Description: S-ISOMAP is a manifold learning algorithm, which is a supervised variant of ISOMAP.
Reference: X. Geng, D.-C. Zhan, and Z.-H. Zhou. Supervised nonlinear dimensionality reduction for visualization and classification. IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics, 2005, vol.35, no.6, pp.1098-1107.
mani: manifold learning demonstration GUI by Todd Wittman, Department of Mathematics, University of Minnesota E-mail wittman@math.umn.edu with comments & questions.
MANI Website: httP://www.math.umn.edu/~wittman/mani/index.html
Last Modified by GUIDE v2.5 10-Apr-2005 13:28:36
Methods obtained from various authors.
(1) MDS -- Michael Lee
(2) ISOMAP -- J. Tenenbaum, de Silva, & Langford
(3) LLE -- Sam Roweis & Lawrence Saul
(4) Hessian LLE -- D. Donoho & C. Grimes
(5) Laplacian -- M. Belkin & P. Niyogi
(6) Diffusion Map -- R. Coifman & S. Lafon
(7) LTSA -- Zhenyue Zhang & Hongyuan Zha
Functions are mappings from one manifold to another. Discrete Functions are functions which can be represented using a finite number of values. Given the finite extent of computer memory, algorithms which compute a function that satisfies some special properties are computing a discrete function which approximates a continuous function. Computing the function involves writing a set of equations that may be solved for the values representing the function.
We describe and demonstrate an algorithm that takes as input an
unorganized set of points fx1 xng IR3 on or near an unknown
manifold M, and produces as output a simplicial surface that
approximates M. Neither the topology, the presence of boundaries,
nor the geometry of M are assumed to be known in advance — all
are inferred automatically from the data. This problem naturally
arises in a variety of practical situations such as range scanning
an object from multiple view points, recovery of biological shapes
from two-dimensional slices, and interactive surface sketching.
The advent of modern wireless devices, such as smart phones and MID 1 terminals,
has revolutionized the way people think of personal connectivity. Such devices
encompass multiple applications ranging from voice and video to high-speed data
transfer via wireless networks. The voracious appetite of twenty-first century users
for supporting more wireless applications on a single device is ever increasing.
These devices employ multiple radios and modems that cover multiple frequency
bands and multiple standards with a manifold of wireless applications often running
simultaneously.
