TY - JOUR
T1 - Unsupervised dimensionality estimation and manifold learning in high-dimensional spaces by tensor voting
AU - Mordohai, Philippos
AU - Medioni, Gérard
PY - 2005
Y1 - 2005
N2 - We address dimensionality estimation and nonlinear manifold inference starting from point inputs in high dimensional spaces using tensor voting. The proposed method operates locally in neighborhoods and does not involve any global computations. It is based on information propagation among neighboring points implemented as a voting process. Unlike other local approaches for manifold learning, the quantity propagated from one point to another is not a scalar, but is in the form of a tensor that provides considerably richer information. The accumulation of votes at each point provides a reliable estimate of local dimensionality, as well as of the orientation of a potential manifold going through the point. Reliable dimensionality estimation at the point level is a major advantage over competing methods. Moreover, the absence of global operations allows us to process significantly larger datasets. We demonstrate the effectiveness of our method on a variety of challenging datasets.
AB - We address dimensionality estimation and nonlinear manifold inference starting from point inputs in high dimensional spaces using tensor voting. The proposed method operates locally in neighborhoods and does not involve any global computations. It is based on information propagation among neighboring points implemented as a voting process. Unlike other local approaches for manifold learning, the quantity propagated from one point to another is not a scalar, but is in the form of a tensor that provides considerably richer information. The accumulation of votes at each point provides a reliable estimate of local dimensionality, as well as of the orientation of a potential manifold going through the point. Reliable dimensionality estimation at the point level is a major advantage over competing methods. Moreover, the absence of global operations allows us to process significantly larger datasets. We demonstrate the effectiveness of our method on a variety of challenging datasets.
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M3 - Conference article
AN - SCOPUS:84880738109
SN - 1045-0823
SP - 798
EP - 803
JO - IJCAI International Joint Conference on Artificial Intelligence
JF - IJCAI International Joint Conference on Artificial Intelligence
T2 - 19th International Joint Conference on Artificial Intelligence, IJCAI 2005
Y2 - 30 July 2005 through 5 August 2005
ER -