Similarity search in Recent Biased time series databases using Vari-DWT and Polar wavelets

Abstract

A time series database is a collection of data that are generated in series as time goes on and constitutes a large portion of data stored in computers like stock-price movements, weather data, bio-medical measurements, video data etc., Two time sequences of same length are said to be similar if the Euclidean distance is less or equal to a given threshold. The main issue of similarity search in time series databases is to improve the search performance since time sequences are usually of high dimension. So it is important to reduce the search space for efficient processing of similarity search in large time series databases. Popular techniques for efficient retrieval of time sequences in time series databases are DFT, DWT, SVD, PAA, PCA, APCA etc,. In this paper we explore the feasibility of using Vari-DWT and Polar wavelet with a comprehensive analysis of the two methods as matching functions which can improve the search performance in Recent-Biased time series databases. Vari-DWT is fast to compute and requires little storage for each sequence, It preserves Euclidean distance and recency and also allows good approximation with a subset of coefficients. But it shows poor performance for locally distributed time series data which are clustered around certain values since it uses averages to reduce the dimensionality of data. Polar wavelet uses polar coordinates which are not affected from averages and so can improve the search performance especially in locally distributed time series databases. Moreover, DWT has the limitation that it works best if the length of time series 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> otherwise it approximates the signal by adding 0 to the right side of the series to make the length to be 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> which distorts the original signal. Polar wavelet works with time sequences of any length without distorting the original signal. The effectiveness of Vari-DWT and Polar wavelets are evaluated empirically on real weather data and synthetic datasets.