How deeply does Graph Neural Networks in Action cover UMAP?

Explains projection goals and tuning parameters, then demonstrates Python usage; stops short of mathematical derivation.

UMAP

As explained in Graph Neural Networks in Action

UMAP is a nonlinear dimensionality-reduction technique that projects high-dimensional data into a lower-dimensional space while attempting to preserve local and global structure.

UMAP reduces high-dimensional embeddings to two or three dimensions for visual analysis, keeping similar nodes near one another while retaining broader structural relationships. section 2.1.3

A practical graph-embedding workflow uses UMAP as a visualization stage:

Generate node embeddings with Node2Vec, convert them to a numerical array, and fit UMAP with a chosen number of components. section 2.1 section 2.1.3
Tune n_neighbors to balance local detail against broader structure, and use min_dist to influence how closely points can cluster. section 2.1.3
Plot the resulting two-dimensional coordinates and use node colors or shapes to inspect possible clusters and relationships. section 2.1.3

Political Books graph

Applying UMAP to Node2Vec embeddings of 105 political books and 441 co-purchase edges reveals potential clusters associated with liberal, conservative, and neutral political leanings. section 2.1 section 2.1.3

Listing 2.2 Visualizing the embeddings using UMAP

node_embeddings = [embeddings[str(node)] \
for node in gml_graph.nodes()]   #1
node_embeddings_array = np.array(node_embeddings)  

umap_model = umap.UMAP(n_neighbors=15, min_dist=0.1, n_components=2, \
random_state=42)
umap_features = umap_model.fit_transform\
(node_embeddings_array)  #2

plt.scatter(umap_features[:, 0], \
umap_features[:, 1], color=node_colors, alpha=0.7)  #3

The implementation initializes UMAP with 15 neighbors, a 0.1 minimum distance, two components, and a fixed random state before plotting the transformed coordinates. section 2.1.3

How Graph Neural Networks in Action covers it

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Also explained in

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Machine Learning for Tabular Data: XGBoost, Deep Learning, and AIUMAP is a nonlinear dimensionality-reduction technique based on manifold-learning principles that constructs a low-dimensional representation of high-dimensional data.
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Data Without LabelsUniform Manifold Approximation and Projection (UMAP) is a nonlinear manifold-learning technique for dimensionality reduction that constructs a low-dimensional embedding while preserving data relationships.

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Related concepts

dimensionality reductionkind of · Dimensionality reduction is the transformation of data into a representation with fewer dimensions while retaining selected information, structure, or relationships.
principal component analysisalternative to · Principal component analysis is a linear dimensionality-reduction technique that transforms data into orthogonal components ordered by the variance they capture.

This explainer was generated by Manning's knowledge graph from the text of Graph Neural Networks in Action. The section links point to the parts of the book it draws on.