• Smart Media Journal
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• v.12 no.6
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• pp.9-14
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• 2023

The longest increasing subsequence is a fundamental problem which has been studied for a long time in computer science. In this paper, we consider the maximal increasing subsequence problem where the constraint is released from the longest to the maximal. For two kinds of increasing (monotone increasing and strictly increasing), we propose linear-time algorithms computing a maximal increasing subsequence of an input sequence from an alphabet Σ. Our algorithm for computing a maximal monotone increasing subsequence requires O(1) space and our algorithm for computing a maximal strictly increasing subsequence requires O(|Σ|) space.

• Journal of Industrial Technology
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• v.21 no.A
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• pp.155-166
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• 2001

This paper deals with the subsequence searching problem under time-warping. Our work is motivated by the observation that subsequence searches slow down quadratically as the average length of data sequences increases. To resolve this problem, the Segment-Based Approach for Subsequence Searches (SBASS) is proposed. The SBASS divides data and query sequences into a series of segments, and retrieves all data subsequences. Our segmentation scheme allows segments to have different lengths; thus we employ the time warping distance as a similarity measure for each segment pair. For efficient retrieval of similar subsequences, we extract feature vectors from all data segments exploiting their monotonically changing properties, and build a spatial index using feature vectors. The effectiveness of our approach is verified through extensive experiments.

• The KIPS Transactions:PartD
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• v.12D no.3 s.99
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• pp.355-364
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• 2005

Previous researches on subsequence matching have been focused on how to make indexes in order to speed up the matching time, and do not take into account the effectiveness issues of subsequence matching methods. This paper considers the effectiveness of subsequence matching methods and proposes two metrics for effectiveness evaluations of subsequence matching algorithms. We have applied the proposed metrics to Korean stock data and five known matching algorithms. The analysis on the empirical data shows that two methods (i.e., the method supporting normalization, and the method supporting scaling and shifting) outperform the others in terms of the effectiveness of subsequence matching.

• Journal of KIISE:Computing Practices and Letters
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• v.16 no.5
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• pp.586-590
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• 2010

In this paper we formally define the linear detrending subsequence matching and propose its efficient index-based solution. To this end, we first present the notion of LD-windows. We eliminate the linear trend from a subsequence rather than each window itself and obtain LD-windows by dividing the subsequence into windows. Using the LD-windows we present a lower bounding theorem of the index-based solution and formally prove its correctness. Based on this lower bounding theorem, we then propose the index building and subsequence matching algorithms, respectively. Finally, we show the superiority of our index- based solution through experiments.

• Journal of Industrial Technology
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• v.21 no.A
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• pp.167-179
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• 2001

This paper discusses an index-based subsequence matching that supports time warping in large sequence databases. Time warping enables finding sequences with similar patterns even when they are of different lengths. In earlier work, we suggested an efficient method for whole matching under time warping. This method constructs a multidimensional index on a set of feature vectors, which are invariant to time warping, from data sequences. For filtering at feature space, it also applies a lower-bound function, which consistently underestimates the time warping distance as well as satisfies the triangular inequality. In this paper, we incorporate the prefix-querying approach based on sliding windows into the earlier approach. For indexing, we extract a feature vector from every subsequence inside a sliding window and construct a multi-dimensional index using a feature vector as indexing attributes. For query precessing, we perform a series of index searches using the feature vectors of qualifying query prefixes. Our approach provides effective and scalable subsequence matching even with a large volume of a database. We also prove that our approach does not incur false dismissal. To verily the superiority of our method, we perform extensive experiments. The results reseal that our method achieves significant speedup with real-world S&P 500 stock data and with very large synthetic data.

• Proceedings of the Korea Information Processing Society Conference
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• 2021.11a
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• pp.15-18
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• 2021

최장 공통 부분 서열(Longest Common Subsequence, LCS)은 서열 유사도(Similarity)를 측정하기 위한 주요 지표 중 하나로 특별한 가정이 없는 한 두 문자열의 LCS 를 계산하기 위해서는 두 문자열의 길이의 곱에 비례하는 시간이 필요하다. 최근 최장(longest)이라는 조건을 극대(maximal)로 완화한 극대 공통 부분 서열(Maximal Common Subsequence, MCS)이 제시되었고, 두 문자열의 MCS 를 선형에 가까운 시간에 찾는 알고리즘이 개발되었다. 극대는 최장을 보장하지 않기 때문에 두 문자열의 MCS 길이는 LCS 길이와 달리 유일하지 않을 수 있고, LCS 길이가 매우 길어도 길이가 1인 MCS가 존재할 수도 있다. 본 논문에서는 기존 알고리즘에 의해 계산되는 MCS 의 효용성을 알아보기 위해, DNA 등 여러 종류의 실제 데이터와 랜덤 생성된 데이터에 대해 LCS 와 MCS 의 길이를 비교했다. MCS 길이는 LCS 길이 대비 실제 데이터에서 32.1 ~ 60.2%, 랜덤 데이터에서는 27.5 ~ 62.9%로 나타났다. 이 비율은 문자열을 이루고 있는 알파벳 수가 많을수록, 문자열의 길이가 길어질수록 감소했다.

• The KIPS Transactions:PartD
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• v.13D no.3 s.106
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• pp.357-368
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• 2006

This paper discusses the way of processing time-series subsequence matching under time warping. Time warping enables finding sequences with similar patterns even when they are of different lengths. The prefix-querying method is the first index-based approach that performs time-series subsequence matching under time warping without false dismissals. This method employs the $L_{\infty}$ as a base distance function for allowing users to issue queries conveniently. In this paper, we extend the prefix-querying method for absorbing $L_1$, which is the most-widely used as a base distance function in time-series subsequence matching under time warping, instead of $L_{\infty}$. We also formally prove that the proposed method does not incur any false dismissals in the subsequence matching. To show the superiority of our method, we conduct performance evaluation via a variety of experiments. The results reveal that our method achieves significant performance improvement in orders of magnitude compared with previous methods.

• The KIPS Transactions:PartD
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• v.13D no.4 s.107
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• pp.513-524
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• 2006

Normalization transform is very useful for finding the overall trend of the time-series data since it enables finding sequences with similar fluctuation patterns. The previous subsequence matching method with normalization transform, however, would incur index overhead both in storage space and in update maintenance since it should build multiple indexes for supporting arbitrary length of query sequences. To solve this problem, we propose a single index approach for the normalization transformed subsequence matching that supports arbitrary length of query sequences. For the single index approach, we first provide the notion of inclusion-normalization transform by generalizing the original definition of normalization transform. The inclusion-normalization transform normalizes a window by using the mean and the standard deviation of a subsequence that includes the window. Next, we formally prove correctness of the proposed method that uses the inclusion-normalization transform for the normalization transformed subsequence matching. We then propose subsequence matching and index building algorithms to implement the proposed method. Experimental results for real stock data show that our method improves performance by up to $2.5{\sim}2.8$ times over the previous method. Our approach has an additional advantage of being generalized to support many sorts of other transforms as well as normalization transform. Therefore, we believe our work will be widely used in many sorts of transform-based subsequence matching methods.

• The KIPS Transactions:PartD
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• v.9D no.4
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• pp.555-560
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• 2002

Subsequence matching, which consists of index searching and post-processing steps, is an operation that finds those subsequences whose changing patterns are similar to that of a given query sequence from a time-series database. This paper discusses optimization of post-processing for subsequence matching. The common problem occurred in post-processing of previous methods is to compare the candidate subsequence with the query sequence for discarding false alarms whenever each candidate subsequence appears during index searching. This makes a sequence containing candidate subsequences to be accessed multiple times from disk, and also have a candidate subsequence to be compared with the query sequence multiple times. These redundancies cause the performance of subsequence matching to degrade seriously. In this paper, we propose a new optimal method for resolving the problem. The proposed method stores ail the candidate subsequences returned by index searching into a binary search tree, and performs post-processing in a batch fashion after finishing the index searching. By this method, we are able to completely eliminate the redundancies mentioned above. For verifying the performance improvement effect of the proposed method, we perform extensive experiments using a real-life stock data set. The results reveal that the proposed method achieves 55 times to 156 times speedup over the previous methods.

• Journal of KIISE:Databases
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• v.33 no.2
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• pp.201-213
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• 2006

A time-series database is a set of time-series data sequences, each of which is a list of changing values of the object in a given period of time. Subsequence matching is an operation that searches for such data subsequences whose changing patterns are similar to a query sequence from a time-series database. This paper addresses a performance issue of time-series subsequence matching. First, we quantitatively examine the performance degradation caused by the window size effect, and then show that the performance of subsequence matching with a single index is not satisfactory in real applications. We argue that index interpolation is fairly useful to resolve this problem. The index interpolation performs subsequence matching by selecting the most appropriate one from multiple indexes built on windows of their inherent sizes. For index interpolation, we first decide the sites of windows for multiple indexes to be built. In this paper, we solve the problem of selecting optimal window sizes in the perspective of physical database design. For this, given a set of query sequences to be peformed in a target time-series database and a set of window sizes for building multiple indexes, we devise a formula that estimates the cost of all the subsequence matchings. Based on this formula, we propose an algorithm that determines the optimal window sizes for maximizing the performance of entire subsequence matchings. We formally Prove the optimality as well as the effectiveness of the algorithm. Finally, we perform a series of extensive experiments with a real-life stock data set and a large volume of a synthetic data set. The results reveal that the proposed approach improves the previous one by 1.5 to 7.8 times.