Download Hierarchical Knowledge Representation: Symbolic Conceptual

INTERNATIONAL JOURNAL OF INTELLIGENT CONTROL AND SYSTEMS
VOL.12, NO.2 JUNE 2007
142-149
Hierarchical Knowledge Representation: Symbolic
Conceptual Trees and Universal Approximation
Luis Fernando de Mingo, Fernando Arroyo, Miguel Angel Dı́az and Juan Castellanos
Abstract— This paper presents a practical example of a system
based on neural networks that permits to build a conceptual
hierarchy. This neural system classifies an input pattern as an
element of each different category or subcategory that the system
has, until an exhaustive classification is obtained. The proposed
neural system is not a hierarchy of neural networks, it establishes
relationships among all the different neural networks in order
to transmit the neural activation when an external stimulus is
presented to the system. Each neural network is in charge of the
input pattern recognition to any prototyped class or category,
and also of transmitting the activation to other neural networks
to be able to continue with the classification. Therefore, the
communication of the neural activation in the system depends on
the output of each one of the neural networks, so as the functional
links established among the different networks to represent the
underlying conceptual hierarchy.
Index Terms— Neural Networks, Function Approximation, Hierarchical Architecture.
1. I NTRODUCTION
ONCEPTS and categories are being objects to study in
practical Psychology and in Artificial Intelligence (AI)
years ago. It deals with the research of how the knowledge
and meaning are represented in the memory [4]. Why are
concepts important?. Concepts or conceptual categories are
stable representations, stored in the memory, that permit to
treat different samples as members of a same class; without
them we will be slaves of particular [5].
From a psychologist point of view, when dealing with
objects, situations and actions as members of conceptual
categories, the perceived reality is mentally being divided into
different groups. A structure is imposed to the world, dividing
mentally the reality [3], [4]. Categories seem to be ruled by
the cognitive economy principle, this is, to extract essential
things from the known world and to represent them in the most
economical way in order to minimize the cognitive effort.
According to Collins and Quillian [2], [3], the importance
of a concept is not the concept by itself, it is determined by
the set of relationships that are established with other different
concepts. These relationships can be of two types: Subset and
Property. The former type expresses the specialization of some
C
L.F. de Mingo and M.A. Dı́az are with Dept. Organización y Estructura de la Información, Escuela Universitaria de Informática - Universidad
Politécnica de Madrid, Crta. de Valencia km. 7 - 28031 Madrid, Spain.
{lfmingo,mdiaz}@eui.upm.es
F. Arroyo is with Dept. Lenguajes, Proyectos y Sistemas Informáticos,
Escuela Universitaria de Informática - Universidad Politécnica de Madrid,
Crta. de Valencia km. 7 - 28031 Madrid, Spain. [email protected]
J. Castellanos is with Dept. Inteligencia Artificial, Facultad de Informática
- Universidad Politécnica de Madrid, Boadilla del Monte - 28660 Madrid,
Spain. [email protected]
concepts into others, it produces the categorization, allowing
to mentally structure the perceived reality.
What could be added from a connectionist point of view to
the concept representation in memory? [6]. Why could not it
be thought that the concepts are supported by some small sets
of neural assemblies? These ones form a mix of specialized
neural networks concerning the samples recognition task and
they determined if a sample belongs or is classified into a
concept.
Concepts are not isolated into the human cognitive system.
They are immersed into a hierarchical structure that facilitates,
among others, classification tasks to the human cognitive system. This conceptual hierarchy expresses a binary relationship
of inclusion defined by the following criterions:
• Inclusion criterion: Each hierarchy node determines a
domain included into domain of its father node. Each
hierarchy node determines a domain that includes every
domain of its son nodes.
• Generalisation-Specialisation criterion: Every node in the
hierarchy, has differentiating properties that make it different from its father node, if it exists, and from the others
son nodes of its father, if they exist.
This Inclusion relation makes possible to keep the maximal
economy criterion in the conceptual hierarchy. The defined
inclusion relation makes also possible to represent a conceptual hierarchy as an acycled directed graph in which nodes
represent concepts and edges the inclusion relation among
them. Edges connecting nodes establishes that the father nodes
are situated in the upper hierarchical level of its son nodes.
Obviously, concepts are generated in a natural manner and it
will not be constrained by these formal restrictions. However,
many of the classifications learnt during our school years are
built using these rules. In this paper, we will focus our work
in this kind of hierarchies, which are learnt with a teacher or
in a supervised manner.
Next sections deal with the representation of any conceptual
hierarchy using a set of neural networks, permitting the
complete or exhaustive classification of an input. Exhaustive
classification means that an input belongs, or not, to each one
of the supported concepts by the system and to their specializations. The hierarchical architecture is controlled using neural
network outputs, that is, depending on the output a different
neural network is activated.
2. P ROBLEM D ESCRIPTION
L
ET D domain of any samples. Let H a conceptual
hierarchy to the elements of the domain D. Let T the
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Mingo et al.: Hierarchical Knowledge Representation: Symbolic Conceptual Trees and Universal Approxination
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Fernando Arroyo Ph.D. on Artificial Intelligence
with a position of full professor at the Universidad
Politécnica de Madrid. He has a great number of international publications in leading journals concerning Membrane Computing and Neural Networks.
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Miguel Angel Dı́az Full professor at the Universidad Politécnica de Madrid. His research interests
lie in the area of membrane computing, especially
in networks of evolutionary processors, but also in
the area of neural networks.He has participated in
several local projects. He has some papers published
in visible journals and in proceedings from notable
conferences (WSEAS, etc.)
[10] Luis Mingo, Levon Aslanyan, Juan Castellanos, Miguel Diaz, and
Vladimir Riazanov. Fourier Neural Networks: An Approach with Sinusoidal Activation Functions. International Journal on INFORMATION
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Luis F. de Mingo Contracted professor at the
Universidad Politécnica de Madrid since 1998 and
Ph.D. on Artificial Intelligence. His research interests lie in the area of learning models, in particular in
the theoretical parts of Neural Networks and Pattern
Recognition, but also in the area of Networks of
Evolutionary Processors. He has participated in several INTAS projects and some local projects. Member
of the editorial board of IJITA, and international reviewer of KDS, ITECH conferences. Active member
of European Molecular Computation Consortium.
Juan Castellanos Full professor at the Universidad
Politécnica de Madrid with a Ph.D. on Artificial
Intelligence. His research interests lie in the area of
bio-computing, in particular in the theoretical parts
of DNA computing and membrane systems, but also
in the area of neural networks. He has more than
sixty papers in these branches of bioinformatics,
many of them published in visible journals and
in proceedings from notable conferences (7th, 8th
International Meeting on DNA Based Computers,
etc.)