• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.5
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• pp.2607-2627
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• 2017

Nonnegative matrix factorization (NMF) has received considerable attention due to its effectiveness of reducing high dimensional data and importance of producing a parts-based image representation. Most of existing NMF variants attempt to address the assertion that the observed data distribute on a nonlinear low-dimensional manifold. However, recent research results showed that not only the observed data but also the features lie on the low-dimensional manifolds. In addition, a few hard priori label information is available and thus helps to uncover the intrinsic geometrical and discriminative structures of the data space. Motivated by the two aspects above mentioned, we propose a novel algorithm to enhance the effectiveness of image representation, called Dual graph-regularized Constrained Nonnegative Matrix Factorization (DCNMF). The underlying philosophy of the proposed method is that it not only considers the geometric structures of the data manifold and the feature manifold simultaneously, but also mines valuable information from a few known labeled examples. These schemes will improve the performance of image representation and thus enhance the effectiveness of image classification. Extensive experiments on common benchmarks demonstrated that DCNMF has its superiority in image classification compared with state-of-the-art methods.

• International Journal of Automotive Technology
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• v.5 no.4
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• pp.297-302
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• 2004

This paper presents the low cycle thermal fatigue of the engine exhaust manifold subject to thermo-mechanical cyclic loading. As a failure of the exhaust manifold is mainly caused by geometric constraints of the less expanded inlet flange and cylinder head, the analysis is based on the exhaust system model with three-dimensional temperature distribution and temperature dependent material properties. The result show that large compressive plastic deformations are generated at an elevated temperature of the exhaust manifold and tensile stresses are remained in several critical zones at a cold condition. From the repetition of these thermal shock cycles, maximum plastic strain range (0.454%) could be estimated by the stabilized stress-strain hysteresis loops. It is used to predict the low cycle thermal fatigue life of the exhaust manifold for the thermal shock test.

• Journal of KIISE:Software and Applications
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• v.36 no.11
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• pp.960-966
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• 2009

A manifold is used to represent a relationship between high-dimensional data samples in low-dimensional space. In human pose estimation, it is created in low-dimensional space for processing image and 3D body configuration data. Manifold learning is to build a manifold. But it is vulnerable to silhouette variations. Such silhouette variations are occurred due to view-change, person-change, distance-change, and noises. Representing silhouette variations in a single manifold is impossible. In this paper, we focus a silhouette variation problem occurred by view-change. In previous view invariant pose estimation methods based on manifold learning, there were two ways. One is modeling manifolds for all view points. The other is to extract view factors from mapping functions. But these methods do not support one by one mapping for silhouettes and corresponding body configurations because of unsupervised learning. Modeling manifold and extracting view factors are very complex. So we propose a method based on triple manifolds. These are view manifold, pose manifold, and body configuration manifold. In order to build manifolds, we employ biased manifold learning. After building manifolds, we learn mapping functions among spaces (2D image space, pose manifold space, view manifold space, body configuration manifold space, 3D body configuration space). In our experiments, we could estimate various body poses from 24 view points.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.189-213
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• 2010

We study Fano manifolds of pseudoindex greater than one and dimension greater than five, which are blow-ups of smooth varieties along smooth centers of dimension equal to the pseudoindex of the manifold. We obtain a classification of the possible cones of curves of these manifolds, and we prove that there is only one such manifold without a fiber type elementary contraction.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1261-1277
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• 2021

An inertial manifold is often constructed as a graph of a function from low Fourier modes to high ones and one used to consider backward bounded (in time) solutions for that purpose. We here show that the proof of the uniqueness of such solutions is crucial in the existence theory of inertial manifolds. Avoiding contraction principle, we mainly apply the Arzela-Ascoli theorem and Laplace transform to prove their existence and uniqueness respectively. A non-self adjoint example is included, which is related to a differential system arising after Kwak transform for Navier-Stokes equations.

• Journal of KIISE
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• v.42 no.2
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• pp.235-241
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• 2015

Locally linear embedding (LLE) [1] is a type of manifold algorithms, which preserves inner product value between high-dimensional data when embedding the high-dimensional data to low-dimensional space. LLE closely embeds data points on the same subspace in low-dimensional space, because the data points have significant inner product values. On the other hand, if the data points are located orthogonal to each other, these are separately embedded in low-dimensional space, even though they are in close proximity to each other in high-dimensional space. Meanwhile, it is well known that the facial images of the same person under varying illumination lie in a low-dimensional linear subspace [2]. In this study, we suggest an improved LLE method for face recognition problem. The method maximizes the characteristic of LLE, which embeds the data points totally separately when they are located orthogonal to each other. To accomplish this, all of the subspaces made by each class are forced to locate orthogonally. To make all of the subspaces orthogonal, the simultaneous Diagonalization (SD) technique was applied. From experimental results, the suggested method is shown to dramatically improve the embedding results and classification performance.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.9
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• pp.2991-3007
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• 2022

Two dimensional locality preserving projections (2D-LPP) is an improved algorithm of 2D image to solve the small sample size (SSS) problems which locality preserving projections (LPP) meets. It's able to find the low dimension manifold mapping that not only preserves local information but also detects manifold embedded in original data spaces. However, 2D-LPP is simple and elegant. So, inspired by the comparison experiments between two dimensional linear discriminant analysis (2D-LDA) and linear discriminant analysis (LDA) which indicated that matrix based methods don't always perform better even when training samples are limited, we surmise 2D-LPP may meet the same limitation as 2D-LDA and propose a novel matrix exponential method to enhance the performance of 2D-LPP. 2D-MELPP is equivalent to employing distance diffusion mapping to transform original images into a new space, and margins between labels are broadened, which is beneficial for solving classification problems. Nonetheless, the computational time complexity of 2D-MELPP is extremely high. In this paper, we replace some of matrix multiplications with multiple multiplications to save the memory cost and provide an efficient way for solving 2D-MELPP. We test it on public databases: random 3D data set, ORL, AR face database and Polyu Palmprint database and compare it with other 2D methods like 2D-LDA, 2D-LPP and 1D methods like LPP and exponential locality preserving projections (ELPP), finding it outperforms than others in recognition accuracy. We also compare different dimensions of projection vector and record the cost time on the ORL, AR face database and Polyu Palmprint database. The experiment results above proves that our advanced algorithm has a better performance on 3 independent public databases.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.775-780
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• 2003

In this study, a computer analysis has been developed for predicting the pipe pressure of the intake and exhaust manifold in a single cylinder engine. To get the boundary conditions for a numerical analysis, one dimensional and unsteady gas dynamic calculation is performed by using the MOC(Method Of Characteristic). The main numerical parameters are the variation of the exhaust pipe diameters to calculate the pulsating flow when the intake and exhaust valves are working. As the results of numerical analysis, the shapes and distributions of the exhaust pipe pressures were influenced strongly on the cylinder pressure. As the exhaust pipe diameter is decreased, the amplitude of exhaust pressure is large and the cylinder pressure was showed low in the region of intake valve opening time.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.1
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• pp.368-391
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• 2018

Face recognition (FR) with a single sample per person (SSPP) is common in real-world face recognition applications. In this scenario, it is hard to predict intra-class variations of query samples by gallery samples due to the lack of sufficient training samples. Inspired by the fact that similar faces have similar intra-class variations, we propose a virtual sample generating algorithm called k nearest neighbors based virtual sample generating (kNNVSG) to enrich intra-class variation information for training samples. Furthermore, in order to use the intra-class variation information of the virtual samples generated by kNNVSG algorithm, we propose image set based multimanifold discriminant learning (ISMMDL) algorithm. For ISMMDL algorithm, it learns a projection matrix for each manifold modeled by the local patches of the images of each class, which aims to minimize the margins of intra-manifold and maximize the margins of inter-manifold simultaneously in low-dimensional feature space. Finally, by comprehensively using kNNVSG and ISMMDL algorithms, we propose k nearest neighbor virtual image set based multimanifold discriminant learning (kNNMMDL) approach for single sample face recognition (SSFR) tasks. Experimental results on AR, Multi-PIE and LFW face datasets demonstrate that our approach has promising abilities for SSFR with expression, illumination and disguise variations.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.2
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• pp.148-155
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• 2014

In this paper a commute time embedding is implemented by organizing patches according to the graph-based metric, and its properties are investigated via changing the number of nodes on the graph.. It is shown that manifold embedding methods generate the intrinsic geometric structures when waveforms such as speech or music instrumental sound signals are embedded on the low dimensional Euclidean space. Basically manifold embedding algorithms only project the training samples on the graph into an embedding subspace but can not generalize the learning results to test samples. They are very effective for data clustering but are not appropriate for classification or recognition. In this paper a commute time guided transform is adopted to enhance the generalization ability and its performance is analyzed by applying it to the classification of 6 kinds of music instrumental sounds.