• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.115-121
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• 1996

Let $\{X(t);\;t{\in}R^n\}$ be a measurable, separable and H-sssis random fields. Here, we suppose that the increments are invariant under all Euclidean rigid body motions. We investigate some properties of H-sssis random fields and monotonicity of projection process $\{X_e(t);\;t{\in}R^1\}$ in any direction $e{\in}R^n$.

• International Journal of Computer Science & Network Security
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• v.23 no.10
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• pp.81-88
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• 2023

In the present scenario, enormous amounts of data are produced every second. These data also contain private information from sources including media platforms, the banking sector, finance, healthcare, and criminal histories. Data mining is a method for looking through and analyzing massive volumes of data to find usable information. Preserving personal data during data mining has become difficult, thus privacy-preserving data mining (PPDM) is used to do so. Data perturbation is one of the several tactics used by the PPDM data privacy protection mechanism. In Perturbation, datasets are perturbed in order to preserve personal information. Both data accuracy and data privacy are addressed by it. This paper will explore and compare several perturbation strategies that may be used to protect data privacy. For this experiment, two perturbation techniques based on random projection and principal component analysis were used. These techniques include Improved Random Projection Perturbation (IRPP) and Enhanced Principal Component Analysis based Technique (EPCAT). The Naive Bayes classification algorithm is used for data mining approaches. These methods are employed to assess the precision, run time, and accuracy of the experimental results. The best perturbation method in the Nave-Bayes classification is determined to be a random projection-based technique (IRPP) for both the cardiovascular and hypothyroid datasets.

• Communications for Statistical Applications and Methods
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• v.27 no.5
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• pp.523-533
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• 2020

This paper suggests three available methods for finding nonnegative estimates of variance components of the random effects in mixed models. The three proposed methods based on the concepts of projections are called projection method I, II, and III. Each method derives sums of squares uniquely based on its own method of projections. All the sums of squares in quadratic forms are calculated as the squared lengths of projections of an observation vector; therefore, there is discussion on the decomposition of the observation vector into the sum of orthogonal projections for establishing a projection model. The projection model in matrix form is constructed by ascertaining the orthogonal projections defined on vector subspaces. Nonnegative estimates are then obtained by the projection model where all the coefficient matrices of the effects in the model are orthogonal to each other. Each method provides its own system of linear equations in a different way for the estimation of variance components; however, the estimates are given as the same regardless of the methods, whichever is used. Hartley's synthesis is used as a method for finding the coefficients of variance components.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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• pp.848-853
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• 2005

3D geometric modeling of an object of interest has been intensively investigated in many fields including CAD/CAM and computer graphics. Traditionally, CAD and geometric modeling tools are widely used to create geometric models that have nearly the same shape of 3D real objects or satisfy designers intent. Recently, with the help of the reverse engineering (RE) technology, we can easily acquire 3D point data from the objects and create 3D geometric models that perfectly fit the scanned data more easily and fast. In this paper, we present 3D geometric model generation based on a stereo vision system (SVS) using random pattern projection. A triangular mesh is considered as the resulting geometric model. In order to obtain reasonable results with the SVS-based geometric model generation, we deal with many steps including camera calibration, stereo matching, scanning from multiple views, noise handling, registration, and triangular mesh generation. To acquire reliable stere matching, we project random patterns onto the object. With experiments using various random patterns, we propose several tips helpful for the quality of the results. Some examples are given to show their usefulness.

• Communications for Statistical Applications and Methods
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• v.25 no.3
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• pp.275-282
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• 2018

This paper discusses the use of projections for the sums of squares in the analyses of variance for two-way nested design data. The model for this data is assumed to only have random effects. Two different sizes of experimental units are required for a given experimental situation, since nesting is assumed to occur both in the treatment structure and in the design structure. So, variance components are coming from the sources of random effects of treatment factors and error terms in different sizes of experimental units. The model for this type of experimental situation is a random effects model with more than one error terms and therefore estimation of variance components are concerned. A projection method is used for the calculation of sums of squares due to random components. Squared distances of projections instead of using the usual reductions in sums of squares that show how to use projections to estimate the variance components associated with the random components in the assumed model. Expectations of quadratic forms are obtained by the Hartley's synthesis as a means of calculation.

• The Korean Journal of Applied Statistics
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• v.34 no.3
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• pp.401-410
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• 2021

Popular in discriminant classification analysis, k-nearest neighbor classification methods have limitations that do not reflect the local characteristic of the data, considering only the number of fixed neighbors. Considering the local structure of the data, the adaptive nearest neighbor method has been developed to select the number of neighbors. In the analysis of high-dimensional data, it is common to perform dimension reduction such as random projection techniques before using k-nearest neighbor classification. Recently, an ensemble technique has been developed that carefully combines the results of such random classifiers and makes final assignments by voting. In this paper, we propose a novel discriminant classification technique that combines adaptive nearest neighbor methods with random projection ensemble techniques for analysis on high-dimensional data. Through simulation and real-world data analyses, we confirm that the proposed method outperforms in terms of classification accuracy compared to the previously developed methods.

• The Korean Journal of Applied Statistics
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• v.30 no.3
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• pp.335-344
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• 2017

This paper discusses a method of analyzing data from split-plot experiments by projections. The assumed model for data has two experimental errors due to two different experimental sizes and some random components in treatment effects. Residual random models are constructed to obtain sums of squares due to random effects. Expectations of sums of squares are obtained by Hartley's synthesis. Estimable functions of fixed effects are discussed.

• The Korean Journal of Applied Statistics
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• v.27 no.5
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• pp.717-729
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• 2014

Projection pursuit classification tree uses a 1-dimensional projection with the view of the most separating classes in each node. These projection coefficients contain information distinguishing two groups of classes from each other and can be used to calculate the importance measure of classification in each variable. This paper reviews the variable importance measure with increasing interest in line with growing data size. We compared the performances of projection pursuit classification tree with those of classification and regression tree(CART) and random forest. Projection pursuit classification tree are found to produce better performance in most cases, particularly with highly correlated variables. The importance measure of projection pursuit classification tree performs slightly better than the importance measure of random forest.

• Communications for Statistical Applications and Methods
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• v.26 no.4
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• pp.337-346
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• 2019

This paper discusses a method for obtaining nonnegative estimates for variance components in a random effects model. A variance component should be positive by definition. Nevertheless, estimates of variance components are sometimes given as negative values, which is not desirable. The proposed method is based on two basic ideas. One is the identification of the orthogonal vector subspaces according to factors and the other is to ascertain the projection in each orthogonal vector subspace. Hence, an observation vector can be denoted by the sum of projections. The method suggested here always produces nonnegative estimates using projections. Hartley's synthesis is used for the calculation of expected values of quadratic forms. It also discusses how to set up a residual model for each projection.

• Journal of the Korean Society for Nondestructive Testing
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• v.30 no.3
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• pp.181-193
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• 2010

The paper presents an alternative way to classical stereocorrelation. First, 2D image processing of random patterns is described. Sub-pixel displacements are determined using phase analysis. Then distortion evaluation is presented. The distortion is identified without any assumption on the lens model because of the use of a grid technique approach. Last, shape measurement and shape variation is caught by fringe projection. Analysis is based on two pin-hole assumptions for the video-projector and the camera. Then, fringe projection is coupled to in-plane displacement to give rise to 3D measurement set-up. Metrological characterization shows a resolution comparable to classical (stereo) correlation technique ($1/100^{th}$ pixel). Spatial resolution seems to be an advantage of the method, because of the use of temporal phase stepping (shape measurement, 1 pixel) and windowed Fourier transform (in plane displacements measurement, 9 pixels). Two examples are given. First one is the study of skin properties; second one is a study on leather fabric. In both cases, results are convincing, and have been exploited to give mechanical interpretation.