This repo includes some of my works involving visualization.

Simulation of the flocking behavior of birds. Build with PyTorch and pygame. Repository

Visualization of Napoleon's Russian Campaign based on the Minard's map, using troop, city nad temperature data.

Original
My visualization

Visualization of UK road accidents based 2018 data.

X-ray image processing, including auto contrast adjustment, image denoising, auto tone mapping, and edge enhancement.

This project uses inverse discrete cosine transform and orthogonal matching pursuit to recover a “damaged” image. The image is divided into numbers of K×K small blocks to speed up the computation, and data are sparse sampled from them. Then the blocks are recovered, stitched together.

Recovered image with different sample size	Sample size vs. computation time
Sample size vs. MSE for different methods	Entropy vs. MSE for different sample size

Findings: as the sample size increase, the computation cost would increase exponentially and the MAE would decrease exponentially in general; as the entropy of each block increase, the MSE increases exponentially and the trial with lower sample size would always have higher MSE in general. This also mean the more complex images (signals) are harder to recover from sparse samples.

This project uses the interior point method to train a support vector machine (SVM) using k-fold cross-validation to classify a dataset of electroencephalogram (EEG) signals with binary labels. The optimal weight is found by using the Newton method and line search.

$$ \begin{aligned} \underset{\mathbf{W, C, \xi}}{\min} & \hspace{2mm} \sum \xi_i + \lambda W^T W\\ \text{S.T.} & \hspace{2mm} y_i (\mathbf{w}^T \mathbf{x}_i + b) \geq 1 \\ & \hspace{2mm} \xi_i \geq 0 \\ & \hspace{2mm} (i = 1, 2, \dots, N) \\ \end{aligned} $$

Data: object moving left or right on screen; 2 classes, 120 trails each, 204 channels; imagined or with actual moving object

	Imagined	Overt
Penalty Weight $\lambda$ vs. Accuracy
ROC curve for each fold
Weights $W$ and magnitude (most sig 5 ch are marked)
2D plot of the magnitude of weights $W$
	Plot of 5 most significant channels of weights $W$	Search the optimal $\lambda$

Findings: Classification accuracy using overt data is only 3.6% higher than imagined data at 94.9% with $\lambda = 10$; by using grid search the optimal $\lambda$ is found to be around 6.5; the most significant channels for overt data are channel 137, 141, and 155, which means they can be strongly related to vision and direction

Visualization of high dimensional function using ParaView, including test functions, Compactly Supported Radial Basis Function (CSRBF) surrogate model, and potential energy of toy proteins.

3D Rosenbrock	3D Styblinski-Tang
4D Styblinski-Tang (4th dimension fixed at [-5, -2.903534, 0, 2.903534, 5])	CSRBF $\psi_{3,1}$ surrogate of 4D Styblinski-Tang (scaling factor, a = 10; data points, n = 1000)
Potential energy of toy protein AAAAA	Potential energy of toy protein AABBB
Potential energy of toy protein ABABAB