Exercise

1. Try to use PCA to reduce the size of the dimension to 1 and compare the result with the projected data in the x, y, and z axes, respectively.
2. Compare the results of PCA and t-SNE that are shown by the Embedding Projector tool. Which is better in terms of visibility?
3. Implement the PCA algorithm without using the numeric library (Hint: the operator for the eigenvalue is necessary).
4. Tune the hyperparameters of the embedding layer in order to visualize the embedding dataset to reflect the semantics of the data.
5. Try to embed MNIST data into a three-dimensional space.