Wladyslaw Homenda

Computer Information Systems and Industrial Management

We survey some critical issues arising in the ubiquitous computing paradigm, in particular the interplay between context-awareness and security. We then overview a language-based approach that addresses these problems from the point of view of Formal Methods. More precisely, we briefly describe a core functional language extended with mechanisms to express adaptation to context changes, to manipulate resources and to enforce security policies. In addition, we shall outline a static analysis for guaranteeing programs to securely behave in the digital environment they are part of.

From Fuzzy Cognitive Maps to Granular Cognitive Maps

Fuzzy cognitive maps (FCMs) form a class of graph-oriented fuzzy models describing causal relationships among concepts. In this study, we augment these models by introducing their generalization coming in the form of granular FCMs. In contrast with FCMs, in the granular FCMs, the connections between the nodes (states) are described in the form of information granules, especially intervals and fuzzy sets. Key scenarios in which granular models (and granular FCMs) arise are presented in order to offer a compelling rationale behind the formation of such models. In the context of system modeling, we show that information granularity emerges as an important design asset. We discuss detailed schemes of allocation of information granularity and quantify a performance of the resulting granular FCM in terms of a coverage criterion. For illustrative purposes, the detailed studies are completed for granular FCMs with interval-valued connections.

Modeling time series with fuzzy cognitive maps

Fuzzy Cognitive Maps are recognized knowledge modeling tool. FCMs are visualized with directed graphs. Nodes represent information, edges represent relations within information. The core element of each Fuzzy Cognitive Map is weights matrix, which contains evaluations of connections between maps nodes. Typically, weights matrix is constructed by experts. Fuzzy Cognitive Map can be also reconstructed in an unmanned mode. In this article authors present their own, new approach to time series modeling with Fuzzy Cognitive Maps. Developed methodology joins Fuzzy Cognitive Map reconstruction procedure with moving window approach to time series prediction. Authors train Fuzzy Cognitive Maps to model and forecast time series. The size of the map corresponds to the moving window size and it informs about the length of historical data, which produces time series model. Developed procedure is illustrated with a series of experiments on three real-life time series. Obtained results are compared with other approaches to time series modeling. The most important contribution of this paper is description of the methodology for time series modeling with Fuzzy Cognitive Maps and moving windows.

Design of Fuzzy Cognitive Maps for Modeling Time Series

This study elaborates on a comprehensive design methodology of fuzzy cognitive maps (FCMs). Here, the maps are regarded as a modeling vehicle of time series. It is apparent that whereas time series are predominantly numeric, FCMs are abstract constructs operating at the level of abstract entities referred to as concepts and represented by the individual nodes of the map. We introduce a mechanism to represent a numeric time series in terms of information granules constructed in the space of amplitude and change of amplitude of the time series, which, in turn, gives rise to a collection of concepts forming the corresponding nodes of the FCMs. Each information granule is mapped onto a node (concept) of the map. We identify two fundamental design phases of FCMs, namely 1) formation of information granules mapping numeric data (time series) into activation levels of information granules (viz., the nodes of the map), and 2) optimization of information granules at the parametric level, viz., learning (estimating) the weights between the nodes of the map. The learning is typically realized in a supervised mode on a basis of some experimental data. A construction of information granules is realized with the aid of fuzzy clustering, namely fuzzy C-means. The optimization is realized with the use of particle swarm optimization. The proposed approach is illustrated in detail by a series of experiments using a collection of publicly available data.

Nodes Selection Criteria for Fuzzy Cognitive Maps Designed to Model Time Series

The article introduces three concepts’ rejection/selection criteria for Fuzzy Cognitive Map-based method of time series modeling and prediction. Proposed criteria are named entropy index, membership index and global distance index. Concepts’ selection strategies facilitate Fuzzy Cognitive Map design procedure. Proposed criteria allow to simplify, otherwise very complex models, and achieve a reasonable balance between complexity and accuracy.

Notes on automatic music conversions

Aspects of automatic conversion between sheet music and Braille music are studied in this paper. The discussion is focused on syntactical structuring of information carried as sheet music and as Braille music (their digital representations). The structuring is founded on context-free methods. Syntactical structures of a given piece of music create so called lexicon. Syntactical structures are reflected in the space of sounds/notes. This dependency is a many-to-one mapping for sheet music and is a many-to-many relation in case of Braille music. The dependency between lexicon and the space of sounds/notes defines semantics of the given language. Both syntactic structuring and semantic valuation produce a basis for an automatic conversion between both languages: printed music notation and Braille music.

Optical Music Recognition: the Case Study of Pattern Recognition

The paper presents a pattern recognition study aimed on music notation recognition. The study is focused on practical aspect of optical music recognition; it presents a variety of methods applied in optical music recognition technology. The following logically separated stages of music notation recognition are distinguished: acquiring music notation structure, recognizing symbols of music notation, analyzing contextual information. The directions for OMR package development are drawn.

Time Series Modeling with Fuzzy Cognitive Maps: Simplification Strategies

The article is focused on the issue of complexity of Fuzzy Cognitive Maps designed to model time series. Large Fuzzy Cognitive Maps are impractical to use. Since Fuzzy Cognitive Maps are graph-based models, when we increase the number of nodes, the number of connections grows quadratically. Therefore, we posed a question how to simplify trained FCM without substantial loss in map’s quality. We proposed evaluation of nodes’ and weights’ relevance based on their influence in the map. The article presents the method first on synthetic time series of different complexity, next on several real-world time series. We illustrate how simplification procedure influences MSE. It turned out that with just a small increase of MSE we can remove up to \(\frac{1}{3}\) of nodes and up to \(\frac{1}{6}\) of weights for real-world time series. For regular data sets, like the synthetic time series, FCM-based models can be simplified even more.

Querying in spaces of music information

This study is focused on querying accomplished on structured spaces of information. Querying is understood in terms of mining structures of information and of knowledge understanding. We consider information as a subject of descriptions expressed in some language. Information is hidden behind such descriptions. Operations done on structured spaces of information are performed on language constructions describing such structures. However, automatic operations not always can be performed directly on language constructions. In such cases it is necessary to expand performance to the space of information. The study concerns paginated (i.e. printed and handwritten) music notation. It is shown that querying in the space of music information requires syntactic structuring as well as its expansion to semantic analysis. It is worth underlining that data understanding requires analysis of uncertainty: analyzed data are usually incomplete, uncertain and with some incorrectness. Such imperfectness of information is hidden under the level of syntax and semantics. Due to limitation of the paper this problem is not studied.

Automatic data understanding: a necessity of intelligent communication

In this paper aspects of intelligent man-machine communication are considered. Selected topics are deemed from a perspective of data processing. Human beings expect that data processing is under a kind of intelligent control. This expectation forms natural properties that communication is focused on revealing structures of data being exchanged and on controlling operations to which these structures of data are subjected to. Such qualities are a scanty substitute of the main goal of communication, which is an understanding data being exchanged. An exposition of these topics is illustrated with an example from the domain of music notation. The discussion leads to a conclusion that structuring and understanding of processed data is a basis of intelligent man-machine communication.