality reduction approaches is sampling [ 1 ].…”

“…PAA has been demonstrated to be effective for time-series representations. Consequently, various extensions have been introduced in time-series representations [ 3 , 4 , 5 , 6 ].…”