Efficient Retrieval of Similar Time Sequences Using DFT

TL;DR

This paper improves DFT-based indexing for time sequence retrieval by leveraging Fourier coefficient symmetry, significantly accelerating search times demonstrated on real and synthetic data.

Contribution

It introduces a novel approach that exploits Fourier coefficient symmetry to enhance DFT-based indexing efficiency for time sequences.

Findings

Search time improved by over 2x using the new method.

Validated on real stock prices and synthetic datasets.

Analytical proof supports the efficiency gain.

Abstract

We propose an improvement of the known DFT-based indexing technique for fast retrieval of similar time sequences. We use the last few Fourier coefficients in the distance computation without storing them in the index since every coefficient at the end is the complex conjugate of a coefficient at the beginning and as strong as its counterpart. We show analytically that this observation can accelerate the search time of the index by more than a factor of two. This result was confirmed by our experiments, which were carried out on real stock prices and synthetic data.