How to draw graphical illustrations for tensor and its factorization in LaTeX?
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 tensor.tex in your overleaf project and compile this .tex file directly.
Part 2: Visualize Tensor Completion Task
For the problem of missing spatiotemporal traffic data imputation, one effective solution is converting missing data imputation as a tensor completion problem. In our latest paper, we present a missing traffic data imputation framework as follows,
where you can see data organization and tensor completion are played as key roles.
If you want to derive this picture by yourself, please open
- tc_framework.tex
and upload
- curve1.pdf
- curve2.pdf
in your overleaf project and compile the tc_framework.tex file directly.
Part 3: Visualize Tensor Factorization
For a third-order tensor, the following tensor factorization model
can be visualized as
If you want to derive this picture by yourself, please open AuTF.tex in your overleaf project and compile this .tex file directly.
Part 4: Visualize Bayesian Tensor Factorization
Following the above tensor factorization model, we can further build its Bayesian model as
In order to understand this Bayesian model intuitively, we can draw a graphical illustration as
Within this picture, you can find observations, parameters, and hyper-parameters. If you want to derive this picture by yourself, please open BATF.tex in your overleaf project and compile this .tex file directly.
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 tensor.tex in your overleaf project and compile this .tex file directly.
Part 2: Visualize Tensor Completion Task
For the problem of missing spatiotemporal traffic data imputation, one effective solution is converting missing data imputation as a tensor completion problem. In our latest paper, we present a missing traffic data imputation framework as follows,
where you can see data organization and tensor completion are played as key roles.
If you want to derive this picture by yourself, please open
- tc_framework.tex
and upload
- curve1.pdf
- curve2.pdf
in your overleaf project and compile the tc_framework.tex file directly.
Part 3: Visualize Tensor Factorization
For a third-order tensor, the following tensor factorization model
If you want to derive this picture by yourself, please open AuTF.tex in your overleaf project and compile this .tex file directly.
Part 4: Visualize Bayesian Tensor Factorization
Following the above tensor factorization model, we can further build its Bayesian model as
In order to understand this Bayesian model intuitively, we can draw a graphical illustration as
Within this picture, you can find observations, parameters, and hyper-parameters. If you want to derive this picture by yourself, please open BATF.tex in your overleaf project and compile this .tex file directly.
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