Objective

Observe the Latent space of Convolutional AutoEncoder for a classification dataset (MNIST)

Architecture of Auto Encoder

The encoder consists of multiple convolutions and batchnormalizations only. We scale a 28x28 to 7x1 vector.
The decoder is again transposed convolutions and batchnormalizations, i.e. 7x1 to 28x28.
Optimizers/LR/decays used have not been hyperparameter optimized yet. Therefore the current loss is 0.02 for 50 epochs.

To Observable

We encode the training images to our latent space as usual. However we then apply LDA transformations with n_components=2. Plotting the transformed data we could observe well formed clusters (refer notebook). Also, there were obviously some overlapping ones, to resolve them, a 3D LDA transformation was obtained. The clusters were amazingly distinguishable with almost 0 overlap.

2D LDA result.

3D LDA plot © Aflah

3D LDA result - Interactive (Click)

Observations

1. We can generate multiple fake samples given the latent space encoding distributed on multivariate gaussian distribution with parameters from MLE estimates of the training data (of a specific class) in latent space.
2. Latent space was initally made keeping in mind a 7-segment decoder. But guess what (HINT: Look at the means)
3. All of the following is synthetic data
   

   array([
       3, 2, 2, 2, 7, 6, 6, 2, 2, 2, 2, 1, 2, 6, 2, 2, 
       2, 2, 6, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 1, 2, 
       8, 2, 2, 2, 2, 6, 2, 2, 6, 0, 7, 2, 0, 2, 2, 9, 
       5, 2, 2, 2, 5, 2, 2, 2, 6, 6, 2, 2, 2, 2, 2, 2, 
       2, 2, 2, 2, 4, 8, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 
       6, 2, 8, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 8, 3, 2, 
       2, 2, 6, 2, 8, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 
       2, 6, 2, 2, 2, 2, 2, 2, 2, 8, 2, 6, 8, 2, 2, 2], dtype=int64)

4. A demo is now live at ghpages. Drag the sliders to move around the Latent space.