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t-SNE (t-Distributed Stochastic Neighbor Embedding)

Non-linear dimensionality reduction algorithm particularly effective for visualizing high-dimensional data by focusing on preserving similar local structures.

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Number of neighbors (n_neighbors)

Fundamental parameter of UMAP determining the size of the local neighborhood used to build the manifold representation, directly affecting structure preservation.

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Repulsive force

Mechanism in visualization algorithms like t-SNE and UMAP preventing point clustering and preserving the local structure of data.

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Gradient descent optimization

Iterative process used to minimize the cost function in t-SNE and UMAP, progressively adjusting point positions in the reduced space.

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Local vs global structure

Fundamental trade-off in dimensionality reduction algorithms between preserving close neighborhood relationships and the global arrangement of clusters.

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Topological manifold

Mathematical concept underlying UMAP assuming that high-dimensional data resides on a lower-dimensional surface embedded in the original space.

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k-nearest neighbors graph (k-NN)

Intermediate data structure used by UMAP to model neighborhood relationships before projection into the reduced-dimensional space.

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Min_distance

UMAP parameter controlling the minimum allowed distance between points in the reduced space, influencing the compactness of resulting clusters.

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Embedding quality

Measure of the fidelity with which the low-dimensional representation preserves the structural relationships of the original data.

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Stochastic embedding

Probabilistic nature of t-SNE where final positions can vary between runs, unlike deterministic dimensionality reduction approaches.

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Cross-entropy optimization

Alternative to Kullback-Leibler divergence used in some t-SNE implementations for more stable optimization convergence.

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