Vol.6, Special Issue, 2007 pp. 221-230
UDC 531/534:611.69:514.76(045)=111
A DIFFERENTIAL GEOMETRY-BASED NEURODYNAMICAL
CLASSIFIER
Tijana T. Ivancevic1,2, Charles
E.M. Pearce1, Murk Bottema3,
Lakhmi C. Jain2
1University of Adelaide,
2University of South Australia,
3Flinders University of South Australia,
AUSTRALIA
e-mail: tivancevic@otpusnet.com.au
Abstract. A new model for a neurodynamical classifier is proposed.
The classifier is viewed as a generalized bi-directional associative memory
(GBAM) [11] and is described in the language of differential geometry [12-14].
GBAM is a tensor-field system resembling a two-phase biological neural
oscillator in which an excitatory neural field excites an inhibitory neural
field, which reciprocally inhibits the excitatory one. GBAM equations have
been directly implemented in the computer algebra system ‘Mathematica’
and tested on two different sets of data related to detection of breast
cancer.• The GBAM classifier outperformed other neural classifiers.
Key words: neurodynamics, differential geometry, classification
NEURODINAMIČKI KLASIFIKATOR BAZIRAN NA
DIFERENCIJALNOJ GEOMETRIJI
Predložen je novi model neurodinamičkog klasifikatora. Ovaj klasifikator
predstavlja generalizaciju asocijativne memorije u dva pravca (GBAM) [11]
i opisan je jezikom diferencijalne geometrije. GBAM sistem je formalno
definisan tenzorskim poljem koje modelira dvo-fazni biološki nervni oscillator,
u kojem ekscitatorno nervno polje pobugjuje inhibitorno nervno polje, koje
povratno inhibira exscitatorno polje. Jednačine GBAM-a su direktno implementirane
u sistemu kompjuterske algebre “Mathematica” i testirane na dva različita
skupa podataka za detekciju karcinoma dojke. GBAM klasifikator se pokazao
superiornijim u odnosu na druge neuralne klasifikatore.
Ključne reči: Neurodinamika, diferencijalna geometrija, klasifikacija
