• The Transactions of the Korea Information Processing Society
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• v.4 no.12
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• pp.3063-3068
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• 1997

In this paper, we have extended the generalization back-propagation algorithm to multi-layer polynomial higher order neural networks. The purpose of this paper is to describe various pattern recognition using polynomial higher-order neural network. And we have applied shift position T-C test pattern for invariant pattern recognition and measured generalization by mirror symmetry problem. simulation result shows that the ability for invariant pattern recognition increase with the proposed technique. Recognition rate of invariant T-C pattern is 90% effective and of mirror symmetry problem is 70% effective when the proposed technique is utilized. These results are much better than those by the conventional methods.

• The KIPS Transactions:PartB
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• v.12B no.3 s.99
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• pp.343-348
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• 2005

The goal of this paper is to study the joint effect of factors of neural network teaming procedure. There are many factors, which may affect the generalization ability and teaming speed of neural networks, such as the initial values of weights, the learning rates, and the regularization coefficients. We will apply a constructive training algerian for neural network, then patterns are trained incrementally by considering them one by one. First, we will investigate the effect of these factors on generalization performance and learning speed. Based on these factors' effect, we will propose a joint method that simultaneously considers these three factors, and dynamically hue the learning rate and regularization coefficient. Then we will present the results of some experimental comparison among these kinds of methods in several simulated nonlinear data. Finally, we will draw conclusions and make plan for future work.

• Journal of Information Technology Services
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• v.15 no.1
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• pp.153-166
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• 2016

Ensemble classification is an approach that combines individually trained classifiers in order to improve prediction accuracy over individual classifiers. Ensemble techniques have been shown to be very effective in improving the generalization ability of the classifier. But base classifiers need to be as accurate and diverse as possible in order to enhance the generalization abilities of an ensemble model. Bagging is one of the most popular ensemble methods. In bagging, the different training data subsets are randomly drawn with replacement from the original training dataset. Base classifiers are trained on the different bootstrap samples. In this study we proposed a new bagging variant ensemble model, Randomized Bagging (RBagging) for improving the standard bagging ensemble model. The proposed model was applied to the bankruptcy prediction problem using a real data set and the results were compared with those of the other models. The experimental results showed that the proposed model outperformed the standard bagging model.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.34C no.6
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• pp.71-78
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• 1997

In this paper, a new neural network training algorithm will be devised for function approximator with good generalization characteristics and tested with the time series prediction problem using santaFe competition data sets. To enhance the generalization ability a constraint term of hidden neuraon activations is added to the conventional output error, which gives the curvature smoothing characteristics to multi-layer neural networks. A hybrid learning algorithm of the error-back propagation and Hebbian learning algorithm with weight decay constraint will be naturally developed by the steepest decent algorithm minimizing the proposed cost function without much increase of computational requriements.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.4
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• pp.271-276
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• 2006

To implement a generalization of value functions in Adaptive Search Element (ASE)-reinforcement learning, CMAC (Cerebellar Model Articulation Controller) is integrated into ASE controller. ASE-reinforcement learning scheme is briefly studied to discuss how CMAC is integrated into ASE controller. Neighbourhood Sequential Training for CMAC is utilized to establish the look-up table and to produce discrete control outputs. In computer simulation, an ASE controller and a couple of ASE-CMAC neural network are trained to balance the inverted pendulum on a cart. The number of trials until the controllers are established and the learning performance of the controllers are evaluated to find that generalization ability of the CMAC improves the speed of the ASE-reinforcement learning enough to realize the cartpole control system.

• School Mathematics
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• v.13 no.4
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• pp.581-598
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• 2011

Given the growing agreement that algebra should be taught in the early stage of the curriculum, considerable studies have been conducted with regard to early algebra in the elementary school. However, there has been lack of research on how to organize mathematic lessons to develop of algebraic reasoning ability of the elementary school students. This research attempted to gain specific and practical information on effective algebraic teaching and learning in the elementary school. An exploratory qualitative case study was conducted to the fourth graders. This paper focused on the associative law of the multiplication. This paper showed what kinds of activities a teacher may organize following three steps: (a) focus on the properties of numbers and operations in specific situations, (b) discovery of the properties of numbers and operations with many examples, and (c) generalization of the properties of numbers and operations in arbitrary situations. Given the steps, this paper included an analysis on how the students developed their algebraic reasoning. This study provides implications on the important factors that lead to the development of algebraic reasoning ability for elementary students.

• School Mathematics
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• v.15 no.4
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• pp.785-799
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• 2013

The researchers developed the teaching-learning materials for 9th grade mathematically gifted students in terms of the hypothesis that the students would have opportunity for problem solving and develop various mathematical thinking through the mathematical modeling lessons. The researchers analyzed what mathematical thinking abilities were shown on each stage of modeling process through the application of the materials. Organization of information ability appears in the real-world exploratory stage. Intuition insight ability, spatialization/visualization ability, mathematical reasoning ability and reflective thinking ability appears in the pre-mathematical model development stage. Mathematical abstraction ability, spatialization/visualization ability, mathematical reasoning ability and reflective thinking ability appears in the mathematical model development stage. Generalization and application ability and reflective thinking ability appears in the model application stage. The developed modeling assignments have provided the opportunities for mathematically-gifted students' mathematical thinking ability to develop and expand.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.619-636
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• 2012

The main purpose of this study was to explore the process of generalization generated by mathematically gifted students. Specifically, this study probed how fourth, fifth, and sixth graders might generalize geometric patterns and represent such generalization. The subjects of this study were a total of 30 students from gifted classes of one elementary school in Korea. The results of this study showed that on the question of the launch stage, students used a lot of recursive strategies that built mainly on a few specific numbers in the given pattern in order to decide the number of successive differences. On the question of the towards a working generalization stage, however, upper graders tend to use a contextual strategy of looking for a pattern or making an equation based on the given information. The more difficult task, more students used recursive strategies or concrete strategies such as drawing or skip-counting. On the question of the towards an explicit generalization stage, students tended to describe patterns linguistically. However, upper graders used more frequently algebraic representations (symbols or formulas) than lower graders did. This tendency was consistent with regard to the question of the towards a justification stage. This result implies that mathematically gifted students use similar strategies in the process of generalizing a geometric pattern but upper graders prefer to use algebraic representations to demonstrate their thinking process more concisely. As this study examines the strategies students use to generalize a geometric pattern, it can provoke discussion on what kinds of prompts may be useful to promote a generalization ability of gifted students and what sorts of teaching strategies are possible to move from linguistic representations to algebraic representations.

• Journal of Educational Research in Mathematics
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• v.17 no.2
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• pp.163-177
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• 2007

Studies on mathematically gifted students have been conducted following Krutetskii. There still exists a necessity for a more detailed research on how these students' mathematical competence is actually displayed during the problem solving process. In this study, it was attempted to analyse the algebraic thinking process in the problem solving a peg puzzle in which 4 mathematically gifted students, who belong to the upper 0.01% group in their grade of elementary school in Korea. They solved and generalized the straight line peg puzzle. Mathematically gifted elementary school students had the tendency to find a general structure using generic examples rather than find inductive rules. They did not have difficulty in expressing their thoughts in letter expressions and in expressing their answers in written language; and though they could estimate general patterns while performing generalization of two factors, it was revealed that not all of them can solve the general formula of two factors. In addition, in the process of discovering a general pattern, it was confirmed that they prefer using diagrams to manipulating concrete objects or using tables. But as to whether or not they verify their generalization results using generalized concrete cases, individual difference was found. From this fact it was confirmed that repeated experiments, on the relationship between a child's generalization ability and his/her behavioral pattern that verifies his/her generalization result through application to a concrete case, are necessary.

• School Mathematics
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• v.16 no.2
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• pp.355-386
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• 2014

Algebraic generalization of patterns is based on the capability of grasping a structure inherent in several objects with awareness that this structure applies to general cases and ability to use it to provide an algebraic expression. The purpose of this study is to investigate how students generalize patterns using an algebraic object such as parameters and what are difficulties in geometric-arithmetic pattern tasks related to algebraic generalization and to determine whether the students can use parameters meaningfully through pattern generalization tasks that this researcher designed. During performing tasks of pattern generalization we designed, students differentiated parameters from letter 'n' that is used to denote a variable. Also, the students understood the relations between numbers used in several linear equations and algebraically expressed the generalized relation using a letter that was functions as a parameter. Some difficulties have been identified such that the students could not distinguish parameters from variables and could not transfer from arithmetical procedure to algebra in this process. While trying to resolve these difficulties, generic examples helped the students to meaningfully use parameters in pattern generalization.