AI 용어집
인공지능 완전 사전
Manifold
A topological space that locally resembles a lower-dimensional Euclidean space, on which high-dimensional data are assumed to lie within the framework of manifold learning.
Floyd-Warshall Algorithm
A dynamic programming algorithm used by Isomap to compute the shortest distances between all pairs of nodes in the neighborhood graph, thereby approximating geodesic distances.
Multidimensional Scaling (MDS)
A multivariate analysis technique applied by Isomap on the computed geodesic distances to find a low-dimensional representation that best preserves these distances.
Intrinsic Metric
A distance measure defined on the manifold itself rather than in the ambient space, approximated by Isomap through the geodesic distances computed on the graph.
Non-linear Dimensionality Reduction
A class of techniques aimed at projecting data into a lower-dimensional space while preserving non-linear structures, of which Isomap is a part as a method preserving geodesic distances.
Landmark Points
A strategically selected subset of points used in some variants of Isomap to reduce computational complexity while preserving the essential geometric structure of the manifold.
Distance Spectrum
The set of eigenvalues obtained during the principal component decomposition of geodesic distances, revealing the intrinsic dimension and structure of the manifold.
Isometric Map
A distance-preserving mapping, sought by Isomap to ensure that distances in the low-dimensional space faithfully reflect the geodesic distances on the original manifold.
Topological preservation
Property of Isomap ensuring the maintenance of neighborhood relationships and global connectivity during projection into the reduced-dimensional space.
Local curvature
Geometric measure of the variation of the manifold in the neighborhood of a point, affecting the accuracy of geodesic distance approximations by Isomap in highly curved regions.
K-nearest neighbors
Method of constructing the neighborhood graph in Isomap connecting each point to its k nearest neighbors, where the choice of k influences the capture of local and global structure.