Write a simplest autoencoder and decoder based on the MNIST data base

[bsonghao]

d65847fafaeee844e8bce9bae40eb99fb22296b7 implement it

Principle Component Analysis (PCA) is a concept that is originally proposed in the quantum physics. The goal is to resolve the wavefunctions that span the full Hilbert space into a few truncated basis set with large coefficients.

PCA can be applied to the generalized unsupervised learning algorithm. Basically, its goal is to do the dimension reduction. In the application of the image recognition, it can extract (clustering) first few key feature of a training set of images among all features.

PCA can also be applied in "feature selection" in general. Examples include extract key factors of the cause of a disease among a large data base and many factors.

[bsonghao]

Try to plot the latent space of PCA and reproduce the result in the lecture note but the data seems not be labeled properly

[bsonghao]

After fix a bug, manage to produced labeled latent space of PCA. Beautiful! see in commit d52b665cb335425e84b09c7f82f6f52a92060798

[bsonghao]

f108a1fb4277c3c92d843d22f718b964f4b1a6ed visualize the latent of a simple autoencoder (RuLU as activation function). We can see obvious difference in their latent space comparing to that of the PCA