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To derive spatial-temporal correlations for modeling, the causality relationship between measurements made in various monitoring stations is analyzed using Transfer Entropy (TE). This work explores the process of identifying a piecewise affine (PWA) model using a larger dataset and suggests a unique hierarchical clustering-based identification technique with model structure selection. This work improves the BIRCH (Balanced Iterative Reducing and Clustering using Hierarchies) by introducing Kullback-Leibler (KL) Divergence as the dissimilarity between clusters for handling clusters with arbitrary shapes. The number of clusters is automatically determined using a cluster validity metric. The task is formulated as a sparse optimization problem, and the model structure is selected using parameter estimations. Beijing air quality data is used to demonstrate the method, and the results show that the proposed strategy may produce acceptable forecast performance.<\/jats:p>","DOI":"10.3233\/jifs-238920","type":"journal-article","created":{"date-parts":[[2024,2,27]],"date-time":"2024-02-27T10:57:31Z","timestamp":1709031451000},"page":"9525-9542","source":"Crossref","is-referenced-by-count":0,"title":["Prediction of PM2.5 with a piecewise affine model considering spatial-temporal correlation"],"prefix":"10.1177","volume":"46","author":[{"given":"Zhenxing","family":"Ren","sequence":"first","affiliation":[{"name":"College of Computer Science and Technology & College of Data Science, Taiyuan University of Technology, Jinzhong, Shanxi, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jia","family":"Zhang","sequence":"additional","affiliation":[{"name":"Hangzhou City University, Hangzhou, Zhejiang, China"},{"name":"xup Architekten Xu und Partner, Hangzhou, Zhejiang, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology & College of Data Science, Taiyuan University of Technology, Jinzhong, Shanxi, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinxin","family":"Ji","sequence":"additional","affiliation":[{"name":"xup Architekten Xu und Partner, Hangzhou, Zhejiang, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-238920_ref2","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1136\/thoraxjnl-2013-204492","article-title":"Epidemiological time series studies of PM2.5 and daily mortality and hospital admissions: a systematic review and meta-analysis","volume":"69","author":"Atkinson","year":"2014","journal-title":"Thorax"},{"key":"10.3233\/JIFS-238920_ref3","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1016\/j.neucom.2018.06.049","article-title":"A deep spatial-temporal ensemble model for air quality prediction","volume":"314","author":"Wang","year":"2018","journal-title":"Neurocomputing"},{"key":"10.3233\/JIFS-238920_ref4","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1023\/A:1009783824328","article-title":"BIRCH: A new data clustering algorithm and its applications","volume":"1","author":"Zhang","year":"1997","journal-title":"Data Mining and Knowledge Discovery"},{"key":"10.3233\/JIFS-238920_ref5","doi-asserted-by":"crossref","first-page":"2050","DOI":"10.4304\/jnw.8.9.2050-2056","article-title":"Advanced split BIRCH algorithm in reconfigurable network","volume":"8","author":"Wan","year":"2013","journal-title":"J Networks"},{"issue":"4","key":"10.3233\/JIFS-238920_ref6","doi-asserted-by":"crossref","first-page":"101731","DOI":"10.1016\/j.apr.2023.101731","article-title":"On prediction of air pollutants with Takagi-Sugeno models based on a hierarchical clustering identification method, 31. 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