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1
Content available remote An algorithm for generalization of decision rules by joining
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EN
An algorithm for rules generalization consisting in joining of rules with the same structure is presented in the paper. The algorithm joins rules conditionals descriptors so as the language of ruies representation is unchanged. A value of rules quality evaluation measure is a criterion deciding about advisability of rules joining. Some exemplary results of algorithm working is described in the paper as well. The tolerance rough sets model is used in ruies induction.
EN
The paper undertakes the subject of spatial data pre-processing for marine mobile information systems. Short review of maritime information systems is given and the focus is laid on mobile systems. The need of spatial data generalization is underlined and the concept of technology for such generalization in mobile system is presented. The research part of the paper presents the results of analyzes on selected parameters of simplification in the process of creating mobile navigation system for inland waters. In the study authors focused on selected layers of system. Models of simplification for layers with line features and with polygons were tested. The parameters of tested models were modified for the purposes of study. The article contains tabular results with statistics and spatial visualization of selected layers for individual scales.
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2019
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tom Vol. 9, No. 2
123--147
EN
The present paper1 aims to propose a new type of information-theoretic method to maximize mutual information between inputs and outputs. The importance of mutual information in neural networks is well known, but the actual implementation of mutual information maximization has been quite difficult to undertake. In addition, mutual information has not extensively been used in neural networks, meaning that its applicability is very limited. To overcome the shortcoming of mutual information maximization, we present it here in a very simplified manner by supposing that mutual information is already maximized before learning, or at least at the beginning of learning. The method was applied to three data sets (crab data set, wholesale data set, and human resources data set) and examined in terms of generalization performance and connection weights. The results showed that by disentangling connection weights, maximizing mutual information made it possible to explicitly interpret the relations between inputs and outputs.
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tom Vol. 3, no. 1/1
59-67
PL
Wśród elementów koncepcji wielorozdzielczej/wieloreprezentacyjnej bazy danych topograficznych (WBDT) związanych z koniecznością harmonizacji baz źródłowych, opracowania technik współistnienia, wymiany, eksploatacji czy aspektów prawnych, należy przewidzieć również wypracowanie modelu niezmienników, który zapewniałby spójność geometrii obiektów bazy. Takie podejście ma kluczowe znaczenie w procesie generalizacji obiektów, wiązania geometrii pierwotnej i wtórnej obiektów bazy, pozwala na fragmentaryczną wymianę czy aktualizację danych. Obiekt bazy posiada geometrię pierwotną (nieprzekształconą) możliwie najdokładniejszą oraz jedną szczegółową informację opisową. Obiekt bazy może przybierać różne wersje (geometrie wtórne) powstałe na skutek generalizacji i/lub redakcji. Koncepcja WBDT powinna zakładać występowanie określonych poziomów uogólnienia obiektów pierwotnych bazy na różnych fragmentach obszarowych oraz występowanie obiektów pierwotnych i wtórnych na tym samym obszarze. W swoim założeniu WBDT jest bazą niejednorodną, dlatego dobra informacja o danych i właściwe zarządzanie bazą są konieczne w celu uniknięcia nieporozumień.
EN
Among the various elements of the Multi-Resolution/Representation- Database (MRDB) that relate to the synchronization of database sources, the objects' correlation techniques, the data exchange and usage, as well as to the legal aspects, one ought to allow for the creation of invariable object features which would make for the cohesion of the database objects. Such an approach is essential in the processes of object generalization and bonding of the original and derivative geometry. Additionally, it allows partial data exchange and object updates. An object in the MRDB database has an original (not yet distorted) geometry which is most accurate and a detailed description. Moreover, the same object can have multiple versions (derivative geometries) created upon its' generalizations and/or editing. The MRDB-type database concept should, therefore, be based on the premise of several given object generalization levels of different special areas as well as on the existence of original and derivate objects in the same area. By definition, MRDB is a heterogeneous database which is why a thorough data information and proper database management is essential in order to avoid possible confusion.
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Content available A task about a cube; or, on generalization in 3D
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The necessity of teaching such an activity as generalization was considered by Z. Krygowska in the ‘70s (Krygowska, 1977). The formation of this ability requires an adequate selection of non-stereotypical tasks, for which the algorithm is unknown to the person solving the task, ones in which a student is forced to search for their own method of solving the task on the basis of their knowledge. In literature, there are known studies concerning the process of generalization of students of different ages which use, at most, 2D visual patterns. However, the author still did not find any research based on tasks which examine the process of generalization in 3D. In this paper, results will be shown of using a task concerning a cube carried out in a diverse group of students from middle school, high school, and university.
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The issue of reconstruction of missing or unreliable parts of an image is one of the basic problems in image processing. For example, there are a number of methods for texture generation on the basis of a small sample. This paper presents a method that 'bottlenecks' an image processing feedforward neural network so that only some basic traits of the image are preserved. These basic traits are in turn used to generalize the image, thus filtering out any unusual parts of the image. The ability of neural networks and several other learning machines to generalize is based on the premise of smoothness of the generalizing function. Thus, in order to detect advanced patterns that exhibit complex traits like repetitiveness, instead of training these machines directly with raw data, transforms of the patterns like the Fast Fourier Transform are sometimes performed. In this paper it is shown, that a simple feedforward neural network, without any pre-processing of the training data, using the described 'bottleneck' architecture, can properly predict a stochastically repetitive pattern in a raster image.
EN
There is a productive and suggestive approach in philosophical logic based on the idea of generalized truth values. This idea, which stems essentially from the pioneering works by J.M. Dunn, N. Belnap, and which has recently been developed further by Y. Shramko and H. Wansing, is closely connected to the power-setting formation on the base of some initial truth values. Having a set of generalized truth values, one can introduce fundamental logical notions, more specifically, the ones of logical operations and logical entailment. This can be done in two different ways. According to the first one, advanced by M. Dunn, N. Belnap, Y. Shramko and H. Wansing, one defines on the given set of generalized truth values a specific ordering relation (or even several such relations) called the logical order(s), and then interprets logical connectives as well as the entailment relation(s) via this ordering(s). In particular, the negation connective is determined then by the inversion of the logical order. But there is also another method grounded on the notion of a quasi-field of sets, considered by Białynicki-Birula and Rasiowa. The key point of this approach consists in defining an operation of quasi-complement via the very specific function g and then interpreting entailment just through the relation of set-inclusion between generalized truth values. In this paper, we will give a constructive proof of the claim that, for any finite set V with cardinality greater or equal 2, there exists a representation of a quasi-field of sets isomorphic to de Morgan lattice. In particular, it means that we offer a special procedure, which allows to make our negation de Morgan and our logic relevant.
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Forecasting the value of real estate is an essential element that should be taken into account by the investor in the process of financing an investment. A similar situation can be observed in the process of land management. In such cases, the reliability of the model used for real estate value prediction becomes a key issue. The geostatic model is designed to be used for diagnosing the land market system in the past and in the present (at the moment the forecast is generated). It then becomes a prognostic geostatic model used for forecasting. Geostatic models can be developed based on a set of artificial neural networks. A set of neural networks is a set of many trained monolithic neural networks, which are combined into one set to eliminate faults assigned to single network models, as well as to improve generalization capability and resistance. The aim of the present study was to develop and test in practice a set of measures enabling to evaluate the quality of a forecasting model as well as its generalization capability.
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Content available remote Random generalization by feedforward neural networks
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A generalization by a feedforward neural network is discussed, such that some samples may be generalized using very dierent, conflicting criteria. A training set is deliberately constructed to show that feedforward neural networks in such a case can generalize very spuriously and randomly. To illustrate the dierences between dierent learning machines, results given by a small subset of the support vector machines are also presented.
PL
W artykule dyskutowane jest uczenie jednokierunkowych sieci neuronowych w którym niektóre próbki mogą być uogólnianie przy użyciu bardzo odmiennych kryteriów. Zbiór uczący jest specjalnie skonstruowany w sposób pokazujący, że w przypadku istnienia bardzo odmiennych kryteriów uogólniania sieć neuronowa może generalizować w sposób przypadkowy, wynikły prawie całkowicie ze struktury wewnętrznej sieci, a nie z zawartości pliku uczącego. Sieci neuronowe są porównane też do SVM-ów, które przy odpowiednich parametrach nie wykazały takiej losowości, jednak z drugiej strony w testowanych przypadkach nie potrafiły uogólnić niektórych wzorców w pliku uczącym.
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Regularizing the gradient norm of the output of a neural network is a powerful technique, rediscovered several times. This paper presents evidence that gradient regularization can consistently improve classification accuracy on vision tasks, using modern deep neural networks, especially when the amount of training data is small. We introduce our regularizers as members of a broader class of Jacobian-based regularizers. We demonstrate empirically on real and synthetic data that the learning process leads to gradients controlled beyond the training points, and results in solutions that generalize well.
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Content available remote Development of Ensemble Tree Models for Generalized Blood Glucose Level Prediction
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Type-1 diabetes (T1D) patients must carefully monitor their insulin doses to avoid serious health complications. An effective regimen can be designed by predicting accurate blood glucose levels (BGLs). Several physiological and data-driven models for BGL prediction have been designed. However, less is known on the combination of different traditional machine learning (ML) algorithms for BGL prediction. Furthermore, most of the available models are patient-specific. This research aims to evaluate several traditional ML algorithms and their novel combinations for generalized BGL prediction. The data of forty T1D patients were generated using the Automated Insulin Dosage Advisor (AIDA) simulator. The twenty-four hour time-series contained samples at fifteen-minute intervals. The training data was obtained by joining eighty percent of each patient's time-series, and the remaining twenty percent time-series was joined to obtain the testing data. The models were trained using multiple patients' data so that they could make predictions for multiple patients. The traditional non-ensemble algorithms: linear regression (LR), support vector regression (SVR), k-nearest neighbors (KNN), multi-layer perceptron (MLP), decision tree (DCT), and extra tree (EXT) were evaluated for forecasting BGLs of multiple patients. A new ensemble, called the Tree-SVR model, was developed. The BGL predictions from the DCT and the EXT models were fed as features into the SVR model to obtain the final outcome. The ensemble approach used in this research was based on the stacking technique. The Tree-SVR model outperformed the non-ensemble models (LR, SVR, KNN, MLP, DCT, and EXT) and other novel Tree variants (Tree-LR, Tree-MLP, and Tree-KNN). This research highlights the utility of designing ensembles using traditional ML algorithms for generalized BGL prediction.
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In this work, a study focusing on proposing generalization metrics for Deep Reinforcement Learning (DRL) algorithms was performed. The experiments were conducted in DeepMind Control (DMC) benchmark suite with parameterized environments. The performance of three DRL algorithms in selected ten tasks from the DMC suite has been analysed with existing generalization gap formalism and the proposed ratio and decibel metrics. The results were presented with the proposed methods: average transfer metric and plot for environment normal distribution. These efforts allowed to highlight major changes in the model’s performance and add more insights about making decisions regarding models’ requirements.
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In the training process of students – future teachers of mathematics, an important role is played by, among others, participation in the diploma seminar, during which the student (being at the final stage of studies)is tasked with preparing a bachelor’s or master’s thesis. This dissertation may be purely mathematical in nature or refer to problems in didactics of mathematics. The article aims to develop and illustrate some thoughts from previous works of the authors (Zaręba, 2009; Major, Olik-Pawlik, Ratusiński, Zaręba, 2016), pointing to the legitimacy of the preparation of teacher diploma theses in the field of didactics of mathematics by students.
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In this paper, feedforward neural networks are presented that have nonlinear weight functions based on look-up tables, that are specially smoothed in a regularization called the diffusion. The idea of such a type of networks is based on the hypothesis that the greater number of adaptive parameters per a weight function might reduce the total number of the weight functions needed to solve a given problem. Then, if the computational complexity of a propagation trough a single such a weight function would be kept low, then the introduced neural networks might possibly be relatively fast.
PL
W artykule opisane są jednokierunkowe sieci neuronowe z funkcjami wag reprezentowanymi przez tablice, specjalnie wygładzane w regularyzacji zwanej dyfuzją. Pomysł użycia tego typu sieci wynika z hipotezy, że więcej adaptatywnych parametrów na jedną funkcję wagi pozwoli na redukcję liczby tych funkcji. Wówczas, w przypadku gdyby tylko niektóre adaptywne parametry wagi były wykorzystywane w czasie pojedynczej propagacji, także czas propagacji przez jedną wagę byłby względnie krótki, sieci takie mogłyby być więc względnie szybkie.
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The article deals with constructing the discovery of the number of combinations. It stems from the approach of genetic constructivism, which works with the generic model theory, and its research goal was to develop the stages of isolated models, particularly using the phenomenon of isomorphism. Children aged 11–13 participated in the experiment during their mathematics club, in which they worked in groups at first and together at the blackboard afterwards. The results come from analyzing the experiment protocol and a video recording of part of the experiment. In this study, the authors focus primarily on a detailed analysis of individual sub-phases of isolated models under the generic model theory. The experiment highlights the importance of isomorphism as a generalization tool. The authors have identified the obstacles on the way to advanced sub-phases of isolated models. Another contribution is the division of the fourth sub-phase into two separate sub-phases, which has been achieved using the method of atomic analysis.
EN
Parallel X-rays are functions that measure the intersection of a given set with lines parallel to a fixed direction in R2. The reconstruction problem concerning parallel X-rays is to reconstruct the set if the parallel X-rays into some directions are given. There are several algorithms to give an approximate solution of this problem. In general we need some additional knowledge on the object to obtain a unique solution. By assuming convexity a suitable finite number of directions is enough for all convex planar bodies to be uniquely determined by their X-rays in these directions [13]. Gardner and Kiderlen [12] presented an algorithm for reconstructing convex planar bodies from noisy X-ray measurements belonging to four directions. For a reconstruction algorithm assuming convexity we can also refer to [17]. An algorithm for the reconstruction of hv-convex planar sets by their coordinate X-rays (two directions) can be found in [18]: given the coordinate X-rays of a compact connected hv-convex planar set K the algorithm gives a sequence of polyominoes Ln all of whose accumulation points (with respect to the Hausdorff metric) have the given coordinate X-rays almost everywhere. If the set is uniquely determined by the coordinate X-rays then Ln tends to the solution of the problem. This algorithm is based on generalized conic functions measuring the average taxicab distance by integration [21]. Now we would like to give an extension of this algorithm that works in the case when only some measurements of the coordinate X-rays are given. Following the idea in [12] we extend the algorithm for noisy X-ray measurements too.
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Content available remote Action Rules of Lowest Cost and Action Set Correlations
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A knowledge discovery system is prone to yielding plenty of patterns, presented in the form of rules. Sifting through to identify useful and interesting patterns is a tedious and time consuming process. An important measure of interestingness is: whether or not the pattern can be used in the decision making process of a business to increase profit. Hence, actionable patterns, such as action rules, are desirable. Action rules may suggest actions to be taken based on the discovered knowledge. In this way contributing to business strategies and scientific research. The large amounts of knowledge in the form of rules presents a challenge of identifying the essence, the most important part, of high usability. We focus on decreasing the space of action rules through generalization. In this work, we present a new method for computing the lowest cost of action rules and their generalizations. We discover action rules of lowest cost by taking into account the correlations between individual atomic action sets.
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Content available Generalized semi-opened axial dispersion model
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EN
The axial dispersion model (ADM) is studied and then generalized by a new form of the left boundary condition of semi-open flow system. The resulting parameter driven model covers the traditional axial models: axial closed-opened dispersion model with enforced input concentration (AEO), axial closed-opened dispersion model with input Danckwerts' condition (ACO), and axial opened-opened model (AOO). It also enables development of the degraded axial model (ADO). The research is concerned with both modeling and mathematical solution. Also, many numerical aspects of computer realization are discussed.
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Content available remote A Tabled Prolog Program for Solving Sokoban
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This paper presents our program in B-Prolog submitted to the third ASP solver competition for the Sokoban problem. This program, based on dynamic programming, treats Sokoban as a generalized shortest path problem. It divides a problem into independent subproblems and uses mode-directed tabling to store subproblems and their answers. This program is very simple but quite efficient. Without use of any sophisticated domain knowledge, it easily solves 14 of the 15 instances used in the competition. We show that the approach can be easily applied to other optimization planning problems.
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Content available remote State Complexity of Multiple Catenations
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We improve some results relative to the state complexity of the multiple catenations described by Gao and Yu. In particular we nearly divide by 2 the size of the alphabet needed for witnesses. We also give some refinements to the algebraic expression of the state complexity, which is especially complex with this operation. We obtain these results by using peculiar DFAs defined by Brzozowski.
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