Two essays on unsupervised learning theory.

[Simone G.O. FIORI]

Dear Connectionists,

I take the liberty to announce the availability of two new 
papers on unsupervised complex-valued neural networks 
learning and on relative uncertainty learning theory.

Best regards,
Simone Fiori

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"Non-linear Complex-Valued Extensions of Hebbian Learning: An 
Essay" by S. Fiori, University of Perugia (Italy)
Accepted on Neural Computation

Abstract: The Hebbian paradigm is perhaps the most known 
unsupervised learning theory in connectionism. It has inspired a 
wide research activity in the artificial neural network field 
because it embodies some interesting properties such as locality 
and the capability of being applicable to the basic weight-and-sum 
structure of neuron models. The plain Hebbian principle, however, 
also presents some inherent theoretical limitations that make it 
unpractical in most cases. Therefore, modifications of the basic 
Hebbian learning paradigm have been proposed over the last twenty 
years in order to design profitable signal/data processing 
algorithms. Such modifications led to the principal-component-
analysis-type class of learning rules along with their non-linear 
extensions. The aim of this essay is primarily to present part of 
the existing fragmented material in the field of principal 
component learning within a unified view and contextually to 
motivate and present extensions of previous works on Hebbian 
learning to complex-weighted linear neural networks. This work 
benefits from previous studies on linear signal decomposition by 
artificial neural networks, non-quadratic component optimization 
and reconstruction error definition, neural parameters adaptation 
by constrained optimization of complex-valued learning criteria 
and orthonormality expression via the insertion of topological 
elements in the networks or by modifying the network learning 
criterion. In particular, the considered learning principles and 
their analysis concern complex-valued principal/minor 
component/subspace linear/non-linear rules for complex-weighted 
neural structures, both feedforward and laterally-connected.

Draft (68 pages) available at: 
http://www.unipg.it/sfr/publications/rcpca.pdf

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"Relative Uncertainty Learning Theory: An Essay"
by S. Fiori, University of Perugia (Italy)
Accepted on International Journal of Neural Systems

Abstract: The aim of this manuscript is to present a detailed 
analysis of the algebraic and geometric properties of relative 
uncertainty theory (RUT) applied to neural networks learning. 
Through the algebraic analysis of the original learning criterion, 
it is shown that RUT gives rise to principal-subspace-analysis-
type learning equations. Through an algebraic-geometric analysis, 
the behavior of such matrix-type learning equations is illustrated, 
with particular emphasis to the existence of certain invariant 
manifolds.

Draft (33 pages) available at: 
http://www.unipg.it/sfr/publications/ijns-mut.pdf


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| Dr Simone FIORI (Elec. Eng., Ph.D.)                   |
| * Faculty of Engineering - Perugia University *       |
| * Polo Didattico e Scientifico del Ternano *          |
| Via Pentima bassa, 21 -  05100 TERNI (Italy)          |
| Tel. 0744 492937 -  Fax: +39 0744 492925              | 
| eMail: fiori at unipg.it - Web: http://www.unipg.it/sfr/ |
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| "Quelli che s'innamoran di pratica sanza scienza, son |
| come il nocchiere, ch'entra in navilio sanza timone o |
| bussola, che mai ha certezza dove si vada."           |
|                                  (Leonardo da Vinci)  | 
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