• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.109.3-109
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• 2001

The so-called curse of dimensionality arises when Gaussian mixture is used on high-dimensional small-sample-size data, since the number of free elements that needs to be specied in each covariance matrix of Gaussian mixture increases exponentially with the number of dimension d. In this paper, by constraining the covariance matrix in its decomposed orthonormal form we get a local PCA model so as to reduce the number of free elements needed to be specified. Moreover, to cope with the small sample size problem, we adopt BYY data smoothing learning which is a regularization over maximum likelihood learning obtained from BYY harmony learning to implement this local PCA model.

• International journal of advanced smart convergence
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• v.1 no.2
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• pp.30-33
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• 2012

This paper propose a new design of fuzzy neural networks based on hard partition to generate the rules of the networks. For this we use hard c-means (HCM) clustering algorithm. The premise part of the rules of the proposed networks is realized with the aid of the hard partition of input space generated by HCM clustering algorithm. The consequence part of the rule is represented by polynomial functions. And the coefficients of the polynomial functions are learned by BP algorithm. The number of the hard partition of input space equals the number of clusters and the individual partitioned spaces indicate the rules of the networks. Due to these characteristics, we may alleviate the problem of the curse of dimensionality. The proposed networks are evaluated with the use of numerical experimentation.

• The Korean Journal of Applied Statistics
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• v.5 no.1
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• pp.103-111
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• 1992

The projection pursuit method has been gussested as a technique for the analysis of the multivariate data. This method seeks out interesting linear projections of the multivariate data onto a line of a plane to solve the curse or dimensionality. In this paper we developed the discriminant analysis by using the projection method and simulations were used for comparison between this and other existing discriminant analysis methods.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.7
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• pp.517-524
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• 2004

For real world applications of reinforcement learning techniques, function approximation or generalization will be required to avoid curse of dimensionality. For this, an improved function approximation-based reinforcement teaming method is proposed to speed up convergence by using CA-CMAC(Credit-Assigned Cerebellar Model Articulation Controller). To show that our proposed CACRL(CA-CMAC-based Reinforcement Learning) performs better than the CRL(CMAC- based Reinforcement Learning), computer simulation and experiment results are illustrated, where a swing-up control Problem of an acrobot is considered.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.11
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• pp.2157-2164
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• 2011

In this paper, we introduce a new category of fuzzy inference system based on Type-2 fuzzy c-means clustering algorithm (T2FCM-based FIS). The premise part of the rules of the proposed model is realized with the aid of the scatter partition of input space generated by Type-2 FCM clustering algorithm. The number of the partition of input space is composed of the number of clusters and the individual partitioned spaces describe the fuzzy rules. Due to these characteristics, we can alleviate the problem of the curse of dimensionality. The consequence part of the rule is represented by polynomial functions with interval sets. To determine the structure and estimate the values of the parameters of Type-2 FCM-based FIS we consider the successive tuning method with generation-based evolution by means of real-coded genetic algorithms. The proposed model is evaluated with the use of numerical experimentation.

• Proceedings of the Korean Information Science Society Conference
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• 2004.10a
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• pp.232-234
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• 2004

강화 학습(Reinforcement Learning)을 실제 문제에 적용하는 데 있어 가장 큰 문제는 차원성의 저주(Curse of dimensionality)이다. 문제가 커짐에 따라 목적을 이루기 위해서 더 않은 단계의 판단이 필요하고 이에 따라 문제의 해결이 지수적으로 어려워지게 된다. 이를 해결하기 위칠 문제를 여러 단계로 나누어 단계별로 학습하는 계층적 강화 학습(Hierarchical Reinforcement Learning)이 제시된 바 있다. 하지만 대부분의 계층적 강화 학습 방법들은 사전에 문제의 구조를 아는 것을 전제로 하며 큰 사이즈의 문제를 간단히 표현할 방법을 제시하지 않는다. 따라서 이들 방법들도 실제적인 문제에 바로 적용하기에는 적합하지 않다. 이러한 문제점들을 해결하기 위해 복잡계 네트워크(Complex Network)가 갖는 작은 세상 성질(Small world Property)에 착안하여 자기조직화 하는 생장 네트워크(Self organizing growing network)를 기반으로 한 환경 표현 모델이 제안된 바 있다. 이러한 모델에서는 문제 크기가 커지더라도 네트워크의 사이즈가 크게 커지지 않기 때문에 문제의 난이도가 크기에 따라 크게 증가하지 않을 것을 기대할 수 있다. 본 논문에서는 이러한 환경 모델을 사용한 강화 학습 알고리즘을 구현하고 실험을 통하여 각 모델이 강화 학습의 문제 사이즈에 따른 성능에 끼치는 영향에 대해 알아보았다.

• Proceedings of the KIEE Conference
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• 2003.11c
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• pp.621-624
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• 2003

For real world applications of reinforcement learning techniques, function approximation or generalization will be required to avoid curse of dimensionality. For this, an improved function approximation-based reinforcement learning method is proposed to speed up convergence by using CA-CMAC(Credit-Assigned Cerebellar Model Articulation Controller). To show that our proposed CACRL(CA-CMAC-based Reinforcement Learning) performs better than the CRL(CMAC-based Reinforcement Learning), computer simulation results are illustrated, where a swing-up control problem of an acrobot is considered.

• Proceedings of the Korean Information Science Society Conference
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• 2004.04b
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• pp.622-624
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• 2004

강화 학습(Reinforcement Learning)을 실제 문제에 적용하는 데 있어 가장 큰 문제는 차원성의 저주(Curse of dimensionality)였다 문제가 커짐에 따라 목적을 이루기 위해서 더 많은 단계의 판단이 필요하고 이에 따라 문제의 해결이 지수적으로 어려워지게 된다. 이를 해결하기 위해 문제를 여러 단계로 나누어 단계별로 학습하는 계층적 강화 학습(Hierarchical Reinforcement Learning)이 제시된 바 있다 하지만 대부분의 계층적 강화 학습 방법들은 사전에 문제의 구조를 아는 것을 전제로 하며 큰 사이즈의 문제를 간단히 표현할 방법을 제시하지 않는다. 따라서 이들 방법들도 실제적인 문제에 바로 적용하기에는 적합하지 않다. 최근 이루어진 복잡계 네트워크(Complex Network)에 대한 연구에 착안하여 본 논문은 자기조직화하는 생장 네트워크(Self organizing growing network)를 기반으로 한 간단한 환경 표현 모델을 사용하는 강화 학습 알고리즘을 제안한다 네트웍은 복잡계 네트웍이 갖는 성질들을 유지하도록 자기 조직화되고, 노드들 간의 거리는 작은 세상 성질(Small World Property)에 따라 전체 네트웍의 큰 사이즈에 비해 짧게 유지된다. 즉 판단해야할 단계의 수가 적게 유지되기 때문에 이 방법으로 차원성의 저주를 피할 수 있다.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.29.1-29
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• 2001

Neuro-fuzzy systems are multi-layered connectionist networks that realize the elements and functions of traditional fuzzy logic control/decision systems. A trained neuro-fuzzy system is isomorphic to a fuzzy logic system, and fuzzy IF-THEN rule knowledge can be explicitly extracted from the network. This talk presents a brief introduction to self-adaptive neuro-fuzzy systems and addresses some recent research results and applications. Most of the existing neuro-fuzzy systems exhibit several major drawbacks that lead to performance degradation. These drawbacks are the curse of dimensionality (i.e., fuzzy rule explosion), inability to re-structure their internal nodes in a changing environment, and their lack of ability to extract knowledge from a given set of training data. This talk focuses on our investigation of network architectures, self-adaptation algorithms, and efficient learning algorithms that will enable existing neuro-fuzzy systems to self-adapt themselves in an unstructured and uncertain environment.

• Communications for Statistical Applications and Methods
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• v.26 no.1
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• pp.69-78
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• 2019

A structured model with both single-index and varying coefficients is a powerful tool in modeling high dimensional data. It has been widely used because the single-index can overcome the curse of dimensionality and varying coefficients can allow nonlinear interaction effects in the model. For high dimensional index vectors, variable selection becomes an important question in the model building process. In this paper, we propose an efficient estimation and a variable selection method based on a smoothing spline approach in a partially linear single-index-coefficient regression model. We also propose an efficient algorithm for simultaneously estimating the coefficient functions in a data-adaptive lower-dimensional approximation space and selecting significant variables in the index with the adaptive LASSO penalty. The empirical performance of the proposed method is illustrated with simulated and real data examples.