French Doctoral Thesis available: Nonlinear Data Analysis through Self-Organizing Neural Networks

[pierre.demartines@csemne.ch]

Hello,

It is my pleasure to inform you about the availability of my doc-
toral  dissertation  (in  french  only) on "Data Analysis through
Self-Organizing Neural Networks". You can get it by FTP from  the
TIRFLab ftp-server (Grenoble, France).

FTP-host: 	tirf.inpg.fr
FTP-name: 	anonymous
FTP-passwd: 	anything (your email for instance)
FTP-file: 	/pub/demartin/demartin.phd94.ps.Z

(2.2 Mo compressed, 8.7 Mo uncompressed, 214 pages) 


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      DATA ANALYSIS THROUGH SELF-ORGANIZED NEURAL NETWORKS

Keywords
--------
Data structure  (submanifold),  Self-Organizing  Maps  (Kohonen),
Fractal Dimension, Dimension Reduction, Nonlinear Projection, Un-
folding, "VQP" algorithm, diffeomorphism, interpolation, extrapo-
lation,  Multidimensional  Scaling, Nonlinear Mapping, Industrial
Applications.

Abstract
--------
Data understanding is often  based  on  hidden  informations  re-
trieval  within  a  big  amount  of  collected variables. It is a
search for linear or non linear dependencies  between  these  ob-
served  variables,  and  consists  in reducing these variables to
small number of parameters.

A classical method, widely used for  this  purpose,  is  the  so-
called  Principal  Component  Analysis (PCA). Unfortunately, this
method is only linear, and fails to reduce data that  are  redun-
dant in a non linear way.

The Kohonen's Self-Organizing Maps are a type of artificial neur-
al  networks,  the  functionality of which can be viewed as a non
linear extension of PCA: data samples are mapped onto a  grid  of
neurons.  A  major  drawback  of  these maps, however, is their a
priori defined shape (generally a square or a  rectangle),  which
is  rarely  adapted  to  the  shape  of  the  parametric space to
represent.

We relax this constraint with a new  algorithm,  called  ``Vector
Quantization  and  Projection''  (VQP).  It  is  a  kind of self-
organizing map, the output space of which is continuous and takes
automatically  the  relevant  shape. From a mathematical point of
view, VQP is the search for a diffeomorphism between the raw data
set  and  an  unknown parametric representation to be found. More
intuitively, this is an unfolding of  data  structure  towards  a
low-dimensional  space,  which dimension is the number of degrees
of freedom of the observed  phenomenon,  and  can  be  determined
through fractal analysis of the data set.

In order to illustrate the generality of  VQP,  we  give  a  wide
range  of  application  examples  (real or simulated), in several
domains such as data fusion, graphes matching, industrial process
monitoring  or analysis, faults detection in devices and adaptive
routing in telecommunications.


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    ANALYSE DE DONNEES PAR RESEAUX DE NEURONES AUTO-ORGANISES

Mots-cles
---------
Structure  de   donnees   (variete),   cartes   auto-organisantes
(Kohonen), dimension fractale, reduction de dimension, projection
non-lineaire, depliage, algorithme "VQP", diffeomorphisme, inter-
polation,  extrapolation,  "Multidimensional Scaling", "Nonlinear
Mapping", applications industrielles.

Resume
------
Chercher a comprendre  des  donnees,  c'est  souvent  chercher  a
trouver  de  l'information  cachee dans un gros volume de mesures
redondantes. C'est chercher des dependances,  lineaires  ou  non,
entre  les variables observees pour pouvoir resumer ces dernieres
par un petit nombre de parametres.

Une  methode  classique,  l'Analyse  en  Composantes  Principales
(ACP),  est abondamment employee dans ce but. Malheureusement, il
s'agit d'une methode exclusivement lineaire, qui est donc incapa-
ble de reveler les dependances non lineaires entre les variables.

Les cartes auto-organisantes de Kohonen sont des reseaux de  neu-
rones artificiels dont la fonction peut etre vue comme une exten-
sion de l'ACP aux cas non-lineaires.  L'espace  parametrique  est
represente  par  une grille de neurones, dont la forme, generale-
ment carree ou rectangulaire, doit malheureusement etre choisie a
priori.  Cette  forme  est  souvent inadaptee a celle de l'espace
parametrique recherche.

Nous liberons cette contrainte avec un nouvel  algorithme,  nomme
``Vector  Quantization  and Projection'' (VQP), qui est une sorte
de carte auto-organisante dont l'espace de sortie est continu  et
prend  automatiquement  la  forme  adequate. Sur le plan mathema-
tique, VQP peut etre defini comme la  recherche  d'un  diffeomor-
phisme  entre l'espace brut des donnees et un espace parametrique
inconnu a trouver. Plus intuitivement, il s'agit d'un depliage de
la structure des donnees vers un espace de plus petite dimension.
Cette dimension, qui correspond au nombre de degres de liberte du
phenomene etudie, peut etre determinee par des methodes d'analyse
fractale du nuage de donnees.

Afin d'illustrer la generalite de l'approche  VQP,  nous  donnons
une  serie  d'exemples  d'applications, simulees ou reelles, dans
des  domaines  varies  qui  vont  de  la  fusion  de  donnees   a
l'appariement de graphes, en passant par l'analyse ou la surveil-
lance de procedes industriels, la detection de defauts  dans  des
machines et le routage adaptatif en telecommunications.
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FTP INSTRUCTIONS:

unix> ftp tirf.inpg.fr (or 192.70.29.33)
    Name: anonymous
    Password: <your e-mail address>
    ftp> cd pub/demartin
    ftp> binary
    ftp> get demartin.phd94.ps.Z
    ftp> quit
unix> uncompress demartin.phd94.ps.Z


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 Pierre Demartines    email: demartin at csemne.ch    
 C.S.E.M.             Phone: (41) 38 205 252
 Maladiere 71         Fax:   (41) 38 205 770 
 CH-2007 Neuchatel    Mosaic: ftp://tirf.inpg.fr/pub/HTML/tirf.html
 Switzerland
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