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Several popular Machine Learning techniques are originally designed for the solution of two-class problems. However, several classification problems have more than two classes. One approach to deal with multiclass problems using b...
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Several popular Machine Learning techniques are originally designed for the solution of two-class problems. However, several classification problems have more than two classes. One approach to deal with multiclass problems using binary classifiers is to decompose the multiclass problem into multiple binary sub-problems disposed in a binary tree. This approach requires a binary partition of the classes for each node of the tree, which defines the tree structure. This paper presents two algorithms to determine the tree structure taking into account information collected from the used dataset. This approach allows the tree structure to be determined automatically for any multiclass dataset.
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We apply Menke's JSJ decomposition for symplectic fillings to several families of contact 3-manifolds. Among other results, we complete the classification up to orientation-preserving diffeomorphism of strong symplectic fillings o...
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We apply Menke's JSJ decomposition for symplectic fillings to several families of contact 3-manifolds. Among other results, we complete the classification up to orientation-preserving diffeomorphism of strong symplectic fillings of lens spaces. We show that exact symplectic fillings of contact manifolds obtained by surgery on certain Legendrian negative cables are the result of attaching a Weinstein 2-handle to an exact filling of a lens space. For large families of contact structures on Seifert fibered spaces over S~2, we reduce the problem of classifying exact symplectic fillings to the same problem for universally tight or canonical contact structures. Finally, virtually overtwisted circle bundles over surfaces with genus greater than one and negative twisting number are seen to have unique exact fillings.
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This expository article provides several concrete classifications of singularities of differentiable mappings, in particular, in situations where various geometric structures come across. We clarify the fundamental methods to stud...
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This expository article provides several concrete classifications of singularities of differentiable mappings, in particular, in situations where various geometric structures come across. We clarify the fundamental methods to study the classification problems and propose one of the principal prospects on the study of geometric singularities and applications.
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Binary classification refers to supervised techniques that split a set of points in two classes, with respect to a training set of points whose membership is known for each class. Binary classification plays a central role in the ...
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Binary classification refers to supervised techniques that split a set of points in two classes, with respect to a training set of points whose membership is known for each class. Binary classification plays a central role in the solution of many scientific, financial, engineering, medical and biological problems. Many methods with good classification accuracy are currently available. This work shows how a binary classification problem can be expressed in terms of a generalized eigenvalue problem. A new regularization technique is proposed, which gives results that are comparable to other techniques in use, in terms of classification accuracy. The advantage of this method relies in its lower computational complexity with respect to the existing techniques based on generalized eigenvalue problems. Finally, the method is compared with other methods using benchmark data sets.
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A new approach for analyzing the “molecule–descriptor” matrix for the QSAR problem (Quan- titative Structure–Activity Relationship) based on a fuzzy cluster structure of the learning sample is pre- sented. The ways for generat...
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A new approach for analyzing the “molecule–descriptor” matrix for the QSAR problem (Quan- titative Structure–Activity Relationship) based on a fuzzy cluster structure of the learning sample is pre- sented. The ways for generating fast rules for refusing prediction and searching the spikes in the learning sam- ple are described. For this purpose, a special space of descriptors, simple for calculation, is introduced. The ways for optimizing the discriminant function according to fuzzy clustering parameters are examined. Highly predictive models based on the presented approach have been generated. The models are compared, and the efficiency of the described methods is revealed.
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Earthflows represent peculiar slope movements, explicitly considered in all proposals of landslide classification, which typically involve indurated fine-grained soils (stiff clays, clay shales and marls). However, they are variou...
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Earthflows represent peculiar slope movements, explicitly considered in all proposals of landslide classification, which typically involve indurated fine-grained soils (stiff clays, clay shales and marls). However, they are variously named (earth-flows, mud-slides, mud-flows) depending on the consolidated local use. The expression earth-flow owns to the American use; mud-slide is the corresponding Brit\ish term. In Italian we use the expression colata di argilla, but when we write in English we have to choose the most appropriate term, and this is not an easy problem for non-native speakers. However that is not our problem.
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SDCP require classifiers with the ability to learn and to adjust to the underlying relationships in data streams in real-time. This requirement poses a challenge to classifiers, because the learning task is no longer just to find ...
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SDCP require classifiers with the ability to learn and to adjust to the underlying relationships in data streams in real-time. This requirement poses a challenge to classifiers, because the learning task is no longer just to find the optimal decision boundaries, but also to track changes in the decision boundaries as new training data is received. Each SDCP can be described in terms of its environment and difficulty. The environment of an SDCP describes the rate and magnitude of changes in the decision boundaries in the data streams. On the other hand, the difficulty of an SDCP describes the availability of the data that define the decision boundaries during an environment instance. In any empirical analysis of streamed data classifiers, a set of SDCP is used. Understanding the environment and difficulty of each SDCP allows for a more holistic analysis of empirical results. This article proposes (i) a novel quantitative method for analysing the environment of SDCP, and (ii) a difficulty classification scheme based on the construction of SDCP. The proposed methods are evaluated by applying them to a benchmark suite of SDCP.
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In this study, a Tchebycheff utility function based approach is proposed for multiple criteria sorting problems in order to classify alternatives into ordered categories, such as A, B, C, etc. Since the Tchebycheff function has th...
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In this study, a Tchebycheff utility function based approach is proposed for multiple criteria sorting problems in order to classify alternatives into ordered categories, such as A, B, C, etc. Since the Tchebycheff function has the ability to reach efficient alternatives located even in the non-convex part of the efficient frontier, it is used in the proposed sorting approach to prevent such alternatives being disadvantages. If the preferences of the DM are not exactly known, each alternative selects its own favorable weights for a weighted Tchebycheff distance function. Then, each alternative is compared with the reference alternatives of a class to compute its strength over them. The average strengths are later used to categorize the alternatives. The experimental analysis results on the performance of the algorithm are presented.
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We analyze the two neuron CNN for the particular parameter range where the system converges to constant outputs. The functional relation between the external inputs and the steady state values of the neuron states is found and pro...
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We analyze the two neuron CNN for the particular parameter range where the system converges to constant outputs. The functional relation between the external inputs and the steady state values of the neuron states is found and proves to be useful to solve classification problems. In fact, an exhaustive classification of the binary inputoutput relations that can be achieved by a two neuron CNN is established. From this relation, we propose an algorithm relating the CNN parameters and each one of the different classification problems. As an illustration, we attempt to implement the header action of a universal Turing machine and Boolean functions. Our results are compared to the CNN universal cell.
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In tins work we describe the isoperimetric regions in complete symmetric annuli of revolution with Gauss curvature non-decreasing from the shortest parallel. This description allows us to complete the classification of isoperimetr...
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In tins work we describe the isoperimetric regions in complete symmetric annuli of revolution with Gauss curvature non-decreasing from the shortest parallel. This description allows us to complete the classification of isoperimetric regions inquadrics of revolution.
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