?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Elastic+principal+manifolds+and+their+practical+applications%0A&rft.creator=Gorban%2C+A.N.&rft.creator=Zinovyev%2C+A.Yu.&rft.subject=Statistical+Models&rft.description=Principal+manifolds+defined+as+lines+or+surfaces+passing+through+%22the+middle%22+of+the+data+distribution+serve+as+useful+objects+for+many+practical+applications.+We+propose+a+new+algorithm+for+fast+construction+of+grid+approximations+of+principal+manifolds+with+given+topology.+One+advantage+of+the+method+is+a+new+form+of+the+functional+to+be+minimized%2C+which+becomes+quadratic+at+the+step+of+the+vertexes+positions+refinement.+This+makes+the+algorithm+very+effective%2C+especially+for+parallel+implementations.+&rft.date=2004-05&rft.type=Preprint&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.identifier=http%3A%2F%2Fcogprints.org%2F3919%2F1%2F0405648.pdf&rft.identifier=++Gorban%2C+A.N.+and+Zinovyev%2C+A.Yu.++(2004)+Elastic+principal+manifolds+and+their+practical+applications.++%5BPreprint%5D+++++&rft.relation=http%3A%2F%2Fcogprints.org%2F3919%2F