Segment-based approach for subsequence searches in sequence databases

TLDR: Time warping as mentioned in this paper is a transformation that allows any sequence element to replicate itself as many times as needed without extra costs without extra computation cost, and is defined as the smallest distance between two sequences transformed by time warping.

Abstract: The sequence database is a set of data sequences, each of which is an ordered list of elements [1]. Sequences of stock prices, money exchange rates, temperature data, product sales data, and company growth rates are the typical examples of sequence databases [2, 8]. Similarity search is an operation that finds sequences or subsequences whose changing patterns are similar to that of a given query sequence [1, 2, 8]. Similarity search is of growing importance in many new applications such as data mining and data warehousing [6, 17]. There have been many research efforts [1, 7, 8, 10, 17] for efficient similarity searches in sequence databases using the Euclidean distance as a similarity measure. However, recent techniques [13–15, 18] tend to favor the time warping distance for its higher accuracy and wider applicability at the expense of high computation cost. Time warping is a transformation that allows any sequence element to replicate itself as many times as needed without extra costs [18]. For → example, two sequences X = 〈20, 21, 21, 20, 20, 23, 23, 23〉 → and Q = 〈20, 20, 21,20, 23〉 can be identically transformed into 〈20, 20, 21, 21, 20, 20, 23, 23, 23〉 by time warping. The time warping distance is defined as the smallest distance between two sequences transformed by time warping. While the Euclidean distance can be used only when two sequences compared are of the same length, the time warping distance can be applied to any two sequences of arbitrary lengths. Therefore, the time warping distance fits well with the databases where sequences are of different lengths. The time warping distance can be applied to both whole sequence and subsequence searches. Let us first consider the