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Variational Autoencoders VAEs | Latent Space Visualization

 

Simple Explanation of AutoEncoders:  In simple terms, an autoencoder performs two tasks: 1) It compresses input data into a smaller, lower-dimensional representation [called Latent Space] 2) It then reconstructs the original input from this compressed representation.

Reconstruction Error = Reconstructed  minus Original

By training the neural network to minimize this error on our dataset,  the network learns to exploits the natural structure in our data and find the efficient lower dimensional representation of data.



AutoEncoders are neural networks that learn to compress and reconstruct data. They consist of two parts: an encoder that squeezes input data (like images) into a compact representation, and a decoder that expands it back to the original size. The network learns by minimizing reconstruction error.

Latent Space is the compressed middle layer where the encoder's output lives—a lower-dimensional representation capturing the data's essential features. Think of it like a zip file: the latent space contains compressed information that can recreate the original. This space often reveals meaningful patterns, where similar inputs cluster together, enabling tasks like generation and interpolation.

Latent Space Visualization involves projecting high-dimensional latent representations into 2D or 3D spaces for visual analysis. Since latent spaces often have dozens or hundreds of dimensions, we need dimensionality reduction techniques to explore patterns, clusters, and relationships in the data.

PCA (Principal Component Analysis) finds linear combinations of features that capture maximum variance. It's fast and deterministic, preserving global structure and distances well. PCA identifies orthogonal axes along which data varies most, making it ideal for understanding overall data distribution. However, it only captures linear relationships and may miss complex nonlinear patterns in the latent space.

t-SNE (t-Distributed Stochastic Neighbor Embedding) focuses on preserving local neighborhoods, making similar points cluster tightly while pushing dissimilar points apart. It excels at revealing clusters and local structure but distorts global distances. Each run produces different results due to its stochastic nature, and it's computationally expensive for large datasets.

UMAP (Uniform Manifold Approximation and Projection) balances local and global structure preservation better than t-SNE while being significantly faster. It maintains more meaningful distances between clusters and produces more consistent results across runs. UMAP often reveals both fine-grained clusters and broader data organization, making it increasingly popular for exploring latent spaces in deep learning models.

Variational Autoencoders

https://www.youtube.com/watch?v=qJeaCHQ1k2w [see here is where the magic happens in Latent Space Models see at 8:30 minutes] [Variational Autoencoders | Generative AI Animated]

https://www.youtube.com/watch?v=o_cAOa5fMhE  [Latent Space Visualisation: PCA, t-SNE, UMAP | Deep Learning Animated]

https://www.youtube.com/watch?v=9zKuYvjFFS8 [Variational Autoencoders]

https://www.youtube.com/watch?v=3jmcHZq3A5s   (Simple Explanation of AutoEncoders)





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