=Paper=
{{Paper
|id=Vol-474/paper-14
|storemode=property
|title=Interweaving Knowledge Representation and Adaptive Neural Networks
|pdfUrl=https://ceur-ws.org/Vol-474/paper12.pdf
|volume=Vol-474
}}
==Interweaving Knowledge Representation and Adaptive Neural Networks==
https://ceur-ws.org/Vol-474/paper12.pdf
Interweaving Knowledge Representation
and Adaptive Neural Networks
Ilianna Kollia, Nikolaos Simou,
Giorgos Stamou and Andreas Stafylopatis
Department of Electrical and Computer Engineering,
National Technical University of Athens,
Zographou 15780, Greece
nsimou@image.ntua.gr
Abstract. Both symbolic knowledge representation systems and ma-
chine learning techniques, including artificial neural networks, play a
significant role in Artificial Intelligence. Interweaving these techniques,
in order to achieve adaptation and robustness in classification problems
is of great importance. In this paper we present a novel architecture
that can provide effective connectionist adaptation of ontological knowl-
edge. The proposed architecture can be used to improve performance of
multimedia analysis and man machine interaction systems.
1 Introduction
Intelligent systems based on symbolic knowledge processing, on the one hand,
and artificial neural networks, on the other, differ substantially. Nevertheless,
they are both standard approaches to artificial intelligence and it is very desir-
able to combine the robustness provided by neural networks, especially when
data are noisy, with the expressivity of symbolic knowledge representation. This
has contributed decisively to the growing interest in developing neural-symbolic
systems [4, 6, 5]. This integration can be realised by an incremental workflow for
knowledge adaptation. Symbolic knowledge bases can be embedded into a con-
nectionist representation, where the knowledge can be adapted and enhanced
from raw data. This knowledge may in turn be extracted into symbolic form,
where it can be further used.
In this paper we focus on developing connectionist adaptation of ontological
knowledge. Section 2 presents the proposed architecture that mainly consists
of the formal knowledge and the knowledge adaptation components, which are
described in sections 3 and 4 respectively. Conclusions and ongoing research
involving semantic multimedia analysis applications are reported in section 6.
2 The Proposed Architecture
Figure 1 summarizes the proposed system architecture, consisting of two main
components: the Formal Knowledge and the Knowledge Adaptation. The Formal
Knowledge stores the knowledge base components that describe the problem
under analysis. More specifically, the Ontologies module formally represents the
general knowledge about the problem (TBox) generated during the Development
Phase by knowledge engineers and experts.
Fig. 1. The semantic adaptation architecture
Moreover, the Formal Knowledge contains the World Description that is
actually a representation of all objects and individuals of the world, as well as
their properties and relationships in terms of the Ontology (ABox). It is evident
that most of the above data involve different types of uncertain information and,
thus, they can be represented as formal (fuzzy) assertions connecting the objects
and individuals of the world with the concepts and relationships of the Ontology.
This operation is performed by the Semantic Interpretation module.
In real environments however, this is a rather optimistic claim. Unfortunately,
there may be lot of reasons that cause inconsistencies in the Formal Knowledge.
For example, it is impossible to model all specific environments and thus, in some
cases, conflicting assertions can arise. In such cases, the Knowledge Adaptation
component of the system tries to resolve the inconsistency through a recursive
learning process. Adaptation improves the knowledge of system by changing the
world description and to some degree the axioms of the terminology. The new
information as represented in a connectionist model and, with the aid of learning
algorithms, is adapted and then re-inserted in the knowledge base through the
Knowledge Extraction and Semantic Interpretation modules for system adapta-
tion.
2
3 The Formal Knowledge Component
The focus of the proposed system architecture in Figure 1 is on adaptation of the
knowledge base, so as to deal with contextual information and raw data peculiar-
ities obtained from multimodal inputs. In the paper we deal with interweaving
of formal knowledge representation and neural-symbolic integration. In particu-
lar, we use recent results that extract parameter kernel functions for individuals
within ontologies [3, 2, 1]. Exploitation of these kernels permits inducing classi-
fiers for individuals in Semantic Web (OWL) ontologies. In this paper, extraction
of kernel functions is the main outcome of the Formal Knowledge component -
assisted by a reasoning engine - for feeding the connectionist-based Knowledge
Adaptation task.
The family of kernel functions kpF : Ind(A)×Ind(A) → [0, 1], for a knowledge
base K = hT, Ai consisting of the TBox T (set of terminological axioms of
concept descriptions) and the ABox A (assertions on the world state); Ind(A)
indicates the set of individuals appeared in A, and F = {F1 , F2 , . . . , Fm } is a
set of concept descriptions. These functions are defined as the Lp mean of the,
say m, simple concept kernel functions κi , i = 1, . . . , m, where, for every two
individuals a,b, and p > 0,
1 (Fi (a) ∈ A ∧ Fi (b) ∈ A) ∨ (¬Fi (a) ∈ A ∧ ¬Fi (b) ∈ A)
κi (a, b) = 0 (Fi (a) ∈ A ∧ ¬Fi (b) ∈ A) ∨ (¬Fi (a) ∈ A ∧ Fi (b) ∈ A) (1)
1
2 otherwise
·Xm ¯ p ¯¸1/p
¯ κi (a, b) ¯
∀a, b ∈ Ind(A) kpF (a, b) := ¯ ¯ (2)
i=1
m
The rationale of these kernels is that similarity between individuals is deter-
mined by their similarity with respect to each concept Fi , i.e, if they both are
instances of the concept or of its negation. It has been shown that kpF is a valid
kernel, based on its composition through simpler matching kernels and on the
closure property with respect to sum, multiplication by a constant and kernel
multiplication.
It should be stressed that the reasoning engine, included in Figure 1, is of
major importance for the whole procedure, because it assists the operation of all
knowledge related components. First, during the knowledge development phase,
it is responsible for enriching manual generation of concepts and relations. In
the operation phase, it interacts with the semantic interpretation layer and the
connectionist system for knowledge adaptation to local environments. Both crisp
and fuzzy reasoners can form this engine, we use the FIRE engine [11] that is
based on the fuzzy extension of the DL SHIN [7].
We use fuzzy reasoning because a fuzzy assertional component permits more
detailed descriptions of a domain. In order to compute (1), (2) the greatest lower
bound (GLB) reasoning service of FiRE defined in [12] is used, but the resulting
greatest lower bound is treated crisply. In other words, if GLB for Fi (a) > 0,
3
then Fi (a) ∈ A, while if GLB for Fi (a) = 0, then ¬Fi (a) ∈ A. We intend to
incorporate the fuzzy element in the estimation of kernel functions using fuzzy
operations like fuzzy aggregation and fuzzy weighted norms for the evaluation
of the individuals.
4 The Adaptation Mechanism
In the proposed architecture of Figure 1, let us assume that the set of individ-
uals (and corresponding features), that have been used to generate the formal
knowledge, is provided, by the Semantic Interpretation Layer, to the Knowl-
edge Adaptation component. Support Vector Machines constitute a well known
method which can be based on kernel functions[2] to efficiently induce classifiers
that work by mapping the instances into an embedding feature space, where
they can be discriminated by means of a linear classifier. Kernel Perceptrons
can be also applied to this linearly separable classification problem.
Let the system be in its -real life- operation phase. Due to local or user
oriented characteristics, real life data can be quite different from those of the
individuals used in the training phase; thus they may be not well represented by
the existing formal knowledge. Whenever a new individual is presented to the
system, it should be related, through the kernel function to each individual of
the knowledge base w.r.t to a specific concept - category; the input data domain
is, thus, transformed to another domain - taking into account the semantics that
have been inserted to the kernel function. However, the kernel function in (1), (2)
is not continuous w.r.t individuals. Consequently, the values of the kernel func-
tions when relating a new individual to any existing one should be computed.
To cope with this problem, it is assumed that the semantic relations, that are
expressed through the above kernel functions, also hold for the syntactic rela-
tions of the individuals, as expressed by their corresponding low level features,
estimated and presented at the system input. Under this assumption, a feature
based matching criterion using a k-means algorithm, is used to relate the new
individual to each one of the cluster centers w.r.t the low level feature vector.
The SVM or Kernel Perceptron can be retrained - including the new individuals
in the training data set, while getting the corresponding desired responses by
the User or by the Semantic Interpretation Layer - adapting its knowledge to
the specific context and use. An hierarchical, multilayer kernel perceptron, the
input layer of which is identical to the trained kernel perceptron can also be used
[9].
Knowledge extraction from trained neural networks has been a topic of ex-
tensive research [8]. One way is to transfer the - most characteristic - new in-
dividuals obtained in the local environment, together with the corresponding
desired outputs - concepts, to the knowledge development module of the main
system (Figure 1), so that with the assistance of the reasoning engine, the system
formal knowledge, i.e., both the T-Box and the A-Box, be updated, w.r.t the
specific context or user. A methodology that can be used to adapt a knowledge
base K = hT, Ai for a concept Fi , is the following. Check all related concepts,
4
denoted as RFi F1 . . . RFi Fi under the specific context, count the number |RFi Fi |
of occurrences of RFi Fi ∈ A, as well as the axioms defined for the concept Fi
in the knowledge base (i.e. Axiom(Fi ) ∈ T ). Let RFi Fi ∈ Axiom(Fi ) when the
concept RFi Fi is used in Axiom(Fi ) and RFi Fi 6∈ Axiom(Fi ) when it is not used.
The related concepts with the highest occurrence are selected for adaptation of
the terminology, while the insignificant ones are removed.
5 Conclusion
In this paper we presented a novel architecture for connectionist adaptation
of ontological knowledge. We are currently performing experimentation of the
system performance for solving an image/video segmentation and classification
problem [9, 10]. Future work, includes the incorporation of fuzzy set theory in
the kernel evaluation. Additionally, we intend to further examine the adaptation
of the knowledge base using the connectionist architecture, mainly focusing on
the selection of the appropriate DL constructors and on inconsistency handling.
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