Forecasting changed segments in random processes through multiple change points detection

Abstract

본 연구에서는 임의의 확률 분포를 따르는 확률과정에서의 변화지점과 변화 세그먼트의 예 측을 다룬다. 예측은 마케팅, 금융 및 기타 많은 산업과 조직의 목표 설정, 용량 계획, 이상 감지 등에서 과거 데이터를 통해 미래 동향을 파악할 수 있는 기법이다. 예측에 대한 많은 접근법이 도입되었지만, 변화지점이 있는 경우에는 적용하는 데에 어려움이 있다. 여기에서 변화지점이란 관측 데이터에서 예상치 못한 편차가 발생하는 시점을 의미한다. 이러한 예상치 못한 변화는 상태 간의 전환을 명시하며 각각 다른 상태로 존재하는데 이러한 상태를 확률과정의 변화된 세그먼트라고 칭한다. 변화지점 탐지는 시계열 데이터 기반에서 예상치 못한 속성 변화를 측정하기 위한 모형에 유용한 기법이다. 본 연구는 주로 확률과정의 관측 데이터에서 변화지점과 세그먼트를 예측하는 새로운 방법론에 초점을 두며, 의료 모니터링, 기후 변화 감지, 이미지 및 음성 분석과 인간의 동작 분석 등 다양한 분야에 적용이 가능하다.

알려지지 않은 변화지점 감지 및 세그먼트 매개변수 추정에는 우도비 검정과 함께 베이지안 이론을 적용하였다. 매개변수 변화는 모든 변화지점 전후의 예상 값을 분석을 통해 평가하였다. 변화 지점 감지 및 세그먼트 추정 후, 회귀 분석을 통해 향후 변화 지점 및 세그먼트를 예측한다. 본 연구에서 제안하는 모형을 인위적으로 만든 데이터 세트에 적용하여 검증한다. 그리고 2004년부터 2013년까지 기간 중 서울 4개 지역(구로, 노원, 송파, 용 산)의 미세먼지 (PM_{2.5}, PM_{10}) 농도 실시간 데이터에 본 연구에서 제안한 기법을 적용하였다. 실험 결과 미세먼지 농도 변화지점 전후 10년간 오염 물질 농도가 감소했음을 확인하였다. 또한, 향후 PM_{2.5} 과 PM_{10} 에 대한 변화지점 및 세그먼트에 대한 예측을 수행하였다. 본 연구는 환경, 인구 밀도, 차량 밀집도 등의 특성을 기반으로 4곳의 데이터를 수집하여, 제안 모형이 다양한 분야의 데이터 구조에서도 수행할 수 있다는 통찰을 제공한다. 추후 연구과제로는 분포가 알려지지 않은 데이터의 변화지점 및 세그먼트 예측에 대한 연구가 있다.|This expected research contains the forecasting of change points and change segments in random processes following any kind of probability distribution. Forecasting is a technique to predict future trends on the basis of historical data, which can help industries and organizations in marketing, finance and many other fields, for goals setting, capacity planning and anomaly detection, etc. A number of approaches have been introduced for this issue but their performance is straightforwardly challenged by the existence of change points. Unexpected deviations in observed data are called change points. These unanticipated changes specify transitions between states and one state is different from the other state, these changed states are also called changed segments of the process. Change point detection is a valuable technique in modeling to estimate unanticipated property changes underlying time series data. This research primarily focuses on a novel methodology of forecasting of change points and changed segments in the observed data of a random process. It is applicable in diverse range of areas like medical condition monitoring, climate change detection, image and speech analysis and human

activity analysis. Bayesian probability along with likelihood ratio test is being used for unknown change points

detection and unknown segments parameters estimations. Parameter change has been evaluated by critically analyzing the parameters expectations before and after every change point. After change points detection and changed segments estimation, regression analysis is performed for forecasting of forthcoming change points and forthcoming changed segments. The recommended model is validated by application on artificial data set of known solutions. Then, real-time data of particulate matter PM2.5 and PM10 concentrations, during the study period 2004 - 2013, for four different sites (Guro,Nowon, Songpa, and Yongsan) in Seoul, South Korea has been used and proposed technique is applied. The results are calculated and conclusions are drawn. The parameters before and after the change point of particulate matter concentrations indicate reduction in pollutant concentrations over a 10- year period. The forecasting has been done, for forthcoming change points and segments expectations of PM2.5 and PM10 concentrations. As data of four different sites has been taken for investigation due to diverse features, i.e. environment, population densities, and transportation vehicle densities,

consequently, this study provides insights how well this recommended model could perform for different areas and data structures. This approach is applicable on probability distribution functions, thus, it needs to be further extended for forecasting of change points and change segments in distribution free data.; This expected research contains the forecasting of change points and change segments in random processes following any kind of probability distribution. Forecasting is a technique to predict future trends on the basis of historical data, which can help industries and organizations in marketing, finance and many other fields, for goals setting, capacity planning and anomaly detection, etc. A number of approaches have been introduced for this issue but their performance is straightforwardly challenged by the existence of change points. Unexpected deviations in observed data are called change points. These unanticipated changes specify transitions between states and one state is different from the other state, these changed states are also called changed segments of the process. Change point detection is a valuable technique in modeling to estimate unanticipated property changes underlying time series data. This research primarily focuses on a novel methodology of forecasting of change points and changed segments in the observed data of a random process. It is applicable in diverse range of areas like medical condition monitoring, climate change detection, image and speech analysis and human

activity analysis. Bayesian probability along with likelihood ratio test is being used for unknown change points

detection and unknown segments parameters estimations. Parameter change has been evaluated by critically analyzing the parameters expectations before and after every change point. After change points detection and changed segments estimation, regression analysis is performed for forecasting of forthcoming change points and forthcoming changed segments. The recommended model is validated by application on artificial data set of known solutions. Then, real-time data of particulate matter PM2.5 and PM10 concentrations, during the study period 2004 - 2013, for four different sites (Guro,Nowon, Songpa, and Yongsan) in Seoul, South Korea has been used and proposed technique is applied. The results are calculated and conclusions are drawn. The parameters before and after the change point of particulate matter concentrations indicate reduction in pollutant concentrations over a 10- year period. The forecasting has been done, for forthcoming change points and segments expectations of PM2.5 and PM10 concentrations. As data of four different sites has been taken for investigation due to diverse features, i.e. environment, population densities, and transportation vehicle densities,

consequently, this study provides insights how well this recommended model could perform for different areas and data structures. This approach is applicable on probability distribution functions, thus, it needs to be further extended for forecasting of change points and change segments in distribution free data.