• Communications for Statistical Applications and Methods
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• v.23 no.2
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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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• v.24 no.1
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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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• v.19 no.3
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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.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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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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• v.23 no.2
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.9
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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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• v.22 no.3
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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.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.15 no.1
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• pp.1-7
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• 2022

It has been found through physiological experiments that the visual neurons constituting the human visual cortex do not respond to all visual stimuli, but to a visual stimuli with specific conditions. In order to interpret such physiological experiments, a model that can simulate the firing characteristics of neurons including a linear filter with random gain was proposed. It has been proven through experiments that subspaces are formed. To verify the validity of the implemented model, the distribution of values for two pixels randomly extracted from four different visual stimulus data was observed. The difference between the two distributions was confirmed by extracting the central coordinate value, that is, the coordinate value with the most values, from the distribution of the total stimulus data and the spike ignition stimulus data. In the case of the entire set, it was verified through experiments that the stimulus data generating spikes is a subset or subspace of the entire stimulus data. This study can be used as a basic study related to the mechanism of spikes in response to visual stimuli.

• The Journal of the Korea Contents Association
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• v.19 no.2
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• pp.516-524
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• 2019

The purpose of this study is to analyze the cases related to the multi-dimensional urban planning and its related systems that can contribute to the urban regeneration as the policies and projects for stereoscopic city increase. Through the case analysis, urban regeneration function and role of multi-dimensional urban planning are identified as connection of places, activation of local economy, expansion of infrastructure and supply of housing. In the institutional sector, private participation is hindered due to the ban on the establishment of the right to hold state property. In addition, it is difficult to utilize the three-dimensional urban space without land securing at a certain rate based on uniform installation standards of the two-dimensional land use plan, and the problem of insufficient interconnection between law and institution is derived. In conclusion, it should actively support and promote the promotion of the three-dimensional facility with the aim of diversifying the regional infrastructure structure and strengthening the urban function. In addition, development of stereoscopic and compound development should be promoted for old urban areas, and parking lots, underground shopping malls, parking lots, etc. should be installed using the subspaces of parks, schools, roads and traditional markets of old residential areas. Finally, cooperation between the central government, the municipalities and the private sector is necessary for the realization of these urban regeneration projects.