Helsinki University of Technology
Neural Networks Research Centre
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In the following, Kohonen's Self-Organizing Maps (SOMs) (Kohonen, 1982, 1995) are introduced. The SOMs may provide a sound basis for modeling the general underlying principles of natural language learning and interpretation. The motivation for such a claim is presented in the rest of the paper.
An important consideration is that in the experiments the input for the SOM did not contain any predetermined classifications. The results indicate that the text input as such, with the statistical properties of the contextual relations, is sufficient for automatical creation of meaningful implicit categories. The categories emerge during the learning process. The symbol grounding task would, of course, be more realistic and complete if it is were possible to provide also other modalities such as pictorial images as a part of the context information.
Consider now that we are about to denote an interval of a single continuous parameter using a limited number of symbols. These symbols are then used in the communication between two subjects (human or artificial). In a trivial case two subjects would have same denotations for the symbols, i.e. the limits of the intervals corresponding to each symbol would be identical. If the "experience" of the subjects is acquired from differing sources, the conceptualization may very well differ.
One may then ask how to deal with this kind of discrepancies. A propositional level is not sufficient. The key idea is to provide the means for a system to associate continuous-valued parameter spaces to sets of symbols, and furthermore, to "be aware" of the differences in this association and to learn those differences explicitly. These kinds of abilities are especially required by highly autonomous systems that need to communicate using an open set of symbols or constructs of a natural language. This kind of association of set of symbols and a set of continuous parameters is a natural extension or modification of the word category maps (see Honkela, 1993; Honkela and Vepsäläinen, 1991). An augmented input consists of three main parts: the encoded symbol, the context which is the parameter vector in this case, and identification of the utterer or source of the symbol being used. The map nodes associate symbols with the continuous parameters. One node corresponds to an area in the multidimensional space, i.e., a Voronoi tessellation determined by the codebook vector associated with the map node and its neighboring nodes. The relation is one-to-many: one symbol is associated with infinitive number of points.
In this kind of mapping, the error (cf. Rosen, 1985), or a kind of relativity is a necessity in communication. One can define the exact reference of a symbol in a continuous space only to a limit that is restricted by several issues, for instance, the limited time available for communication in which the level of intersubjectivity is raised. A common source of context is often not available either. Von Foerster (1972b) has outlined the very basic epistemological questions that are closely related to the topics of the present discussion. He states, among other things, that by keeping track of the computational pathways for establishing equivalence, "objects" and "events" emerge as consequences of branches of computation which are identified as the processes of abstraction and memorization. In the realm of symbolic logic the invariance and change are paradoxical: "the distinct being the same", and "the same being distinct". In a model that includes both the symbolic description as well as the continuous counterpart, there is no paradox, and the relationship may be computed, e.g., by the self-organizing map.
The previously presented framework also provides a means to consider the relationship between language and thoughts. In the case of colors, one may hypothesize that the perceptual input in the human experience is overwhelming when compared with the symbolic descriptions. Thus, the "color map" is based on the physical properties of the input. On the other hand, abstract concepts are based on the cultural "agreements" and they are communicated symbolically so that the relation to external, physical counterparts is less straightforward. A natural result would be that such concepts are much more prone to subjective differences based on the cultural environment. Even if the original perceptual input is available but it is constantly associated with a systematic classifying symbolic input, the result deviates strongly compared with the case in which the latter information is not available. Von Foerster (1972a) has described the phenomenon and its consequences in the following way: "We seem to be brought up in a world seen through descriptions by others rather than through our own perceptions. This has the consequence that instead of using language as a tool with which to express thoughts and experience, we accept language as a tool that determines our thoughts and experience." In linguistics this kind of idea is referred to as the Sapir-Whorf hypothesis.
Music involves the expectation and anticipation of situations on the one hand, and confirmation or disconfirmation of them on the other. Kaipainen (1994) has studied the use of SOMs in modeling musical perception. In addition to the basic SOM, Kaipainen uses a a list of lateral connections that record the transition probabilities from one map node to another. The model is based on the specific use of the SOM in which the time dynamics of a process are characterized by the trajectory path on the map. This aspect has been important already in the first application area of the SOMs, namely speech recognition, and more recently in process monitoring. The model of musical perception was tested in three modes called "Gibsonian", "autistic", and "Neisserian". The Gibsonian and autistic are the two extremes regarding the use of anticipation recorded in the trajectory memory: the first model was designed so that it did not use the trajectory information at all. The result was that continuity from one variation to another could not be maintained. On the other extreme, the autistic model was parameterized so that it developed a deterministically strong schematic drive. It began to use its internal representational states, eventually becoming ignorant of the input flow of musical patterns. The intermediate model, denoted as Neisserian, was the one that performed best in musical terms. It was open to to the input having at the same time an internal schematic drive, anticipation, which intentionally actualized musical situations rather than just recognizing them as given.
When the relationship between Rosen's formulations and Kohonen's self-organizing maps is considered the following quote may be of interest (Rosen, 1985): "Briefly, we believe that one of the primary functions of the mind is precisely to organize percepts. That is, the mind is not merely a passive receiver of perceptual images, but rather takes an active role in processing them and ultimately in responding to them through effector mechanism. The organization of percepts means precisely the establishment of relations between them. But we then must admit such relations reflect the properties of the active mind as much as they do the percepts which the mind organizes." It seems that the SOM concretizes this idea. In general, Rosen's point of view may be characterized as physical and biological whereas Kohonen's main results are related to computational, epistemological, neurophysiological, and cognitive aspects. Many basic issues are interrelated, though, including those of error, order and disorder, similarity, and encoding.
von Foerster Heinz (1972a). Perception of the Future and the Future of Perception. Instructional Science 1, 1, R.W. Smith, and G.F. Brieske (eds.), Elsevier/North-Holland, New York/Amsterdam, pp. 31-43. (Also appeared in von Foerster, H.: Observing Systems, Intersystems Publications, Seaside, CA, 1981, pp. 189-204.)
von Foerster Heinz (1972b). Notes on an Epistemology for Living Things. BCL Report No. 9.3, Biological Computer Laboratory, Department of Electrical Engineering, University of Illinois, Urbana, 22 p. (Also appeared in von Foerster, H.: Observing Systems, Intersystems Publications, Seaside, CA, 1981, pp. 258-271.)
Honkela Timo and Vepsäläinen Ari M. (1991). Interpreting Imprecise Expressions: Experiments with Kohonen's Self-Organizing Maps and Associative Memory. Artificial Neural Networks, T. Kohonen and K. Mäkisara (eds.), vol. I, 897-902.
Honkela Timo (1993). Neural Nets that Discuss: A General Model of Communication Based on Self-Organizing Maps. Proc. ICANN'93, Int. Conf. on Artificial Neural Networks, S. Gielen and B. Kappen, Springer, London, 408-411.
Honkela Timo, Pulkki Ville, and Kohonen Teuvo (1995). Contextual relations of words in Grimm tales analyzed by self-organizing map. In F. Fogelman-Soulie and P. Gallinari (eds.) ICANN-95, Proceedings of International Conference on Artificial Neural Networks, vol. 2, pp. 3-7. EC2 et Cie, Paris.
Honkela Timo, Kaski Samuel, Lagus Krista, and Kohonen Teuvo. Newsgroup Exploration with WEBSOM Method and Browsing Interface. Report A32, Helsinki University of Technology, Laboratory of Computer and Information Science, January, 1996.
Honkela Timo (1997). Self-Organizing Maps of Words for Natural Language Processing Applications. Proceedings of Soft Computing '97, in print, September 17-19, 1997, 7 p.
Honkela Timo (1997). Emerging categories and adaptive prototypes: Self-organizing maps for cognitive linguistics. Extended abstract, accepted to be presented in the International Cognitive Linguistics Conference, Amsterdam, July 14-19, 1997.
Kaipainen Mauri (1994). Dynamics of Musical Knowledge Ecology - Knowing-What and Knowing-How in the World of Sounds. PhD thesis, University of Helsinki, Helsinki, Finland, Acta Musicologica Fennica 19.
Kaski Samuel (1997). Data Exploration Using Self-Organizing Maps. Dr.Tech thesis. Helsinki University of Technology, Espoo, Finland, Acta Polytechnica Scandinavica, no. 82.
Kaski Samuel, Honkela Timo, Lagus Krista, and Kohonen Teuvo (1996). Creating an order in digital libraries with self-organizing maps. Proceedings of WCNN'96, World Congress on Neural Networks, Lawrence Erlbaum and INNS Press, Mahwah, NJ, pp. 814-817.
Kohonen Teuvo (1982). Self-organized formation of topologically correct feature maps. Biological Cybernetics, 43, pp. 59-69.
Kohonen Teuvo (1995). Self-Organizing Maps. Springer-Verlag.
Kohonen Teuvo, Kaski Samuel, Lagus Krista, and Honkela Timo (1996). Very large two-level SOM for the browsing of newsgroups. Proceedings of ICANN'96, International Conference on Artificial Neural Networks.
Lagus Krista, Honkela Timo, Kaski Samuel, and Kohonen Teuvo (1996). Self-organizing maps of document collections: a new approach to interactive exploration. E. Simoudis, J. Han, and U. Fayyad (eds.), Proceedings of the Second International Conference on Knowledge Discovery & Data Mining, AAAI Press, Menlo Park, CA, pp. 238-243.
Miikkulainen Risto (1993). Subsymbolic Natural Language Processing: An Integrated Model of Scripts, Lexicon, and Memory. MIT Press, Cambridge, MA.
Ritter Helge and Kohonen Teuvo (1989). Self-organizing semantic maps. Biological Cybernetics, vol. 61, no. 4, pp. 241-254.
Rosen Robert (1985). Anticipatory Systems. Pergamon Press.
Scholtes Jan C. (1993). Neural Networks in Natural Language Processing and Information Retrieval. PhD thesis, University of Amsterdam, Amsterdam.