GR1008730B - System and method for dimensionality reduction using efficient generalized eigenpairs computation - Google Patents

System and method for dimensionality reduction using efficient generalized eigenpairs computation

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Publication number
GR1008730B
GR1008730B GR20150100147A GR20150100147A GR1008730B GR 1008730 B GR1008730 B GR 1008730B GR 20150100147 A GR20150100147 A GR 20150100147A GR 20150100147 A GR20150100147 A GR 20150100147A GR 1008730 B GR1008730 B GR 1008730B
Authority
GR
Greece
Prior art keywords
matrix
dimensionality reduction
gsmp
expansion coefficient
kernel
Prior art date
Application number
GR20150100147A
Other languages
Greek (el)
Inventor
Νικολαος Γεωργιου Γκαλελης
Βασιλειος Θωμα Μεζαρης
Original Assignee
Εθνικο Κεντρο Ερευνας Και Τεχνολογικης Αναπτυξης/Ινστιτουτο Τεχνολογιων Πληροφορικης Και Επικοινωνιων,
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Εθνικο Κεντρο Ερευνας Και Τεχνολογικης Αναπτυξης/Ινστιτουτο Τεχνολογιων Πληροφορικης Και Επικοινωνιων, filed Critical Εθνικο Κεντρο Ερευνας Και Τεχνολογικης Αναπτυξης/Ινστιτουτο Τεχνολογιων Πληροφορικης Και Επικοινωνιων,
Priority to GR20150100147A priority Critical patent/GR1008730B/en
Publication of GR1008730B publication Critical patent/GR1008730B/en

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Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N20/00—Machine learning
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N5/00—Computing arrangements using knowledge-based models
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N99/00—Subject matter not provided for in other groups of this subclass

Abstract

Systems based on dimensionality reduction are very useful in several application domains, such as event and concept detection, data visualization and data compression. However, the computational cost for computing the dimensionality reduction matrix has restricted the widespread use of this technology. In this disclosure, a dimensionality reduction method and system for the efficient computation of the nonzero generalized eigenpairs of the Gram scatter matrix pencil (GSMP), and more specifically of the expansion coefficient matrix and the respective GSMP diagonal matrix is presented. In a first embodiment the expansion coefficient matrix and the respective GSMP diagonal matrix of kernel discriminant analysis are efficiently derived. In a second and third embodiment the expansion coefficient matrix and the respective GSMP diagonal matrix of heteroskedastic kernel weighted discriminant analysis and kernel subclass discriminant analysis are efficiently derived, respectively.
GR20150100147A 2015-03-30 2015-03-30 System and method for dimensionality reduction using efficient generalized eigenpairs computation GR1008730B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
GR20150100147A GR1008730B (en) 2015-03-30 2015-03-30 System and method for dimensionality reduction using efficient generalized eigenpairs computation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
GR20150100147A GR1008730B (en) 2015-03-30 2015-03-30 System and method for dimensionality reduction using efficient generalized eigenpairs computation

Publications (1)

Publication Number Publication Date
GR1008730B true GR1008730B (en) 2016-03-31

Family

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Family Applications (1)

Application Number Title Priority Date Filing Date
GR20150100147A GR1008730B (en) 2015-03-30 2015-03-30 System and method for dimensionality reduction using efficient generalized eigenpairs computation

Country Status (1)

Country Link
GR (1) GR1008730B (en)

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2002091211A1 (en) * 2001-05-07 2002-11-14 Biowulf Technologies, Llc Kernels and methods for selecting kernels for use in learning machines

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2002091211A1 (en) * 2001-05-07 2002-11-14 Biowulf Technologies, Llc Kernels and methods for selecting kernels for use in learning machines

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
MATHIEU RAMONA ET AL: "Multiclass Feature Selection With Kernel Gram-Matrix-Based Criteria", IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, IEEE, PISCATAWAY, NJ, USA, vol. 23, no. 10, 31 October 2012 (2012-10-31), pages 1611 - 1623, XP011460813, ISSN: 2162-237X, DOI: 10.1109/TNNLS.2012.2201748 *
PETROS DRINEAS ET AL: "Approximating a Gram Matrix for Improved Kernel-Based Learning", 19 June 2005, LEARNING THEORY; [LECTURE NOTES IN COMPUTER SCIENCE;LECTURE NOTES IN ARTIFICIAL INTELLIGENCE;LNCS], SPRINGER-VERLAG, BERLIN/HEIDELBERG, PAGE(S) 323 - 337, ISBN: 978-3-540-26556-6, XP019011413 *
THOMAS HOFMANN ET AL: "Kernel methods in machine learning", ARXIV.ORG, CORNELL UNIVERSITY LIBRARY, 201 OLIN LIBRARY CORNELL UNIVERSITY ITHACA, NY 14853, 31 January 2007 (2007-01-31), XP080268650, DOI: 10.1214/009053607000000677 *

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Effective date: 20160505