一、个人简介

曹飞龙，男，二级教授，博士生导师。2003 年 4 月获西安交通大学理学博士学位，现为浙江师范大学杰出教授，工作单位为浙江师范大学数学科学学院交叉科学系、杭州数学与交叉科学研究院。入选浙江省高校中青年学科带头人、浙江省 “新世纪 151 优秀人才” 第二层次，2022 至 2024 年均入选全球前 2% 顶尖科学家 “年度科学影响力排行榜” 和 “终身科学影响力排行榜” 榜单。现任中国人工智能学会粒计算与知识发现专业委员会荣誉常务委员、中国人工智能学会机器学习专业委员会委员、浙江省数学会常务理事、浙江省应用数学会常务理事。

二、主要研究兴趣

人工智能的数学基础、机器学习理论及其应用

三、主持的主要科研项目

1. 1. 国家自然科学基金重点项目 “深度神经网络的逼近理论与高效算法”，批准号：62536006，执行时间：2026.01-2030.12

2. 2. 国家自然科学基金重点项目 “面向 3D 对象分析与生成的深度学习理论与方法”（合作单位负责人），批准号：62032022，执行时间：2021.01-2025.12

3. 3. 国家自然科学基金 “高性能计算与可计算建模” 重大研究计划项目 “矩阵恢复的稀疏正则化算法及其应用”，批准号：91330118，执行时间：2014.01-2016.12

4. 4. 国家自然科学基金 “可信软件” 重大研究计划项目 “基于逼近理论的误差可控计算与可信算法研究”，批准号：90818020，执行时间：2009.01-2011.12

5. 5. 国家自然科学基金面上项目 “深度神经网络逼近问题”，批准号：62176244，执行时间：2022.01-2025.12

6. 6. 国家自然科学基金面上项目 “基于稀疏表示的超分辨率重建自适应算法与深度卷积神经网络方法”，批准号：61672477，执行时间：2017.01-2020.12

7. 7. 国家自然科学基金面上项目 “基于球调和分析理论的信号稀疏表示与重构算法”，批准号：61272023，执行时间：2013.01-2016.12

8. 8. 国家自然科学基金面上项目 “球面学习理论研究”，批准号：60873206，执行时间：2009.01-2011.12

9. 9. 国家自然科学基金面上项目 “关于神经网络结构复杂性与本质逼近阶研究”，批准号：60473034，执行时间：2005.01-2007.12

10. 10. 国家自然科学基金国际合作与交流项目 “超强学习机”，批准号：61110306122，执行时间：2011.01-2012.12

11. 11. 浙江省自然科学基金重点项目 “深度学习的逼近理论、方法及应用”，批准号：LZ20F030001，执行时间：2020.01-2023.12

12. 12. 浙江省高校科技重点项目 “球面数据挖掘与神经计算”，批准号：20060543，执行时间：2006.01-2008.12

13. 13. 教育部科学技术重点基金项目 “前向人工神经网络逼近算法与逼近阶估计”，批准号：03142，执行时间：2003.01-2004.12

14. 14. 企业横向课题 “血液细胞图像、数据分析与处理”，浙江嘉克戴斯医疗器械公司委托，时间：2013.09-2014.12

四、代表性论文

1. 1. Yao K, Liang J-Y, Liang J, Li M, Cao F. Multi-view graph convolutional networks with attention mechanism. Artificial Intelligence, 2022, 307: 103708（中科院一区，Top 期刊，CCF、CAAI A 类）.

2. 2. Du Z, Liang J-Y, Liang J, Yao K, Cao F. Graph regulation network for point cloud segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024, 46 (12): 7940-7955（中科院一区，Top 期刊，CCF、CAAI A 类）.

3. 3. Liang J-Y, Du Z, Liang J, Yao K, Cao F. Long and short-range dependency graph structure learning framework on the point cloud. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2023, 45 (12): 14975-14989（中科院一区，Top 期刊，CCF、CAAI A 类）.

4. 4. Huang C, Li M, Cao F, Fujita H, Li Z, Wu X. Are graph convolutional networks with random weights feasible? IEEE Transactions on Pattern Analysis and Machine Intelligence, 2023, 45 (3): 2751-2768（中科院一区，Top 期刊，CCF、CAAI A 类）.

5. 5. Xu Z-B, Cao F. The essential order of approximation for neural networks. Science in China, Series F: Information Sciences, 2004, 47: 97-112（中科院一区，Top 期刊，CCF、CAAI A 类）.

6. 6. Cao F, Zhang Y, Xu Z-B. The lower estimation of approximation rate for neural networks. Science in China, Series F: Information Sciences, 2009, 52 (8): 1321-1327（中科院一区，Top 期刊，CCF、CAAI A 类）.

7. 7. Xu Z-B, Zhang Y, Cao F*. Estimation of convergence rate for multi-regression learning algorithm. Science in China, Series F: Information Sciences, 2012, 55 (3): 701-713（中科院一区，Top 期刊，CCF、CAAI A 类）.

8. 8. Cao F, Lin S, Chang X-Y, Xu Z-B. Learning rates of regularized regression on the unit sphere. Science in China, Series A: Mathematics, 2013, 56 (4): 861-876（中科院一区，Top 期刊）.

9. 9. Lin S, Cao F, Xu Z-B. The essential rate of approximation for radial function manifold. Science in China, Series A: Mathematics, 2011, 54 (9): 1985-1994（中科院一区，Top 期刊）.

10. 10. Cao F, Cai M, Tan Y, Zhao J. Image super-resolution via adaptive ℓp (0 < p < 1) regularization and sparse representation. IEEE Transactions on Neural Networks Learning Systems, 2016, 27 (7): 1550-1561（中科院一区，Top 期刊，CAAI A 类）.

11. 11. Du Z, Ye H, Cao F*. A novel local–global graph convolutional method for point cloud semantic segmentation. IEEE Transactions on Neural Networks and Learning Systems, 2024, 35 (4): 4798-4812（中科院一区，Top 期刊，CAAI A 类）.

12. 12. Wu J, Cao F, Yin J. Nonlocaly multi-morphological representation for image reconstruction from compressive measurements. IEEE Transactions Image Processing, 2017, 26 (12): 5730-5742（中科院一区，Top 期刊，CCF、CAAI A 类）.

13. 13. Pan C, Liu J, Yan W, Cao F, He W, Zhou Y. Salient object detection based on visual perceptual saturation and two-stream hybrid networks. IEEE Transactions on Image Processing, 2021, 30: 4773-4787（中科院一区，Top 期刊，CCF、CAAI A 类）.

14. 14. Ye H, Li H, Cao F, Zhang L. A hybird truncated norm regularization method for matrix completion. IEEE Transactions on Image Processing, 2019, 28 (10): 5171-5186（中科院一区，Top 期刊，CCF、CAAI A 类）.

15. 15. Cao F, Situ Y, Ye H. A Joint Multiscale graph attention and classify-driven autoencoder framework for hyperspectral unmixing. IEEE Transactions on Geoscience and Remote Sensing, 2025, 63: 5504514（中科院一区，Top 期刊，CAAI A 类）.

16. 16. Guo W, Ye H, Cao F*. Feature-grouped network with spectral–spatial connected attention for hyperspectral image classification. IEEE Transactions Geosciens and Remote Sensing, 2022, 60: 1-13（中科院一区，Top 期刊，CAAI A 类）.

17. 17. Yang B, Cao F, Ye H. A novel method for hyperspectral image classification: Deep network with adaptive graph structure integration. IEEE Transactions on Geoscience and Remote Sensing, 2022, 60: 5523512（中科院一区，Top 期刊，CAAI A 类）.

18. 18. Ye H, Li H, Yang B, Cao F, Tang Y Y. A novel rank approximation method for mixture noise removal of hyperspectral images. IEEE Transactions Geosciens and Remote Sensing, 2019, 57 (7): 4457-4469（中科院一区，Top 期刊）.

19. 19. Yang B, Ye H, Li M, Cao F, Pan S. GoLoG: Global-to-local decoupling graph network with joint optimization for hyperspectral image classification. IEEE Transactions on Geoscience and Remote Sensing, 2023, 61: 5528014（中科院一区，Top 期刊，CAAI A 类）.

20. 20. Cao F, Xu Q, Ye H. Adaptive Prior and Long-Range Dependency-Based Learners for Image Inpainting. IEEE Transactions on Circuits and Systems for Video Technology, 2025, DOI: 10.1109/TCSVT.2025.3574529（中科院一区，Top 期刊）.

21. 21. Cao F, Wang L, Ye H. SharpGConv: A Novel graph method with plug-and-play sharpening convolution for point cloud registration. IEEE Transactions on Circuits and Systems for Video Technology, 2024, 34 (8): 7095-7105（中科院一区，Top 期刊）.

22. 22. Cao F, Cai M, Tan Y. Image interpolation via low-rank matrix completion and recovery. IEEE Transactions Circus Systems for Video Technology, 2015, 25 (8): 1261-1270（中科院一区，Top 期刊）.

23. 23. Cao F, Ye X, Ye H. A multi-view graph contrastive learning framework for defending against adversarial attacks. IEEE Transactions on Emerging Topics in Computational Intelligence, 2024, 8 (6): 4022-4032（中科院一区）.

24. 24. Cao F, Chen Q, Ye H. A New strategy of graph structure attack: Multi-view perturbation candidate edge learning. IEEE Transactions on Network Science and Engineering, 2024, 11 (5): 4158-4168（中科院一区）.

25. 25. Liu Y, Cao F*, Zhao J, Chu J. Segmentation of white blood cells image using adaptive location and iteration. IEEE Journal of Biomedical and Health Informatics, 2017, 21 (6): 1644-1655（中科院一区，Top 期刊）.

26. 26. Jiang Q, Ye H, Yang B, Cao F*. Label-decoupled medical image segmentation with spatial-channel graph convolution and dual attention enhancement. IEEE Journal of Biomedical and Health Informatics, 2024, 28 (5): 2830-2841（中科院一区，Top 期刊）.

27. 27. Cao F, Dai T, Zhang Y, Tan Y. Compressed classification learning with Markov chain samples. Neural Networks, 2014, 50: 90-97（国际神经网络学会、欧洲神经网络学会、日本神经网络学会会刊，中科院一区，Top 期刊）.

28. 28. Cao F, Chen J, Ye H, Zhao J, Zhou Z. A novel approach for recovering low-rank and sparse matrix based on the truncated nuclear norm. Neural Networks, 2017, 85: 1020（中科院一区，Top 期刊）.

29. 29. Miao J, Cao F*, Ye H, Li M, Yang B. Revisiting graph neural networks from hybrid regularized graph signal reconstruction. Neural Networks, 2023, 157: 444-459（中科院一区，Top 期刊）.

30. 30. Zhang Y, Cao F*. Analysis of convergence performance of neural networks ranking algorithm. Neural Networks, 2012, 34: 65-71（中科院一区，Top 期刊）.

31. 31. Chen Q, Cao F*. Distributed support vector machine in master-slave mode. Neural Networks, 2018, 101: 94-100（中科院一区，Top 期刊）.

32. 32. Liu H, Cao F*. Improved dual-scale residual network for image super-resolution. Neural Networks, 2020, 132: 84-95（中科院一区，Top 期刊）.

33. 33. Ye H, Wang Y, Cao F*. A novel meta-learning framework: Multi-features adaptive aggregation method with information enhancer. Neural Networks, 2020, 132: 84-95（中科院一区，Top 期刊）.

34. 34. Cao F, Yao K, Liang J-Y. Deconvolutional neural network for image super-resolution. Neural Networks, 2020, 132: 394-404（中科院一区，Top 期刊）.

35. 35. Zhou T, Ye H, Cao F*. Node-personalized multi-graph convolutional networks for recommendation. Neural Networks, 2024, 173: 106169（中科院一区，Top 期刊）.

36. 36. Cao F, Zhang Y, He Z-R. Interpolation and rate of convergence by a class of neural networks. Applied Mathematical Modelling, 2009, 33: 1441-1456（中科院一区，Top 期刊）.

37. 37. Cao F, Yuan Y. Learning errors of linear programming support vector regression. Applied Mathematical Modelling, 2011, 35: 1820–1828（中科院一区，Top 期刊）.

38. 38. Miao J, Cao F*, Ye H, Li M, Yang B. Triplet Teaching Graph Contrastive Networks with Self-evolving Adaptive Augmentation. Pattern Recognition, 2023, 142: 109687（中科院一区，Top 期刊）.

39. 39. Yao K, Cao F*, Leung Y, Liang J-Y. Deep neural network compression through interpretability-based filter pruning. Pattern Recognition, 2021, 119: 108056（中科院一区，Top 期刊）.

40. 40. Cao F, Shi J, Wen C. A dynamic graph aggregation framework for 3D point cloud registration. Engineering Applications of Artificial Intelligence, 2023, 120: 105817（中科院一区，Top 期刊）.

41. 41. Dai K, Zhao J, Cao F*. A novel algorithm of extended neural networks for image recognition. Engineering Applications of Artificial Intelligence, 2015, 42: 57–66（中科院一区，Top 期刊）.

42. 42. Ye H, Song Y, Li M, Cao F*. A new deep graph attention approach with influence and preference relationship reconstruction for rate prediction recommendation. Information Processing and Management, 2023, 6 (5): 103439（中科院一区，Top 期刊）.

43. 43. Cao F, Tan Y, Cai M. Sparse algorithms of Random Weight Networks and applications. Expert Systems with Applications, 2014, 41: 2457-2462（中科院一区，Top 期刊）.

44. 44. Ye H, Cao F*, Wang D. A hybrid regularization approach for random vector functionallink networks. Expert Systems with Applications, 2020, 140: 112912（中科院一区，Top 期刊）.

45. 45. Cao F, Chen Q, Ye H. An effective targeted label adversarial attack on graph neural networks by strategically allocating the attack budget. Knowledge-Based Systems, 2024, 293: 111689（中科院一区，Top 期刊）.

46. 46. Cao F, Chen B. New architecture of deep recursive convolution networks for superresolution. Knowledge-Based Systems, 2019, 178: 98-110（中科院一区，Top 期刊）.

47. 47. Yu D, Cao F*. Construction and approximation rate for feedforward neural network operators with sigmoidal functions. Journal of Computational and Applied Mathematics, 2025, 453: 116150（ESI 高被引论文，Top 期刊）.

48. 48. Chen Z, Cao F*. The approximation operators with sigmoidal functions. Computers and Mathematics with Applications, 2009, 58: 758-765（ESI 高被引论文，Top 期刊）.

49. 49. 曹飞龙，夏晟。球面混合插值的逼近性质。中国科学，A 辑：数学，2013, 43 (1): 45-60（权威期刊）.

五、代表性专利

1. 1. 曹飞龙，怀听听，赵建伟，周正华，冯爱明，楚建军。一种基于随机森林算法的白细胞五分类方法，专利号：ZL201510398384.1  

2. 2. 曹飞龙，刘月华，楚建军，赵建伟，周正华。一种白细胞定位和迭代方法，专利号：ZL201610227867X  

3. 3. 曹飞龙，冯鑫山，赵建伟，周正华。一种基于字典学习和稀疏表示的人脸识别方法，专利号：ZL20161074469.5  

4. 4. 蔡苗苗，楚建军，曹飞龙，赵建伟，周正华。一种基于直方图阈值及低秩表示的白细胞细胞核分割方法，专利号：ZL2015101410991  

5. 5. 黄震，孔巢城，曹飞龙，赵建伟，周正华。一种基于边界的白细胞分割评价标准，专利号：ZL201510141013.5  

6. 6. 陆晶，楚建军，曹飞龙，赵建伟，周正华。血液白细胞显微图像的随机权网络分割方法，专利号：ZL201510066975.9  

7. 7. 黄震，楚建军，曹飞龙，赵建伟，周正华。一种基于多特征非线性组合的白细胞分割方法，专利号：ZL201510141209.4  

8. 8. 武娇，曹飞龙，银俊成，武丹。基于图像块聚类和稀疏字典学习的分块压缩感知重构方法，专利号：ZL201410314084.6  

9. 9. 武娇，曹飞龙。基于分层高斯混合模型的统计压缩感知图像重构方法，专利号：ZL201610110804.6，授权日期：2018.08.28  

10. 10. 曹飞龙，张焯林。串联式单图像超分辨率重建方法，专利号：ZL202010218654.7，授权日期：2024.02.09  

六、研究生情况

（一）指导研究生

所指导的研究生已获硕士学位 80 多人，推荐出国攻读博士学位 6 人，在国内 985、211 等高校继续深造 29 人，其余大多在 IT 行业工作；6 人获省优秀硕士学位论文，10 人获校优秀硕士学位论文，3 人获浙江省 “新苗人才计划” 资助，5 人次获国家奖学金，历年省硕士学位抽检优秀率 100%。指导的博士研究生已获博士学位 3 人，在读 4 人。

（二）招生情况

招收应用数学方向硕士生和博士生，欢迎数学与应用数学、信息与计算科学、大数据专业及相近专业的同学报考。要求：热爱数学与人工智能交叉研究、能吃苦耐劳。