{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T17:01:35Z","timestamp":1757610095393,"version":"3.44.0"},"reference-count":44,"publisher":"Association for Computing Machinery (ACM)","issue":"8","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["Proc. VLDB Endow."],"published-print":{"date-parts":[[2025,4]]},"abstract":"<jats:p>Trajectory metric learning, which supports the trajectory similarity search, is one of the most fundamental tasks in spatial-temporal data analysis. However, existing trajectory metric learning methods rely on massive labels of pairwise trajectory distance, and thus cannot be applied to few-shot scenarios frequently occurring in real-world applications. Though performance drops caused by insufficient labels can be alleviated by knowledge distillation, we demonstrate that they cannot be directly applied to few-shot trajectory metric learning due to the domain shift problem. To this end, this paper proposes invariant and relaxed learning enhanced knowledge distillation method TMLKD for few-shot trajectory metric learning, such that domain-invariant representation and rank knowledge can be distilled. Specifically, in the representation learning phase, it first employs an adversarial sub-network to distinguish domain-specific and domain-invariant information, so as to distill transferable representation knowledge from teacher models. To mitigate the few-shot problem in student model training, we further enrich sparse labels of the target domain by utilizing the rank knowledge revealed in teachers' predictions. Particularly, TMLKD employs a list-wise learning-to-rank approach to learn the relaxed trajectory ranking orders instead of focusing on all the samples inefficiently. Finally, to guide accurate distillation, we adaptively assign reliability of teacher prediction by utilizing the ground-truth labels, to avoid misleading the student model with low-quality teacher predictions. Extensive experiments on three real-world datasets demonstrate the superiority of our model.<\/jats:p>","DOI":"10.14778\/3742728.3742729","type":"journal-article","created":{"date-parts":[[2025,9,3]],"date-time":"2025-09-03T13:32:53Z","timestamp":1756906373000},"page":"2308-2320","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["TMLKD: Few-Shot Trajectory Metric Learning via Knowledge Distillation"],"prefix":"10.14778","volume":"18","author":[{"given":"Danling","family":"Lai","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Soochow University, Suzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiajie","family":"Xu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Data Intelligence and Advanced Computing, Soochow University, Suzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianfeng","family":"Qu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Data Intelligence and Advanced Computing, Soochow University, Suzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pingfu","family":"Chao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Data Intelligence and Advanced Computing, Soochow University, Suzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junhua","family":"Fang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Data Intelligence and Advanced Computing, Soochow University, Suzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chengfei","family":"Liu","sequence":"additional","affiliation":[{"name":"Swinburne University of Technology, Melbourn, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2025,9,3]]},"reference":[{"volume-title":"Efficient Algorithms, Essays Dedicated to Kurt Mehlhorn on the Occasion of His 60th Birthday (Lecture Notes in Computer Science), Susanne Albers, Helmut Alt, and Stefan N\u00e4her (Eds.)","author":"Alt Helmut","key":"e_1_2_1_1_1","unstructured":"Helmut Alt. 2009. The Computational Geometry of Comparing Shapes. In Efficient Algorithms, Essays Dedicated to Kurt Mehlhorn on the Occasion of His 60th Birthday (Lecture Notes in Computer Science), Susanne Albers, Helmut Alt, and Stefan N\u00e4her (Eds.), Vol. 5760. 235\u2013248."},{"key":"e_1_2_1_2_1","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1142\/S0218195995000064","article-title":"Computing the Fr\u00e9chet distance between two polygonal curves","volume":"5","author":"Alt Helmut","year":"1995","unstructured":"Helmut Alt and Michael Godau. 1995. Computing the Fr\u00e9chet distance between two polygonal curves. Int. J. Comput. Geom. Appl. 5 (1995), 75\u201391.","journal-title":"Int. J. Comput. Geom. Appl."},{"volume-title":"AAAI Workshop, Usama M. Fayyad and Ramasamy Uthurusamy (Eds.). 359\u2013370","author":"Donald","key":"e_1_2_1_3_1","unstructured":"Donald J. Berndt and James Clifford. 1994. Using Dynamic Time Warping to Find Patterns in Time Series. In AAAI Workshop, Usama M. Fayyad and Ramasamy Uthurusamy (Eds.). 359\u2013370."},{"key":"e_1_2_1_4_1","unstructured":"Konstantinos Bousmalis George Trigeorgis Nathan Silberman Dilip Krishnan and Dumitru Erhan. 2016. Domain Separation Networks. In NIPS. 343\u2013351."},{"key":"e_1_2_1_5_1","doi-asserted-by":"crossref","unstructured":"Wei-Lun Chang Hui-Po Wang Wen-Hsiao Peng and Wei-Chen Chiu. 2019. All about structure: Adapting structural information across domains for boosting semantic segmentation. In CVPR. 1900\u20131909.","DOI":"10.1109\/CVPR.2019.00200"},{"key":"e_1_2_1_6_1","doi-asserted-by":"crossref","unstructured":"Yanchuan Chang Jianzhong Qi Yuxuan Liang and Egemen Tanin. 2023. Contrastive Trajectory Similarity Learning with Dual-Feature Attention. In ICDE. 2933\u20132945.","DOI":"10.1109\/ICDE55515.2023.00224"},{"key":"e_1_2_1_7_1","doi-asserted-by":"crossref","unstructured":"Cen Chen Chengyu Wang Minghui Qiu Dehong Gao Linbo Jin and Wang Li. 2021. Cross-domain knowledge distillation for retrieval-based question answering systems. In WWW. 2613\u20132623.","DOI":"10.1145\/3442381.3449814"},{"key":"e_1_2_1_8_1","volume-title":"Ng","author":"Chen Lei","year":"2004","unstructured":"Lei Chen and Raymond T. Ng. 2004. On The Marriage of Lp-norms and Edit Distance. In VLDB, Mario A. Nascimento, M. Tamer \u00d6zsu, Donald Kossmann, Ren\u00e9e J. Miller, Jos\u00e9 A. Blakeley, and K. Bernhard Schiefer (Eds.). 792\u2013803."},{"key":"e_1_2_1_9_1","doi-asserted-by":"crossref","unstructured":"Lei Chen M. Tamer \u00d6zsu and Vincent Oria. 2005. Robust and Fast Similarity Search for Moving Object Trajectories. In SIGMOD Fatma \u00d6zcan (Ed.). 491\u2013502.","DOI":"10.1145\/1066157.1066213"},{"key":"e_1_2_1_10_1","doi-asserted-by":"crossref","unstructured":"Wei Chen Shuzhe Li Chao Huang Yanwei Yu Yongguo Jiang and Junyu Dong. 2022. Mutual Distillation Learning Network for Trajectory-User Linking. In IJCAI. 1973\u20131979.","DOI":"10.24963\/ijcai.2022\/274"},{"key":"e_1_2_1_11_1","first-page":"1","article-title":"Approximating the (Continuous) Fr\u00e9chet Distance","volume":"189","author":"Colombe Connor","year":"2021","unstructured":"Connor Colombe and Kyle Fox. 2021. Approximating the (Continuous) Fr\u00e9chet Distance. In SoCG, Vol. 189. 26:1\u201326:14.","journal-title":"SoCG"},{"volume-title":"Few-Shot Class-Incremental Learning via Relation Knowledge Distillation","author":"Dong Songlin","key":"e_1_2_1_12_1","unstructured":"Songlin Dong, Xiaopeng Hong, Xiaoyu Tao, Xinyuan Chang, Xing Wei, and Yihong Gong. 2021. Few-Shot Class-Incremental Learning via Relation Knowledge Distillation. In AAAI. AAAI Press, 1255\u20131263."},{"key":"e_1_2_1_13_1","doi-asserted-by":"crossref","unstructured":"Ziquan Fang Yuntao Du Lu Chen Yujia Hu Yunjun Gao and Gang Chen. 2021. E2DTC: An End to End Deep Trajectory Clustering Framework via Self-Training. In ICDE. 696\u2013707.","DOI":"10.1109\/ICDE51399.2021.00066"},{"volume-title":"E2dtc: An end to end deep trajectory clustering framework via self-training","author":"Fang Ziquan","key":"e_1_2_1_14_1","unstructured":"Ziquan Fang, Yuntao Du, Lu Chen, Yujia Hu, Yunjun Gao, and Gang Chen. 2021. E2dtc: An end to end deep trajectory clustering framework via self-training. In ICDE. IEEE, 696\u2013707."},{"key":"e_1_2_1_15_1","doi-asserted-by":"crossref","unstructured":"Takashi Fukuda Masayuki Suzuki Gakuto Kurata Samuel Thomas Jia Cui and Bhuvana Ramabhadran. 2017. Efficient Knowledge Distillation from an Ensemble of Teachers. In INTERSPEECH. 3697\u20133701.","DOI":"10.21437\/Interspeech.2017-614"},{"key":"e_1_2_1_16_1","first-page":"108","article-title":"Fast Similarity Search of Multi-Dimensional Time Series via Segment Rotation","volume":"9049","author":"Gong Xudong","year":"2015","unstructured":"Xudong Gong, Yan Xiong, Wenchao Huang, Lei Chen, Qiwei Lu, and Yiqing Hu. 2015. Fast Similarity Search of Multi-Dimensional Time Series via Segment Rotation. In DASFAA, Vol. 9049. 108\u2013124.","journal-title":"DASFAA"},{"key":"e_1_2_1_17_1","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1109\/LRA.2020.3048652","article-title":"Human Trajectory Prediction Using Similarity-Based Multi-Model Fusion","volume":"6","author":"Habibi Golnaz","year":"2021","unstructured":"Golnaz Habibi and Jonathan P. How. 2021. Human Trajectory Prediction Using Similarity-Based Multi-Model Fusion. IEEE Robotics Autom. Lett. 6, 2 (2021), 715\u2013722.","journal-title":"IEEE Robotics Autom. Lett."},{"key":"e_1_2_1_18_1","volume-title":"Distilling the Knowledge in a Neural Network. CoRR abs\/1503.02531","author":"Hinton Geoffrey E.","year":"2015","unstructured":"Geoffrey E. Hinton, Oriol Vinyals, and Jeffrey Dean. 2015. Distilling the Knowledge in a Neural Network. CoRR abs\/1503.02531 (2015)."},{"key":"e_1_2_1_19_1","volume-title":"Spatio-Temporal Trajectory Similarity Measures: A Comprehensive Survey and Quantitative Study. CoRR abs\/2303.05012","author":"Hu Danlei","year":"2023","unstructured":"Danlei Hu, Lu Chen, Hanxi Fang, Ziquan Fang, Tianyi Li, and Yunjun Gao. 2023. Spatio-Temporal Trajectory Similarity Measures: A Comprehensive Survey and Quantitative Study. CoRR abs\/2303.05012 (2023)."},{"key":"e_1_2_1_20_1","first-page":"8150","article-title":"POEM","volume":"37","author":"Jo Sang-Yeong","year":"2023","unstructured":"Sang-Yeong Jo and Sung Whan Yoon. 2023. POEM: Polarization of Embeddings for Domain-Invariant Representations. 37 (2023), 8150\u20138158.","journal-title":"Polarization of Embeddings for Domain-Invariant Representations."},{"key":"e_1_2_1_21_1","volume-title":"DERRD: A Knowledge Distillation Framework for Recommender System. In CIKM. 605\u2013614.","author":"Kang SeongKu","year":"2020","unstructured":"SeongKu Kang, Junyoung Hwang, Wonbin Kweon, and Hwanjo Yu. 2020. DERRD: A Knowledge Distillation Framework for Recommender System. In CIKM. 605\u2013614."},{"key":"e_1_2_1_22_1","doi-asserted-by":"crossref","unstructured":"Jingzhi Li Zidong Guo Hui Li Seungju Han Ji-Won Baek Min Yang Ran Yang and Sungjoo Suh. 2023. Rethinking Feature-based Knowledge Distillation for Face Recognition. In CVPR. 20156\u201320165.","DOI":"10.1109\/CVPR52729.2023.01930"},{"volume-title":"Deep representation learning for trajectory similarity computation","author":"Li Xiucheng","key":"e_1_2_1_23_1","unstructured":"Xiucheng Li, Kaiqi Zhao, Gao Cong, Christian S Jensen, and Wei Wei. 2018. Deep representation learning for trajectory similarity computation. In ICDE. IEEE, 617\u2013628."},{"key":"e_1_2_1_24_1","unstructured":"Pengfei Liu Xipeng Qiu and Xuanjing Huang. 2017. Adversarial Multi-task Learning for Text Classification. In ACL Regina Barzilay and Min-Yen Kan (Eds.). 1\u201310."},{"key":"e_1_2_1_25_1","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.neucom.2020.07.048","article-title":"Adaptive multi-teacher multi-level knowledge distillation","volume":"415","author":"Liu Yuang","year":"2020","unstructured":"Yuang Liu, Wei Zhang, and Jun Wang. 2020. Adaptive multi-teacher multi-level knowledge distillation. Neurocomputing 415 (2020), 106\u2013113.","journal-title":"Neurocomputing"},{"key":"e_1_2_1_26_1","doi-asserted-by":"crossref","unstructured":"Alessio Monti Angelo Porrello Simone Calderara Pasquale Coscia Lamberto Ballan and Rita Cucchiara. 2022. How many Observations are Enough? Knowledge Distillation for Trajectory Forecasting. In CVPR. 6543\u20136552.","DOI":"10.1109\/CVPR52688.2022.00644"},{"key":"e_1_2_1_27_1","volume-title":"Time-evolving OD matrix estimation using high-speed GPS data streams. Expert systems with Applications 44","author":"Moreira-Matias Lu\u00eds","year":"2016","unstructured":"Lu\u00eds Moreira-Matias, Jo\u00e3o Gama, Michel Ferreira, Jo\u00e3o Mendes-Moreira, and Luis Damas. 2016. Time-evolving OD matrix estimation using high-speed GPS data streams. Expert systems with Applications 44 (2016), 275\u2013288."},{"key":"e_1_2_1_28_1","volume-title":"Fahad Shahbaz Khan, and Mubarak Shah","author":"Rajasegaran Jathushan","year":"2021","unstructured":"Jathushan Rajasegaran, Salman Khan, Munawar Hayat, Fahad Shahbaz Khan, and Mubarak Shah. 2021. Self-supervised Knowledge Distillation for Few-shot Learning. In BMVC. 179\u2013192."},{"volume-title":"Indexing and matching trajectories under inconsistent sampling rates","author":"Ranu Sayan","key":"e_1_2_1_29_1","unstructured":"Sayan Ranu, Padmanabhan Deepak, Aditya D Telang, Prasad Deshpande, and Sriram Raghavan. 2015. Indexing and matching trajectories under inconsistent sampling rates. In ICDE. IEEE, 999\u20131010."},{"key":"e_1_2_1_30_1","volume-title":"Antoine Chassang, Carlo Gatta, and Yoshua Bengio.","author":"Romero Adriana","year":"2015","unstructured":"Adriana Romero, Nicolas Ballas, Samira Ebrahimi Kahou, Antoine Chassang, Carlo Gatta, and Yoshua Bengio. 2015. FitNets: Hints for Thin Deep Nets. In ICLR."},{"key":"e_1_2_1_31_1","doi-asserted-by":"crossref","unstructured":"Yasushi Sakurai Masatoshi Yoshikawa and Christos Faloutsos. 2005. FTW: fast similarity search under the time warping distance. In ACM SIGACT-SIGMOD-SIGART. 326\u2013337.","DOI":"10.1145\/1065167.1065210"},{"key":"e_1_2_1_32_1","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s00778-019-00574-9","article-title":"A survey of trajectory distance measures and performance evaluation","volume":"29","author":"Su Han","year":"2020","unstructured":"Han Su, Shuncheng Liu, Bolong Zheng, Xiaofang Zhou, and Kai Zheng. 2020. A survey of trajectory distance measures and performance evaluation. VLDB J. 29, 1 (2020), 3\u201332.","journal-title":"VLDB J."},{"key":"e_1_2_1_33_1","volume-title":"Ranking Distillation: Learning Compact Ranking Models With High Performance for Recommender System. In SIGKDD. 2289\u20132298.","author":"Tang Jiaxi","year":"2018","unstructured":"Jiaxi Tang and Ke Wang. 2018. Ranking Distillation: Learning Compact Ranking Models With High Performance for Recommender System. In SIGKDD. 2289\u20132298."},{"key":"e_1_2_1_34_1","volume-title":"Distilling task-specific knowledge from bert into simple neural networks. arXiv preprint arXiv:1903.12136","author":"Tang Raphael","year":"2019","unstructured":"Raphael Tang, Yao Lu, Linqing Liu, Lili Mou, Olga Vechtomova, and Jimmy Lin. 2019. Distilling task-specific knowledge from bert into simple neural networks. arXiv preprint arXiv:1903.12136 (2019)."},{"key":"e_1_2_1_35_1","doi-asserted-by":"crossref","first-page":"3048","DOI":"10.1109\/TPAMI.2021.3055564","article-title":"Knowledge distillation and student-teacher learning for visual intelligence: A review and new outlooks","volume":"44","author":"Wang Lin","year":"2021","unstructured":"Lin Wang and Kuk-Jin Yoon. 2021. Knowledge distillation and student-teacher learning for visual intelligence: A review and new outlooks. IEEE Transactions on Pattern Analysis and Machine Intelligence 44, 6 (2021), 3048\u20133068.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"e_1_2_1_36_1","volume-title":"Enhancing Mapless Trajectory Prediction through Knowledge Distillation. CoRR abs\/2306.14177","author":"Wang Yuning","year":"2023","unstructured":"Yuning Wang, Pu Zhang, Lei Bai, and Jianru Xue. 2023. Enhancing Mapless Trajectory Prediction through Knowledge Distillation. CoRR abs\/2306.14177 (2023)."},{"key":"e_1_2_1_37_1","unstructured":"Meng-Chieh Wu Ching-Te Chiu and Kun-Hsuan Wu. 2019. Multi-teacher Knowledge Distillation for Compressed Video Action Recognition on Deep Neural Networks. In ICASSP. 2202\u20132206."},{"key":"e_1_2_1_38_1","first-page":"1","article-title":"Approximating Dynamic Time Warping Distance Between Run-Length Encoded Strings","volume":"244","author":"Xi Zoe","year":"2022","unstructured":"Zoe Xi and William Kuszmaul. 2022. Approximating Dynamic Time Warping Distance Between Run-Length Encoded Strings. In ESA, Vol. 244. 90:1\u201390:19.","journal-title":"ESA"},{"key":"e_1_2_1_39_1","doi-asserted-by":"crossref","unstructured":"Chenxiao Yang Junwei Pan Xiaofeng Gao Tingyu Jiang Dapeng Liu and Guihai Chen. 2022. Cross-Task Knowledge Distillation in Multi-Task Recommendation. In AAAI. 4318\u20134326.","DOI":"10.1609\/aaai.v36i4.20352"},{"key":"e_1_2_1_40_1","doi-asserted-by":"crossref","unstructured":"Peilun Yang Hanchen Wang Ying Zhang Lu Qin Wenjie Zhang and Xuemin Lin. 2021. T3S: Effective Representation Learning for Trajectory Similarity Computation. In ICDE. 2183\u20132188.","DOI":"10.1109\/ICDE51399.2021.00221"},{"key":"e_1_2_1_41_1","doi-asserted-by":"crossref","unstructured":"Ze Yang Linjun Shou Ming Gong Wutao Lin and Daxin Jiang. 2020. Model Compression with Two-stage Multi-teacher Knowledge Distillation for Web Question Answering System. In WSDM. 690\u2013698.","DOI":"10.1145\/3336191.3371792"},{"key":"e_1_2_1_42_1","doi-asserted-by":"crossref","unstructured":"Di Yao Gao Cong Chao Zhang and Jingping Bi. 2019. Computing Trajectory Similarity in Linear Time: A Generic Seed-Guided Neural Metric Learning Approach. In ICDE. 1358\u20131369.","DOI":"10.1109\/ICDE.2019.00123"},{"key":"e_1_2_1_43_1","doi-asserted-by":"crossref","unstructured":"Di Yao Haonan Hu Lun Du Gao Cong Shi Han and Jingping Bi. 2022. Traj-GAT: A Graph-based Long-term Dependency Modeling Approach for Trajectory Similarity Computation. In SIGKDD. 2275\u20132285.","DOI":"10.1145\/3534678.3539358"},{"key":"e_1_2_1_44_1","doi-asserted-by":"crossref","unstructured":"Hanyuan Zhang Xinyu Zhang Qize Jiang Baihua Zheng Zhenbang Sun Weiwei Sun and Changhu Wang. 2020. Trajectory Similarity Learning with Auxiliary Supervision and Optimal Matching. In IJCAI. 3209\u20133215.","DOI":"10.24963\/ijcai.2020\/444"}],"container-title":["Proceedings of the VLDB Endowment"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.14778\/3742728.3742729","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,3]],"date-time":"2025-09-03T13:34:37Z","timestamp":1756906477000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.14778\/3742728.3742729"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4]]},"references-count":44,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2025,4]]}},"alternative-id":["10.14778\/3742728.3742729"],"URL":"https:\/\/doi.org\/10.14778\/3742728.3742729","relation":{},"ISSN":["2150-8097"],"issn-type":[{"type":"print","value":"2150-8097"}],"subject":[],"published":{"date-parts":[[2025,4]]},"assertion":[{"value":"2025-09-03","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}