Multiscale Analysis of Spatio-Temporal Data

Abstract

This thesis presents a multiscale analysis of spatio-temporal data. The content of this thesis consists of three chapters. First, we suggest an enhancement of the lifting scheme, one of the popular multiscale method, by using clustering-based network design. The proposed method is originally developed for enhancement of graph signal data, and the simulation and real data analysis results show that the proposed method has the advantage to reconstruct the noisy data compared to conventional lifting scheme method. Moreover, the advantage of the proposed method is not limited to the graph signal denoising. It is also shown that the proposed method the proposed neighborhood selection is able to combine with lifting one coefficient at a time (LOCAAT) algorithm, which is a lifting scheme algorithm frequently used in signal denoising. Second, we suggest a new lifting scheme concept which could be applied for streamflow data. It is impossible to apply the original lifting scheme to streamflow data directly because of its complex structure. In this thesis, to adapt the concept of lifting scheme to streamflow data, we suggest a new lifting scheme algorithm for streamflow data with flow-adaptive neighborhood selection, flow proportional weight generation, and flow-length adaptive removal point selection. By using the proposed method, we can successfully construct a multiscale analysis of streamflow data. Simulation study supports the performance of the lifting scheme for streamflow data is competitive for signal denoising. Besides, the proposed methods can visualize the multiscale structure of the network by adding or subtracting observations. Third, multiscale analysis for particulate matter data in Seoul is provided as a case study. We suggest a new method, which is a novel combi- nation of multiscale analysis and extreme value theory. The study starts from the idea that every climate event has its spatial or temporal event lengths. By changing the event area and duration time, we can estimate multiple extreme value parameters using generalized extreme value (GEV) distribution. Besides, we suggest a new property, called piecewise scaling property to combine multiple GEV estimators into a single equation. By using the proposed method, we can construct a return level map with ar- bitrary duration time and event area.

이 논문은 다중 척도 분석을 시공간 자료에 응용한 방법들을 제시한다. 첫째, 그래프 신호 자료에서의 다중 척도 분석 방법 중 하나인 리프팅 스킴을 군집 에 기반한 이웃 재설정을 통해 기대 예측 오차를 줄일 수 있음을 보이고 이를 통해 리프팅 스킴의 성능을 향상하였다. 둘째, 공간적으로 복잡하고 방향성이 있는 구조에서 생성된 유량 네트워크 자료에 알맞는 리프팅 스킴을 구성하기 위해 네트워크의 특성을 반영한 이웃 선택, 예측 필터 구성 및 영역 설정으로 유량 네트워크 자료에 대한 리프팅 스킴을 구성하고 시공간 자료에의 확장 가능성을 살펴보았다. 마지막으로 서울특별시 고농도 미세먼지 자료를 다양 한 시간, 공간 및 시공간 집적을 통해 변환한 후 얻어진 일반화 극단값 모형의 모수들의 관계를 수문학에서 사용하는 강도-지속시간-발생빈도 곡선에 매듭 을 추가한 변형된 형태의 강도-지속시간-발생빈도 곡선을 따라 모델링하였고 사례 연구를 통해 원 자료의 복귀 수준 지도를 좀 더 정확히 묘사할 수 있음을 보였다.