I would like to highlight the importance of some principles such as "温故而知新,可以为师矣" and "三人行,必有我师焉". Your contibutions to my materials would be highly appreciated.

Teaching Assistant

Upcoming soon.

Teaching Activities

Definition, properties, and derivatives of matrix traces. March 31, 2024. [Slides] [Video]

Blog Post

I enjoy writing some stories for explaining my research. The content includes spatial (geospatial) data science, machine learning, matrix computations, and high-dimensional data analysis.


37. An introduction to Laplacian convolutional representation. July 22, 2023. [Link]
36. Derivatives with circular convolution in machine learning. June 23, 2023. [Link]
35. Kronecker product: A tutorial. June 13, 2023. [Link]
33. Low-rank matrix and tensor factorization for speed field reconstruction. March 9, 2023. [Link]
32. Intuitive understanding of tensors in machine learning. January 21, 2023. [Link]


30. Low-rank Laplacian convolution model for color image inpainting. December 17, 2022. [Link]
29. Low-rank Laplacian convolution model for time series imputation and image inpainting. December 10, 2022. [Link]
28. Circulant matrix nuclear norm minimization for image inpainting in Python. December 9, 2022. [Link]
27. Matrix factorization for image inpainting in Python. December 8, 2022. [Link]
26. Discrete convolution and fast Fourier transform explained and implemented step by step. October 19, 2022. [Link]
25. Simple linear models for image deblurring. October 12, 2022. [Link]
24. Visualizing station-level USA temperature data in Python. October 8, 2022. [Link]
23. Reinforce matrix factorization for time series modeling: Probabilistic sequential matrix factorization. October 5, 2022. [Link]
22. Convolution nuclear norm minimization for time series modeling. October 3, 2022. [Link]
20. Reproducing dynamic mode decomposition on fluid flow data in Python. September 6, 2022. [Link] [Data]
19. Tensor autoregression: A multidimensional time series model. September 3, 2022. [Link]
18. Montreal bikeshare data analysis II: Visualizing bike trips on road networks. August 29, 2022. [Link]
17. Montreal bikeshare data analysis I: Bikeshare station visualization and analysis. August 25, 2022. [Link]
16. Implementing Kronecker product decomposition with NumPy. June 20, 2022. [Link]
14. Forecasting multivariate time series with nonstationary temporal matrix factorization. April 25, 2022. [Link]
13. Temporal matrix factorization for multivariate time series forecasting. March 20, 2022. [Link] 5,000+ views
12. Inpainting fluid dynamics with tensor decomposition (NumPy). March 15, 2022. [Link]
11. Using conjugate gradient to solve matrix equations. February 23, 2022. [Link]
10. Intuitive understanding of Newton-Raphson method. February 16, 2022. [Link]
9. Awesome-LaTeX-drawing: A collection of academic drawing examples using LaTeX. February 14, 2022. [Link]
8. Analyzing missing data problem in Uber movement speed data. February 14, 2022. [Link]


7. Dynamic mode decomposition for spatiotemporal traffic speed time series in Seattle freeway. October 29, 2021. [Link]
6. Reduced-rank vector autoregressive model for high-dimensional time series forecasting. October 16, 2021. [Link] 4,000+ views
4. Generating random numbers and arrays in Matlab and Numpy. October 9, 2021. [Link]
3. Understanding Lyapunov equation through Kronecker product and linear equation. October 8, 2021. [Link]


1. Intuitive understanding of randomized singular value decomposition. July 1, 2020. [Link] 10,000+ views

Favoriate Books/Textbooks

Computer Vision

Per Christian Hansen, James G. Nagy, and Dianne P. O'Leary (2006). Deblurring images: Matrices, spectra, and filtering. SIAM. [Book notes] [LaTeX code]
Richard Szeliski (2022). Computer Vision: Algorithms and Applications. Springer. Second Edition. [Book website]

Machine Learning

Jean Gallier and Jocelyn Quaintance (2022). Algebra, topology, differential calculus, and optimization theory for computer science and machine learning. [PDF]
Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar (2018). Foundations of Machine Learning. MIT Press. Second Edition. [Book website]
Shai Shalev-Shwartz and Shai Ben-David (2014). Understanding Machine Learning: From Theory to Algorithms. Cambridge University Press. [PDF]
Andreas Lindholm, Niklas Wahlström, Fredrik Lindsten, and Thomas B. Schön (2022). Machine Learning: A First Course for Engineers and Scientists. [PDF]
Francis Bach (2023). Learning Theory from First Principles. Draft. [PDF]
Jeff Erickson (2019). Algorithms. [Book website] [GitHub]
Mykel J. Kochenderfer, Tim A. Wheeler, and Kyle H. Wray (2020). Algorithms for Decision Making. MIT Press. [PDF]
Tong Zhang (2023). Mathematical Analysis of Machine Learning Algorithms. Cambridge University Press. [Book website]

Deep Learning

Simon J.D. Prince (2023). Understanding Deep Learning. MIT Press. [Book website]
Daniel A. Roberts, Sho Yaida, and Boris Hanin (2021). The Principles of Deep Learning Theory. [PDF]
M. Weiler (2023). Equivariant and Coordinate Independent Convolutional Networks: A Guide Field Theory of Neural Networks. [PDF]

Data Science

Jesús Rogel-Salazar (2020). Advanced Data Science and Analytics with Python. CRC Press. [PDF]
Dirk P. Kroese, Zdravko I. Botev, Thomas Taimre, and Radislav Vaisman (2022). Data Science and Machine Learning: Mathematical and Statistical Methods. [PDF]
Giacomo Bonanno (2018). Game Theory. Second Edition. [PDF]
Vijay Kotu and Bala Deshpande (2019). Data Science: Concepts and Practice. Elsevier. Second Edition. [PDF]

Optimization Problem

B. Guenin, J. Konemann, and L. Tuncel (2014). A Gentle Introduction to Optimization. Cambridge University Press. [PDF]

Information Theory

Yury Polyanskiy and Yihong Wu (2022). Information Theory: From Coding to Learning. [PDF]
Gabriel Peyre (2020). The Discrete Algebra of the Fourier Transform. [PDF]