--- abstract: "Slow feature analysis is an algorithm for unsupervised learning of invariant representations from data with temporal correlations. Here, we present a mathematical analysis of slow feature analysis for the case where the input-output functions are not restricted in complexity. We show that the optimal functions obey a partial differential eigenvalue problem of a type that is common in theoretical physics. This analogy allows the transfer of mathematical techniques and intuitions from physics to concrete applications of slow feature analysis, thereby providing the means for analytical predictions and a better understanding of simulation results. We put particular emphasis on the situation where the input data are generated from a set of statistically independent sources.\r\nThe dependence of the optimal functions on the sources is calculated analytically for the cases where the sources have Gaussian or uniform distribution." altloc: [] chapter: ~ commentary: ~ commref: ~ confdates: ~ conference: ~ confloc: ~ contact_email: ~ creators_id: - henning.sprekeler@epfl.ch - l.wiskott@biologie.hu-berlin.de creators_name: - family: Sprekeler given: Henning honourific: '' lineage: '' - family: Wiskott given: Laurenz honourific: 'Dr. ' lineage: '' date: 2008-08-19 date_type: submitted datestamp: 2008-10-16 13:47:35 department: ~ dir: disk0/00/00/62/23 edit_lock_since: ~ edit_lock_until: ~ edit_lock_user: ~ editors_id: [] editors_name: [] eprint_status: archive eprintid: 6223 fileinfo: /style/images/fileicons/application_pdf.png;/6223/2/SprekelerWiskott08.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: 'slow feature analysis, unsupervised learning, invariant representations, statistically independent sources, theoretical analysis' lastmod: 2011-03-11 08:57:12 latitude: ~ longitude: ~ metadata_visibility: show note: ~ number: ~ pagerange: ~ pubdom: FALSE publication: ~ publisher: ~ refereed: FALSE referencetext: ~ relation_type: [] relation_uri: [] reportno: ~ rev_number: 35 series: ~ source: ~ status_changed: 2008-10-16 13:47:35 subjects: - comp-neuro-sci - comp-sci-mach-learn succeeds: ~ suggestions: ~ sword_depositor: ~ sword_slug: ~ thesistype: ~ title: 'Understanding Slow Feature Analysis: A Mathematical Framework' type: preprint userid: 6764 volume: ~