Latent space

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

A latent space is a lower-dimensional representation space whose vectors encode information about observed data or structures.

A latent space is a lower-dimensional continuous space whose vectors compress information while preserving useful structure. For graphs, an encoder maps nodes into vectors using position, neighborhood structure, features, or a combination of these. section 11.3.1

Graph embeddings organize latent vectors according to graph relationships:

• Place connected or nearby nodes close together, and separate disconnected or distant nodes. section 11.3.1
• Use an encoder alone, or jointly optimize an encoder and decoder to preserve specified graph information. section 11.3.1
• Distinguish transductive methods, which represent only training nodes, from inductive methods, which generalize to unseen nodes or graphs. section 11.3.1

Node embeddings with a graph convolutional network

A practical pipeline loads the Cora dataset with PyTorch Geometric, applies two GCNConv layers with ReLU and dropout, trains with Adam for 200 epochs, and evaluates the model.

Figure 11.4 Graph embedding

Visualizes the mapping from graph space into a low-dimensional embedding or latent space. section 11.3.1

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

How deep it goes

Explains the encoding objective, encoder-decoder variant, and transductive-inductive distinction, then demonstrates GCN training.

Examples

Demonstrates node embeddings with a two-layer GCN trained on the Cora dataset using PyTorch Geometric.

What you can do after

Builds node embeddings by implementing and training a GCN with PyTorch Geometric.

How it connects

Connects graph embedding with graph convolutional networks, encoder-decoder architectures, transductive learning, and inductive learning.

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Related concepts

• encoderproduced by · An encoder is a component that transforms input data into an encoded representation for subsequent processing, reconstruction, comparison, or transmission.
• decodeused by · Decoding is the process of transforming an encoded or internal representation into an interpretable or target-form output.
• generatorused by · A generator is a computational component or construct that produces data or values from inputs, representations, context, or specified constraints.
• encodingproduced by · Encoding is the transformation of information into a representation defined by a scheme for storage, processing, transmission, or interpretation.
• diffusion modelused by · A diffusion model is a generative model that learns to produce data by reversing a process that progressively adds noise to data.
• image generationused by · Image generation is the computational creation of new images from learned models, input data, or specified conditions.

This explainer was generated by Manning's knowledge graph from the text of Optimization Algorithms: AI techniques for design, planning, and control problems. The section links point to the parts of the book it draws on.