• Communications for Statistical Applications and Methods
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• v.11 no.1
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• pp.49-58
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• 2004

In this talk we proposed an asymptotic test for dimensionality in the latent variable model for probabilistic principal component analysis with missing values at random. Proposed algorithm is a sequential likelihood ratio test for an appropriate Normal latent variable model for the principal component analysis. Modified EM-algorithm is used to find MLE for the model parameters. Results from simulations and real data sets give us promising evidences that the proposed method is useful in finding necessary number of components in the principal component analysis with missing values at random.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.151-156
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• 2003

Variable selection algorithm for principal component analysis using penalized likelihood method is proposed. We will adopt a probabilistic principal component idea to utilize likelihood function for the problem and use HARD penalty function to force coefficients of any irrelevant variables for each component to zero. Consistency and sparsity of coefficient estimates will be provided with results of small simulated and illustrative real examples.

• Communications for Statistical Applications and Methods
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• v.24 no.2
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• pp.143-154
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• 2017

A variable selection method based on probabilistic principal component analysis (PCA) using penalized likelihood method is proposed. The proposed method is a two-step variable reduction method. The first step is based on the probabilistic principal component idea to identify principle components. The penalty function is used to identify important variables in each component. We then build a model on the original data space instead of building on the rotated data space through latent variables (principal components) because the proposed method achieves the goal of dimension reduction through identifying important observed variables. Consequently, the proposed method is of more practical use. The proposed estimators perform as the oracle procedure and are root-n consistent with a proper choice of regularization parameters. The proposed method can be successfully applied to high-dimensional PCA problems with a relatively large portion of irrelevant variables included in the data set. It is straightforward to extend our likelihood method in handling problems with missing observations using EM algorithms. Further, it could be effectively applied in cases where some data vectors exhibit one or more missing values at random.

• Proceedings of the Korean Information Science Society Conference
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• 2001.04b
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• pp.529-531
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• 2001

We present an expectation-maximization algorithm for principal component analysis via orthogonalization. The algorithm finds actual principal components, whereas previously proposed EM algorithms can only find principal subspace. New algorithm is simple and more efficient thant probabilistic PCA specially in noiseless cases. Conventional PCA needs computation of inverse of the covariance matrices, which makes the algorithm prohibitively expensive when the dimensions of data space is large. This EM algorithm is very powerful for high dimensional data when only a few principal components are needed.

• Smart Structures and Systems
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• v.15 no.3
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• pp.751-767
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• 2015

A new procedure is proposed for assessing probabilistic condition of structures considering effect of measured data uncertainty. In this procedure, multiple Finite Element (FE) models are identified by using weighting vectors that represent the uncertainty conditions of measured data. The distribution of structural parameters is analysed using a Principal Component Analysis (PCA) in relation to uncertainty conditions, and the identified models are classified into groups according to their similarity by using a K-means method. The condition of a structure is then assessed probabilistically using FE models in the classified groups, each of which represents specific uncertainty condition of measured data. Yeondae bridge, a steel-box girder expressway bridge in Korea, is used as an illustrative example. Probabilistic condition of the bridge is evaluated by the distribution of load rating factors obtained using multiple FE models. The numerical example shows that the proposed method can quantify uncertainty of measured data and subsequently evaluate efficiently the probabilistic condition of bridges.

• The Korean Journal of Applied Statistics
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• v.36 no.4
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• pp.279-294
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• 2023

It is well known to generate synthetic data sets by the sequential regression multiple imputation (SRMI) method. The R-package synthpop are widely used for generating synthetic data by the SRMI approaches. In this paper, I suggest generating synthetic data based on the probabilistic principal component analysis (PPCA) method. Two simple data sets are used for a simulation study to compare the SRMI and PPCA approaches. Simulation results demonstrate that pairwise coefficients in synthetic data sets by PPCA can be closer to original ones than by SRMI. Furthermore, for the various data types that PPCA applications are well established, such as time series data, the PPCA approach can be extended to generate synthetic data sets.

• Advances in aircraft and spacecraft science
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• v.3 no.4
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• pp.503-521
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• 2016

Variances in turbomachinery blades caused by manufacturing, operation or regeneration can result in modified structural behavior. In this work, the scatter of geometrical and material properties of a turbine blade and its influence on structure performance is discussed. In particular, the vibration characteristics and the lifetime of a turbine blade are evaluated. Geometrical variances of the surface of the blades are described using the principal component analysis. The scatter in material properties is considered by 16 varying material parameters. Maximum vibration amplitudes and the number of load cycles the turbine blade can withstand are analyzed by finite element simulations incorporating probabilistic principles. The probabilistic simulations demonstrate that both geometrical and material variances have a significant influence on the scatter of vibration amplitude and lifetime. Dependencies are quantified and correlations between varied input parameters and the structural performance of the blade are detected.

• 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.

• Geomechanics and Engineering
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• v.27 no.6
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• pp.551-560
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• 2021

Due to the low strength and high compressibility characteristics, the loess deposits tunnels are prone to large deformations and collapse. An accurate stability evaluation for loess deposits is of considerable significance in deformation control and safety work during tunnel construction. 37 groups of representative data based on real loess deposits cases were adopted to establish the stability evaluation model for the tunnel project in Yan'an, China. Physical and mechanical indices, including water content, cohesion, internal friction angle, elastic modulus, and poisson ratio are selected as index system on the stability level of loess. The data set is randomly divided into 80% as the training set and 20% as the test set. Firstly, principal component analysis (PCA) is used to convert the five index system to three linearly independent principal components X1, X2 and X3. Then, the principal components were used as input vectors for probabilistic neural network (PNN) to map the nonlinear relationship between the index system and stability level of loess. Furthermore, Leave-One-Out cross validation was applied for the training set to find the suitable smoothing factor. At last, the established model with the target smoothing factor 0.04 was applied for the test set, and a 100% prediction accuracy rate was obtained. This intelligent classification method for loess deposits can be easily conducted, which has wide potential applications in evaluating loess deposits.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.55 no.5
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• pp.185-190
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• 2006

The security analysis relates to the ability of the electric systems to survive sudden disturbances such as electric short circuits or unanticipated loss of system elements. It is composed of both steady state and dynamic security analyses, which are not two separate issues but should be considered together. In steady state security analysis including voltage security analysis, the analysis checks that the system is operated within security limits by OPF (optimal power flow) after the transition of a new operating point. On the other hand, dynamic security analysis deals that the transition will lead to an acceptable operating condition. Transient stability, which is the ability of power systems to maintain synchronism when subjected to a large disturbance, is a principal component in dynamic security analysis. Usually any loss of synchronism will cause additional outages. They make the present steady state analysis of the post-contingency condition inadequate for unstable cases. This is the reason of the need for dynamics of systems. Probabilistic criterion can be used to recognize the probabilistic nature of system components and shows the possibility of system security. A comprehensive conceptual framework for probabilistic static and dynamic assessment is presented in this paper. The simulation results of the Western System Coordinating Council (WSCC) system compare an analytical method with Monte-Carlo simulation (MCS). Also, a case study of the extended IEEE Reliability Test System (RTS) shows the efficiency of this approach.