{"type":"ScholarlyArticle","title":"VCformer: Variable Correlation Transformer with Inherent Lagged Correlation for Multivariate Time Series Forecasting","authors":[{"name":"Yingnan Yang","slug":"yingnan-yang","given":"Yingnan","family":"Yang","affiliation":"College of Computer Science and Software Engineering , Shenzhen University , Shenzhen , China"},{"name":"Qingling Zhu","slug":"qingling-zhu","given":"Qingling","family":"Zhu","affiliation":"National Engineering Laboratory for Big Data System Computing Technology , Shenzhen University , Shenzhen , China"},{"name":"Jianyong Chen","slug":"jianyong-chen","given":"Jianyong","family":"Chen","affiliation":"College of Computer Science and Software Engineering , Shenzhen University , Shenzhen , China"}],"abstract":"Multivariate time series (MTS) forecasting has been extensively applied across diverse domains, such as weather prediction and energy consumption. However, current studies still rely on the vanilla point-wise self-attention mechanism to capture cross-variable dependencies, which is inadequate in extracting the intricate cross-correlation implied between variables. To fill this gap, we propose Variable Correlation Transformer (VCformer), which utilizes Variable Correlation Attention (VCA) module to mine the correlations among variables. Specifically, based on the stochastic process theory, VCA calculates and integrates the cross-correlation scores corresponding to different lags between queries and keys, thereby enhancing its ability to uncover multivariate relationships. Additionally, inspired by Koopman dynamics theory, we also develop Koopman Temporal Detector (KTD) to better address non-stationarity in time series. The two key components enable VCformer to extract both multivariate correlations and temporal dependencies. Our extensive experiments on eight real-world datasets demonstrate the effectiveness of VCformer, achieving top-tier performance compared to other state-of-the-art baseline models. Code is available at this repository: https://github.com/CSyyn/VCformer.","doi":"10.24963/ijcai.2024/590","url":"https://ijcai.org/proceedings/2024/590","pdf":"https://ijcai.org/proceedings/2024/0590.pdf","markdown":"https://ijcai.org/proceedings/2024/590.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/590","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Machine Learning","track":"Main Track","number":590,"pages":{"first":5335,"last":5343},"keywords":["Machine Learning: ML: Attention models","Machine Learning: ML: Time series and data streams"],"videos":[],"references":[{"position":1,"raw":"MAE MSE MAE Weather 96 0.171 0.220 0.174 0.214 0.177 0.218 0.170 0.217 0.177 0.226 0.185 0.248 0.172 0.220 0.196 0.255 0.205 0.265 192 0.230 0.266 0.221 0.254 0.242 0.271 0.253 0.296 0.223 0.257 0.229 0.305 0.230 0.281 0.253 0.323 0.233 0.274 336 0.280 0.299 0.278 0.296 0.290 0.305 0.285 0.310 0.281 0.299 0.323 0.285 0.335 0.311 0.325 0.390 0.296 0.317 720 0.352 0.344 0.354 0.349 0.362 0.350 0.395 0.391 0.360 0.350 0.665 0.356 0.398 0.356 0.389 0.437 0.372 0.365 Electricity 96 0.150 0.242 0.154 0.245 0.188 0.280 0.164 0.261 0.174 0.273 0.153 0.250 0.182 0.285 0.195 0.276 0.172 0.275 192 0.167 0.255 0.169 0.258 0.193 0.285 0.177 0.272 0.195 0.291 0.223 0.329 0.247 0.329 0.194 0.280 0.187 0.287 336 0.182 0.270 0.185 0.275 0.211 0.302 0.201 0.294 0.216 0.310 0.191 0.291 0.256 0.338 0.207 0.295 0.208 0.307 720 0.221 0.302 0.225 0.308 0.253 0.335 0.242 0.327 0.265 0.346 0.609 0.568 0.311 0.382 0.242 0.328 0.235 0.329 Traffic 96 0.454 0.310 0.717 0.466 0.475 0.303 0.546 0.352 0.539 0.368 0.530 0.285 0.592 0.315 0.640 0.388 0.732 0.418 192 0.468 0.315 0.472 0.320 0.474 0.322 0.547 0.347 0.552 0.375 0.607 0.311 0.645 0.336 0.593 0.362 0.756 0.425 336 0.486 0.325 0.488 0.330 0.489 0.332 0.562 0.352 0.573 0.383 0.642 0.324 0.659 0.347 0.600 0.365 1.172 0.680 720 0.524 0.348 0.530 0.361 0.526 0.356 0.597 0.370 0.632 0.407 0.592 0.380 0.723 0.388 0.634 0.388 0.896 0.516 ETTh1 96 0.376 0.397 0.380 0.398 0.378 0.396 0.373 0.397 0.389 0.403 0.384 0.409 0.438 0.447 0.479 0.471 0.761 0.612 192 0.431 0.427 0.433 0.428 0.433 0.427 0.419 0.425 0.438 0.431 0.461 0.459 0.488 0.472 0.448 0.443 0.746 0.599 336 0.473 0.449 0.475 0.451 0.471 0.448 0.457 0.446 0.479 0.451 0.521 0.496 0.510 0.480 0.489 0.467 0.739 0.572 720 0.476 0.474 0.486 0.480 0.472 0.471 0.499 0.497 0.486 0.474 0.627 0.586 0.511 0.497 0.511 0.509 0.757 0.612 ETTh2 96 0.292 0.344 0.292 0.344 0.292 0.345 0.296 0.351 0.306 0.355 0.596 0.532 0.337 0.375 0.299 0.351 0.477 0.462 192 0.377 0.396 0.375 0.396 0.388 0.405 0.399 0.414 0.388 0.408 0.880 0.663 0.442 0.435 0.385 0.413 0.571 0.507 336 0.417 0.430 0.418 0.430 0.427 0.436 0.434 0.443 0.430 0.443 1.988 1.097 0.476 0.468 0.511 0.490 0.608 0.534 720 0.423 0.443 0.424 0.443 0.447 0.458 0.454 0.463 0.472 0.470 2.526 1.285 0.496 0.484 0.741 0.603 0.508 0.487 ETTm1 96 0.319 0.359 0.345 0.369 0.326 0.361 0.326 0.364 0.334 0.372 0.352 0.388 0.334 0.375 0.336 0.362 0.386 0.398 192 0.364 0.382 0.386 0.391 0.372 0.381 0.360 0.382 0.374 0.391 0.409 0.436 0.385 0.401 0.378 0.389 0.459 0.434 336 0.399 0.405 0.423 0.416 0.404 0.403 0.394 0.405 0.409 0.414 0.424 0.428 0.410 0.411 0.413 0.416 0.551 0.485 720 0.467 0.442 0.491 0.445 0.467 0.438 0.474 0.451 0.473 0.448 0.569 0.528 0.513 0.473 0.475 0.454 0.585 0.516 ETTm2 96 0.180 0.266 0.190 0.276 0.193 0.280 0.201 0.286 0.187 0.271 0.297 0.370 0.185 0.267 0.188 0.284 0.240 0.320 192 0.245 0.306 0.251 0.311 0.246 0.307 0.281 0.335 0.253 0.314 0.499 0.492 0.249 0.306 0.259 0.337 0.314 0.367 336 0.307 0.345 0.315 0.352 0.314 0.351 0.336 0.367 0.323 0.358 0.597 0.684 0.314 0.346 0.334 0.389 0.340 0.371 720 0.406 0.402 0.413 0.404 0.410 0.405 0.430 0.417 0.416 0.407 0.835 0.659 0.411 0.399 0.463 0.466 0.438 0.421 Exchange 96 0.085 0.205 0.090 0.211 0.100 0.231 0.092 0.216 0.092 0.217 0.139 0.265 0.108 0.244 0.110 0.266 0.154 0.297 192 0.176 0.299 0.186 0.307 0.215 0.344 0.189 0.312 0.182 0.304 0.241 0.375 0.278 0.391 0.218 0.376 0.374 0.447 336 0.328 0.415 0.339 0.424 0.403 0.473 0.348 0.430 0.349 0.432 0.392 0.468 0.523 0.556 0.387 0.497 0.548 0.563 720 0.830 0.688 0.898 0.718 1.057 0.782 0.947 0.740 1.178 0.830 1.11 0.802 1.224 0.856 0.839 0.695 0.987 0.777","title":"MAE MSE MAE Weather","authors":null,"year":null,"venue":"MAE MSE MAE Weather","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Blight and Chatfield, 1991] P. A. Blight and C. Chatfield. The analysis of time series: An introduction. 4th edn. Ap- plied Statistics, 40(1):178, Jan 1991.","title":"The analysis of time series: An introduction. 4th edn","authors":"P A Blight, C Chatfield","year":"1991","venue":"Applied Statistics","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Brown et al., 2020] Tom B. Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel M. Ziegler, Jeffrey Wu, Clemens Winter, Christo- pher Hesse, Mark Chen, Eric Sigler, Mateusz Litwin, Scott Gray, Benjamin Chess, Jack Clark, Christopher Berner, Sam McCandlish, Alec Radford, Ilya Sutskever, and Dario Amodei. Language models are few-shot learners. In Pro- ceedings of the 34th International Conference on Neural Information Processing Systems, Red Hook, NY, USA, 2020.","title":"Language models are few-shot learners","authors":"B Tom, Benjamin Brown, Nick Mann, Melanie Ryder, Jared Subbiah, Prafulla Kaplan, Arvind Dhariwal, Pranav Neelakantan, Girish Shyam, Amanda Sastry, Sandhini Askell, Ariel Agarwal, Gretchen Herbert-Voss, Tom Krueger, Rewon Henighan, Aditya Child, Daniel M Ramesh, Jeffrey Ziegler, Clemens Wu, Christopher Winter, Mark Hesse, Eric Chen, Mateusz Sigler, Scott Litwin, Benjamin Gray, Jack Chess, Christopher Clark, Sam Berner, Alec Mccandlish, Ilya Radford, Dario Sutskever, Amodei","year":"2020","venue":"Proceedings of the 34th International Conference on Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"Curran Associates Inc. [Brunton et al., 2022]","title":null,"authors":"Curran Associates, Inc [ Brunton","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":5,"raw":"Steven L. Brunton, Marko Budišić, Eu- rika Kaiser, and J. Nathan Kutz. Modern koopman theory for dynamical systems. SIAM Review, page 229-340, May 2022.","title":"Modern koopman theory for dynamical systems","authors":"L Steven, Marko Brunton, Eurika Budišić, J Nathan Kaiser, Kutz","year":"2022","venue":"SIAM Review","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Castán-Lascorz et al., 2022] M.A. Castán-Lascorz, P. Jiménez-Herrera, A. Troncoso, and G. Asencio- Cortés. A new hybrid method for predicting univariate and multivariate time series based on pattern forecasting. Inf. Sci., 586(C):611-627, mar 2022.","title":"A new hybrid method for predicting univariate and multivariate time series based on pattern forecasting","authors":"M A Castán-Lascorz, P Jiménez-Herrera, A Troncoso, G Asencio-Cortés","year":"2022","venue":"Inf. Sci","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Chandereng and Gitter, 2020] Thevaa Chandereng and An- thony Gitter. Lag penalized weighted correlation for time series clustering. BMC bioinformatics, 21:1-15, 2020.","title":"Thevaa Chandereng and Anthony Gitter. Lag penalized weighted correlation for time series clustering","authors":"Gitter Chandereng","year":"2020","venue":"BMC bioinformatics","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Chatfield and Xing, 2019] Chris Chatfield and Haipeng Xing. The analysis of time series: an introduction with R. CRC press, 2019.","title":"The analysis of time series: an introduction with R","authors":"Chris Chatfield, Haipeng Xing","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Choi et al., 2022] Taesung Choi, Dongkun Lee, Yuchae Jung, and Ho-Jin Choi. Multivariate time-series anomaly detection using seqvae-cnn hybrid model. In 2022 Inter- national Conference on Information Networking (ICOIN), pages 250-253, Jan 2022.","title":"Multivariate time-series anomaly detection using seqvae-cnn hybrid model","authors":"Choi","year":"2022","venue":"2022 International Conference on Information Networking (ICOIN)","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Guo et al., 2023] Wei Guo, Chang Meng, Enming Yuan, Zhicheng He, Huifeng Guo, Yingxue Zhang, Bo Chen, Yaochen Hu, Ruiming Tang, Xiu Li, et al. Compressed interaction graph based framework for multi-behavior rec- ommendation. In Proceedings of the ACM Web Conference 2023, pages 960-970, 2023.","title":"Compressed interaction graph based framework for multi-behavior recommendation","authors":"Wei Guo, Chang Meng, Enming Yuan, Zhicheng He, Huifeng Guo, Yingxue Zhang, Bo Chen, Yaochen Hu, Ruiming Tang, Xiu Li","year":"2023","venue":"Proceedings of the ACM Web Conference 2023","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Han et al., 2020] Yiqiang Han, Wenjian Hao, and Umesh Vaidya. Deep learning of koopman representation for con- trol. In 2020 59th IEEE Conference on Decision and Con- trol (CDC), pages 1890-1895. IEEE, 2020.","title":"Deep learning of koopman representation for control","authors":"Han","year":"2020","venue":"59th IEEE Conference on Decision and Control (CDC)","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Han et al., 2023] Lu Han, Han-Jia Ye, and De-Chuan Zhan. The capacity and robustness trade-off: Revisiting the chan- nel independent strategy for multivariate time series fore- casting. arXiv preprint arXiv:2304.05206, 2023.","title":"The capacity and robustness trade-off: Revisiting the channel independent strategy for multivariate time series forecasting","authors":"Lu Han, Han-Jia Ye, De-Chuan Zhan","year":"2023","venue":null,"doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Hornik, 1991] Kurt Hornik. Approximation capabilities of multilayer feedforward networks. Neural Networks, page 251-257, Jan 1991.","title":"Approximation capabilities of multilayer feedforward networks","authors":"Kurt Hornik","year":"1991","venue":"Neural Networks","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[John and Ferbinteanu, 2021] Majnu John and Janina Ferbin- teanu. Detecting time lag between a pair of time se- ries using visibility graph algorithm. Communications in Statistics: Case Studies, Data Analysis and Applications, 7(3):315-343, Jul 2021.","title":"Majnu John and Janina Ferbinteanu. Detecting time lag between a pair of time series using visibility graph algorithm","authors":"Ferbinteanu John","year":"2021","venue":"Communications in Statistics: Case Studies, Data Analysis and Applications","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Koopman, 1931] Bernard O Koopman. Hamiltonian systems and transformation in hilbert space. Proceedings of the National Academy of Sciences, 17(5):315-318, 1931.","title":"Hamiltonian systems and transformation in hilbert space","authors":"Bernard O Koopman","year":"1931","venue":"Proceedings of the National Academy of Sciences","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Lai et al., 2018] Guokun Lai, Wei-Cheng Chang, Yiming Yang, and Hanxiao Liu. Modeling long-and short-term temporal patterns with deep neural networks. In The 41st international ACM SIGIR conference on research & devel- opment in information retrieval, pages 95-104, 2018.","title":"Modeling long-and short-term temporal patterns with deep neural networks","authors":"Lai","year":"2018","venue":"The 41st international ACM SIGIR conference on research & development in information retrieval","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Li and Jiang, 2021] Mengnan Li and Lijian Jiang. Deep learning nonlinear multiscale dynamic problems using koopman operator. Journal of Computational Physics, page 110660, Dec 2021.","title":"Deep learning nonlinear multiscale dynamic problems using koopman operator","authors":"Li, Jiang ; ] Mengnan Li, Lijian Jiang","year":"2021","venue":"Journal of Computational Physics","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Li et al., 2019a] Shiyang Li, Xiaoyong Jin, Yao Xuan, Xiyou Zhou, Wenhu Chen, Yuxiang Wang, and Xifeng Yan. En- hancing the locality and breaking the memory bottleneck of transformer on time series forecasting. arXiv: Learn- ing,arXiv: Learning, Jun 2019.","title":"Enhancing the locality and breaking the memory bottleneck of transformer on time series forecasting","authors":"Li","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Li et al., 2019b] Yunzhu Li, Hao He, Jiajun Wu, Dina Katabi, and Antonio Torralba. Learning compositional koopman operators for model-based control. arXiv preprint arXiv:1910.08264, 2019.","title":"Learning compositional koopman operators for model-based control","authors":"Li","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Li et al., 2023] Zhe Li, Shiyi Qi, Yiduo Li, and Zenglin Xu. Revisiting long-term time series forecasting: An investiga- tion on linear mapping. arXiv preprint arXiv:2305.10721, 2023.","title":"Revisiting long-term time series forecasting: An investigation on linear mapping","authors":"Zhe Li, Shiyi Qi, Yiduo Li, Zenglin Xu","year":"2023","venue":null,"doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Liu et al., 2022a] Shizhan Liu, Hang Yu, Cong Liao, Jian- guo Li, Weiyao Lin, Alex X. Liu, and Schahram Dustdar. Pyraformer: Low-complexity pyramidal attention for long- range time series modeling and forecasting. In Interna- tional Conference on Learning Representations, 2022.","title":"Pyraformer: Low-complexity pyramidal attention for longrange time series modeling and forecasting","authors":"Liu","year":"2022","venue":"International Conference on Learning Representations","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Liu et al., 2022b] Yong Liu, Haixu Wu, Jianmin Wang, and Mingsheng Long. Non-stationary transformers: Exploring the stationarity in time series forecasting. Advances in Neural Information Processing Systems, 35:9881-9893, 2022.","title":"Non-stationary transformers: Exploring the stationarity in time series forecasting","authors":"Liu","year":"2022","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Liu et al., 2023a] Yong Liu, Tengge Hu, Haoran Zhang, Haixu Wu, Shiyu Wang, Lintao Ma, and Mingsheng Long. itransformer: Inverted transformers are effective for time series forecasting. arXiv preprint arXiv:2310.06625, 2023.","title":"itransformer: Inverted transformers are effective for time series forecasting","authors":"Liu","year":"2023","venue":null,"doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Liu et al., 2023b] Yong Liu, Chenyu Li, Jianmin Wang, and Mingsheng Long. Koopa: Learning non-stationary time se- ries dynamics with koopman predictors. In Thirty-seventh Conference on Neural Information Processing Systems, 2023.","title":"Koopa: Learning non-stationary time series dynamics with koopman predictors","authors":"Liu","year":"2023","venue":"Thirty-seventh Conference on Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Lusch et al., 2018] Bethany Lusch, J. Nathan Kutz, and Steven L. Brunton. Deep learning for universal linear em- beddings of nonlinear dynamics. Nature Communications, Nov 2018.","title":"Deep learning for universal linear embeddings of nonlinear dynamics","authors":"Bethany Lusch, J Nathan Kutz, Steven L Brunton","year":"2018","venue":"Nature Communications","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Morton et al., 2019] Jeremy Morton, Freddie D Witherden, and Mykel J Kochenderfer. Deep variational koopman models: Inferring koopman observations for uncertainty- aware dynamics modeling and control. arXiv preprint arXiv:1902.09742, 2019.","title":"Deep variational koopman models: Inferring koopman observations for uncertaintyaware dynamics modeling and control","authors":"Jeremy Morton, Freddie D Witherden, Mykel, Kochenderfer","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Nie et al., 2023] Yuqi Nie, Nam H Nguyen, Phanwadee Sinthong, and Jayant Kalagnanam. A time series is worth 64 words: Long-term forecasting with transformers. In The Eleventh International Conference on Learning Represen- tations, 2023.","title":"A time series is worth 64 words: Long-term forecasting with transformers","authors":"Yuqi Nie, Nam H Nguyen, Phanwadee Sinthong, Jayant Kalagnanam","year":"2023","venue":"The Eleventh International Conference on Learning Representations","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Salinas et al., 2020] David Salinas, Valentin Flunkert, Jan Gasthaus, and Tim Januschowski. Deepar: Probabilistic forecasting with autoregressive recurrent networks. Inter- national Journal of Forecasting, 36(3):1181-1191, 2020.","title":"Deepar: Probabilistic forecasting with autoregressive recurrent networks","authors":"David Salinas, Valentin Flunkert, Jan Gasthaus, Tim Januschowski","year":"2020","venue":"International Journal of Forecasting","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Schmid and Sesterhenn, 2008] PeterJ. Schmid and Jörn Ses- terhenn. Dynamic mode decomposition of numerical and experimental data. Bulletin of the American Physical Soci- ety,Bulletin of the American Physical Society, Nov 2008.","title":"PeterJ. Schmid and Jörn Sesterhenn. Dynamic mode decomposition of numerical and experimental data","authors":"Sesterhenn Schmid","year":"2008","venue":"Bulletin of the American Physical Society","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Sen et al., 2019] Rajat Sen, Hsiang-Fu Yu, and Inderjit S Dhillon. Think globally, act locally: A deep neural net- work approach to high-dimensional time series forecasting. Advances in neural information processing systems, 32, 2019.","title":"Think globally, act locally: A deep neural network approach to high-dimensional time series forecasting","authors":"Rajat Sen, Hsiang-Fu Yu, Inderjit S Dhillon","year":"2019","venue":"Advances in neural information processing systems","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Shao et al., 2022] Zezhi Shao, Zhao Zhang, Wei Wei, Fei Wang, Yongjun Xu, Xin Cao, and ChristianS. Jensen. De- coupled dynamic spatial-temporal graph neural network for traffic forecasting. Proceedings of the VLDB Endowment, 15(11):2733-2746, Jul 2022.","title":"Decoupled dynamic spatial-temporal graph neural network for traffic forecasting","authors":"Shao","year":"2022","venue":"Proceedings of the VLDB Endowment","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Shen, 2015] Chenhua Shen. Analysis of detrended time- lagged cross-correlation between two nonstationary time series. Physics Letters A, 379(7):680-687, Mar 2015.","title":"Analysis of detrended timelagged cross-correlation between two nonstationary time series","authors":"Chenhua Shen, Shen","year":"2015","venue":"Physics Letters A","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Vaswani et al., 2017] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Proceedings of the 31st International Confer- ence on Neural Information Processing Systems, page 6000-6010, Red Hook, NY, USA, 2017.","title":"Attention is all you need","authors":"Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, Illia Polosukhin","year":"2017","venue":"Proceedings of the 31st International Conference on Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Curran Associates Inc. Wang et al., 2023] Fei Wang, Di Yao, Yong Li, Tao Sun, and Zhao Zhang. Ai-enhanced spatial-temporal data-mining technology: New chance for next-generation urban com- puting. The Innovation, 4(2):100405, Mar 2023.","title":"Ai-enhanced spatial-temporal data-mining technology: New chance for next-generation urban computing","authors":"Fei Wang, Di Yao, Yong Li, Tao Sun, Zhao Zhang","year":"2023","venue":"The Innovation","doi":null,"url":null,"internal_url":null},{"position":35,"raw":"[Wen et al., 2023] Qingsong Wen, Tian Zhou, Chaoli Zhang, Weiqi Chen, Ziqing Ma, Junchi Yan, and Liang Sun. Trans- formers in time series: A survey. In Edith Elkind, editor, Proceedings of the Thirty-Second International Joint Con- ference on Artificial Intelligence, IJCAI-23, pages 6778- 6786, August 2023.","title":"Transformers in time series: A survey","authors":"Qingsong Wen, Tian Zhou, Chaoli Zhang, Weiqi Chen, Ziqing Ma, Junchi Yan, Liang Sun","year":"2023","venue":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence, IJCAI-23","doi":null,"url":null,"internal_url":"/proceedings/2023/759"},{"position":36,"raw":"[Wiener, 1930] Norbert Wiener. Generalized harmonic analy- sis. Acta mathematica, 55(1):117-258, 1930.","title":"Generalized harmonic analysis","authors":"Norbert Wiener, Wiener","year":"1930","venue":"Acta mathematica","doi":null,"url":null,"internal_url":null},{"position":37,"raw":"[Williams et al., 2015] Matthew O. Williams, Ioannis G. Kevrekidis, and Clarence W. Rowley. A data-driven ap- proximation of the koopman operator: Extending dynamic mode decomposition. Journal of Nonlinear Science, page 1307-1346, Dec 2015.","title":"A data-driven approximation of the koopman operator: Extending dynamic mode decomposition","authors":"Matthew O Williams, Ioannis G Kevrekidis, Clarence W Rowley","year":"2015","venue":"Journal of Nonlinear Science","doi":null,"url":null,"internal_url":null},{"position":38,"raw":"[Wu et al., 2021] Haixu Wu, Jiehui Xu, Jianmin Wang, and Mingsheng Long. Autoformer: Decomposition transform- ers with auto-correlation for long-term series forecasting. In Advances in Neural Information Processing Systems, volume 34, pages 22419-22430, 2021.","title":"Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting","authors":"Wu","year":"2021","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":39,"raw":"[Wu et al., 2023] Haixu Wu, Tengge Hu, Yong Liu, Hang Zhou, Jianmin Wang, and Mingsheng Long. Timesnet: Temporal 2d-variation modeling for general time series analysis. In The Eleventh International Conference on Learning Representations, 2023.","title":"Timesnet: Temporal 2d-variation modeling for general time series analysis","authors":"Wu","year":"2023","venue":"The Eleventh International Conference on Learning Representations","doi":null,"url":null,"internal_url":null},{"position":40,"raw":"[Yu et al., 2023] Chengqing Yu, Fei Wang, Zezhi Shao, Tao Sun, Lin Wu, and Yongjun Xu. Dsformer: A double sam- pling transformer for multivariate time series long-term prediction. In Proceedings of the 32nd ACM International Conference on Information and Knowledge Management, pages 3062-3072, 2023.","title":"Dsformer: A double sampling transformer for multivariate time series long-term prediction","authors":"Yu","year":"2023","venue":"Proceedings of the 32nd ACM International Conference on Information and Knowledge Management","doi":null,"url":null,"internal_url":null},{"position":41,"raw":"[Zeng et al., 2023] Ailing Zeng, Muxi Chen, Lei Zhang, and Qiang Xu. Are transformers effective for time series fore- casting? Proceedings of the AAAI Conference on Artificial Intelligence, 37(9):11121-11128, Jun. 2023.","title":"Are transformers effective for time series forecasting","authors":"Ailing Zeng, Muxi Chen, Lei Zhang, Qiang Xu","year":"2023","venue":"Proceedings of the AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":42,"raw":"[Zhang and Yan, 2023] Yunhao Zhang and Junchi Yan. Cross- former: Transformer utilizing cross-dimension dependency for multivariate time series forecasting. In The Eleventh In- ternational Conference on Learning Representations, 2023.","title":"Crossformer: Transformer utilizing cross-dimension dependency for multivariate time series forecasting","authors":"Yan ; ] Yunhao Zhang, Junchi Zhang, Yan","year":"2023","venue":"The Eleventh International Conference on Learning Representations","doi":null,"url":null,"internal_url":null},{"position":43,"raw":"[Zhou et al., 2022a] Haoyi Zhou, Shanghang Zhang, Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, and Wancai Zhang. Informer: Beyond efficient transformer for long sequence time-series forecasting. Proceedings of the AAAI Conference on Artificial Intelligence, page 11106-11115, Sep 2022.","title":"Informer: Beyond efficient transformer for long sequence time-series forecasting","authors":"Zhou","year":"2022","venue":"Proceedings of the AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":44,"raw":"[Zhou et al., 2022b] Tian Zhou, Ziqing Ma, Qingsong Wen, Xue Wang, Liang Sun, and Rong Jin. Fedformer: Fre- quency enhanced decomposed transformer for long-term series forecasting. In International Conference on Machine Learning, pages 27268-27286. PMLR, 2022.","title":"Fedformer: Frequency enhanced decomposed transformer for long-term series forecasting","authors":"Zhou","year":"2022","venue":"International Conference on Machine Learning","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}