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How to draw graphical illustrations for tensor and its factorization in LaTeX?

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Throughout this post, I want to write something down about LaTeX visualization as a way to remember it myself. So this post focuses on visualization especially with LaTeX. I think LaTeX visualization is a good choice for some graphical illustrations obtaining (complex) mathematical symbols and equations. In this post, I will start with many visualization cases (e.g., tensors and its factorization) on a popular online LaTeX system--- overleaf  ( here, you need to log in your overleaf account, or register an account first ). If you want to understand more details and more visualization cases in LaTeX, please read our GitHub project--- awesome-latex-drawing . Part 1: Visualize Real-World Data Tensors For example, mobility demand/flow for travelers using different modes can be modeled as a 3-d (origin zone, destination zone, time slot) tensor time series and all dimensions have strong interactions with each other. If you want to derive this picture by yourself, please open  tenso