TY - GEN
T1 - Nonlinear dimensionality reduction using circuit models
AU - Andersson, Fredrik
AU - Nilsson, Jens
PY - 2005
Y1 - 2005
N2 - The problem addressed in nonlinear dimensionality reduction, is to find lower dimensional configurations of high dimensional data, thereby revealing underlying structure. One popular method in this regard is the Isomap algorithm, where local information is used to find approximate geodesic distances. From such distance estimations, lower dimensional representations, accurate on a global scale, are obtained by multidimensional scaling. The property of global approximation sets Isomap in contrast to many competing methods, which approximate only locally. A serious drawback of Isomap is that it is topologically instable, i.e., that incorrectly chosen algorithm parameters or perturbations of data may abruptly alter the resulting configurations. To handle this problem, we propose new methods for more robust approximation of the geodesic distances. This is done using a viewpoint of electric circuits. The robustness is validated by experiments. By such an approach we achieve both the stability of local methods and the global approximation property of global methods.
AB - The problem addressed in nonlinear dimensionality reduction, is to find lower dimensional configurations of high dimensional data, thereby revealing underlying structure. One popular method in this regard is the Isomap algorithm, where local information is used to find approximate geodesic distances. From such distance estimations, lower dimensional representations, accurate on a global scale, are obtained by multidimensional scaling. The property of global approximation sets Isomap in contrast to many competing methods, which approximate only locally. A serious drawback of Isomap is that it is topologically instable, i.e., that incorrectly chosen algorithm parameters or perturbations of data may abruptly alter the resulting configurations. To handle this problem, we propose new methods for more robust approximation of the geodesic distances. This is done using a viewpoint of electric circuits. The robustness is validated by experiments. By such an approach we achieve both the stability of local methods and the global approximation property of global methods.
KW - Topological instability
KW - Laplacian Eigenmaps
KW - Manifold learning
KW - Isomap
KW - Multidimensional scaling
U2 - 10.1007/11499145_96
DO - 10.1007/11499145_96
M3 - Paper in conference proceeding
VL - 3540
SP - 950
EP - 959
BT - Lecture Notes in Computer Science
PB - Springer
T2 - 14th Scandinavian Conference on Image Analysis, SCIA 2005
Y2 - 19 June 2005 through 22 June 2005
ER -