--- abstract: 'Principal manifolds defined as lines or surfaces passing through "the middle" 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, which becomes quadratic at the step of the vertexes positions refinement. This makes the algorithm very effective, especially for parallel implementations. ' altloc: - http://mystic.math.neu.edu/gorban/ - http://www.ihes.fr/~zinovyev/ chapter: ~ commentary: ~ commref: ~ confdates: ~ conference: ~ confloc: ~ contact_email: ~ creators_id: [] creators_name: - family: Gorban given: A.N. honourific: '' lineage: '' - family: Zinovyev given: A.Yu. honourific: '' lineage: '' date: 2004-05 date_type: published datestamp: 2004-11-06 department: ~ dir: disk0/00/00/39/19 edit_lock_since: ~ edit_lock_until: ~ edit_lock_user: ~ editors_id: [] editors_name: [] eprint_status: archive eprintid: 3919 fileinfo: /style/images/fileicons/application_pdf.png;/3919/1/0405648.pdf full_text_status: public importid: ~ institution: ~ isbn: ~ ispublished: ~ issn: ~ item_issues_comment: [] item_issues_count: 0 item_issues_description: [] item_issues_id: [] item_issues_reported_by: [] item_issues_resolved_by: [] item_issues_status: [] item_issues_timestamp: [] item_issues_type: [] keywords: 'principal surface, machine learning, SOM, vizualization' lastmod: 2011-03-11 08:55:43 latitude: ~ longitude: ~ metadata_visibility: show note: ~ number: ~ pagerange: ~ pubdom: FALSE publication: ~ publisher: ~ refereed: FALSE referencetext: |- Aizenberg, L. 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