• Communications for Statistical Applications and Methods
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• 제23권2호
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• pp.93-103
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• 2016

In the paper, we discuss dimension reduction of predictors ${\mathbf{X}}{\in}{{\mathbb{R}}^p}$ in a regression of $Y{\mid}{\mathbf{X}}$ with a notion of sufficiency that is called sufficient dimension reduction. In sufficient dimension reduction, the original predictors ${\mathbf{X}}$ are replaced by its lower-dimensional linear projection without loss of information on selected aspects of the conditional distribution. Depending on the aspects, the central subspace, the central mean subspace and the central $k^{th}$-moment subspace are defined and investigated as primary interests. Then the relationships among the three subspaces and the changes in the three subspaces for non-singular transformation of ${\mathbf{X}}$ are studied. We discuss the two conditions to guarantee the existence of the three subspaces that constrain the marginal distribution of ${\mathbf{X}}$ and the conditional distribution of $Y{\mid}{\mathbf{X}}$. A general approach to estimate them is also introduced along with an explanation for conditions commonly assumed in most sufficient dimension reduction methodologies.

• Communications for Statistical Applications and Methods
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• 제24권1호
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• pp.97-113
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• 2017

This paper proposes a method for sufficient dimension reduction (SDR) of mixture data. We consider mixture data containing more than one component that have distinct central subspaces. We adopt an approach of a model-based sliced inverse regression (MSIR) to the mixture data in a simple and intuitive manner. We employed mixture probabilistic principal component analysis (MPPCA) to estimate each central subspaces and cluster the data points. The results from simulation studies and a real data set show that our method is satisfactory to catch appropriate central spaces and is also robust regardless of the number of slices chosen. Discussions about root selection, estimation accuracy, and classification with initial value issues of MPPCA and its related simulation results are also provided.

• Communications for Statistical Applications and Methods
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• 제19권3호
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• pp.501-506
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• 2012

This paper investigates the central subspace related with SIR, DOC and SAVE when the response has more than two values. The subspaces constructed by SIR, DOC and SAVE are investigated and compared. The SAVE paradigm is the most comprehensive. In addition, the SAVE coincides with the central subspace when the conditional distribution of predictors given the response is normally distributed.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2003년도 춘계 학술발표회 논문집
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• pp.213-217
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• 2003

In this paper we discuss graphical and diagnostic methods for logistic regression, in which the response is the number of successes in a fixed number of trials.

• Communications for Statistical Applications and Methods
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• 제23권2호
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• pp.105-117
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• 2016

In the paper, as a sequence of the first tutorial, we discuss sufficient dimension reduction methodologies used to estimate central subspace (sliced inverse regression, sliced average variance estimation), central mean subspace (ordinary least square, principal Hessian direction, iterative Hessian transformation), and central $k^{th}$-moment subspace (covariance method). Large-sample tests to determine the structural dimensions of the three target subspaces are well derived in most of the methodologies; however, a permutation test (which does not require large-sample distributions) is introduced. The test can be applied to the methodologies discussed in the paper. Theoretical relationships among the sufficient dimension reduction methodologies are also investigated and real data analysis is presented for illustration purposes. A seeded dimension reduction approach is then introduced for the methodologies to apply to large p small n regressions.

• 대한기계학회논문집A
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• 제26권9호
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• pp.1822-1830
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• 2002

The paper describes the development of a decomposition based multidisciplinary design optimization (MDO) method that coordinates each of disciplinary subspace optimization (DSO). A multidisciplinary design system considered in the present study is decomposed into a number of subspaces based on their own design objective and constraints associated with engineering discipline. The coupled relations among subspaces are identified by interdisciplinary design variables. Each of subsystem level optimization, that is DSO would be performed in parallel, and the system level coordination is determined by the first order optimal sensitivities of subspace objective functions with respect to interdisciplinary design variables. The central of the present work resides on the formulation of system level coordination strategy and its capability in decomposition based MDO. A fluid-structure coupled design problem is explored as a test-bed to support the proposed MDO method.

• Communications for Statistical Applications and Methods
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• 제22권3호
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• pp.305-312
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• 2015

We extend a generalized partially linear single-index model and newly define a generalized partially double-index model (GPDIM). The philosophy of sufficient dimension reduction is adopted in GPDIM to estimate unknown coefficient vectors in the model. Subsequently, various combinations of popular sufficient dimension reduction methods are constructed with the best combination among many candidates determined through a bootstrapping procedure that measures distances between subspaces. Distinguishing values are newly defined to match the estimates to the corresponding population coefficient vectors. One of the strengths of the proposed model is that it can investigate the appropriateness of GPDIM over a single-index model. Various numerical studies confirm the proposed approach, and real data application are presented for illustration purposes.

• 한국정보전자통신기술학회논문지
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• 제15권1호
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• pp.1-7
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• 2022

인간의 시각 피질을 구성하고 있는 시각 뉴런은 모든 시각적 자극에 반응하는 것이 아니라 특정한 조건을 갖춘 시각적 자극에 반응한다는 것이 생리학적 실험을 통하여 밝혀졌다. 본 연구에서는 이와 같은 생리학적 실험을 해석하기 위하여 랜덤한 이득을 갖는 선형 필터를 포함하는 뉴런의 발화 특성을 시뮬레이션하고 설명할 수 있는 모델을 제안하였고 또한 제안한 모델의 선형 필터의 출력이 전체 자극 데이터의 부공간을 형성하고 있음을 실험을 통하여 증명하였다. 구현된 모델의 타당성을 검증하기 위하여 서로 다른 4개의 시각적 자극 데이터들로부터 임의로 추출한 2개의 화소에 대한 값의 분포를 관찰하였다. 전체 자극 데이터와 스파이크 발화 자극 데이터의 분포로부터 중심 좌표 값 즉, 가장 많은 값이 분포하는 좌표 값을 추출하여 두 분포 사이의 차이를 확인할 수 있었고 구현된 모델이 전형적인 LNP 모델과 동일하게 전체 자극 데이터가 전체 집합일 경우 스파이크를 발생시키는 자극 데이터가 전체 자극 데이터의 부공간 임을 실험을 통하여 증명하였다. 본 연구는 시각적 자극에 대한 스파이크의 발생기전과 관련된 기초 연구로 활용할 수 있다.

• 한국콘텐츠학회논문지
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• 제19권2호
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• pp.516-524
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• 2019

본 연구는 도시재생 관점에서 입체도시의 효과를 밝히고, 국내 입체도시계획 관련 제도의 문제점과 한계를 고찰함으로써 제도적 개선방안을 제시하고자 수행되었다. 그리하여 사례 분석을 통해 도시공간 연결, 지역경제 활성화, 기반시설 확충, 주택 공급 등 입체도시의 도시재생 기능과 역할을 파악하였으며, 제도적 문제점으로 국유재산에 대한 사권설정 금지로 민간참여가 저해되고, 2차원적 토지이용계획에 의거한 획일적인 기반시설 설치 기준으로 일정비율 이상의 토지 확보가 없으면 입체공간 활용이 어려우며, 법률간 연계성이 미흡한 문제를 도출하였다. 결론적으로 지역기반 산업구조 다양화 및 도시기능 강화 등을 목표로 입체시설 추진을 적극 지원 유도하고, 구도심 구역을 대상으로 입체 복합개발을 추진하며, 노후주택가의 공원, 학교, 도로, 전통시장의 하부공간을 활용한 보행로, 지하상가, 주차장 등의 도시재생사업 실현을 위해 중앙정부, 지자체, 민간부문 간 협력이 이루어져야 한다.