• Title/Summary/Keyword: linear embedding

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HEPTAGONAL KNOTS AND RADON PARTITIONS

  • Huh, Young-Sik
    • Journal of the Korean Mathematical Society
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    • v.48 no.2
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    • pp.367-382
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    • 2011
  • We establish a necessary and sufficient condition for a heptagonal knot to be figure-8 knot. The condition is described by a set of Radon partitions formed by vertices of the heptagon. In addition we relate this result to the number of nontrivial heptagonal knots in linear embeddings of the complete graph $K_7$ into $\mathbb{R}^3$.

MEASURE THEORETICAL APPROACH FOR OPTIMAL SHAPE DESIGN OF A NOZZLE

  • FARAHI M. H.;BORZABADI A. H.;MEHNE H. H.;KAMYAD A. V.
    • Journal of applied mathematics & informatics
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    • v.17 no.1_2_3
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    • pp.315-328
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    • 2005
  • In this paper we present a new method for designing a nozzle. In fact the problem is to find the optimal domain for the solution of a linear or nonlinear boundary value PDE, where the boundary condition is defined over an unspecified domain. By an embedding process, the problem is first transformed to a new shape-measure problem, and then this new problem is replaced by another in which we seek to minimize a linear form over a subset of linear equalities. This minimization is global, and the theory allows us to develop a computational method to find the solution by a finite-dimensional linear programming problem.

A Novel Approach of Feature Extraction for Analog Circuit Fault Diagnosis Based on WPD-LLE-CSA

  • Wang, Yuehai;Ma, Yuying;Cui, Shiming;Yan, Yongzheng
    • Journal of Electrical Engineering and Technology
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    • v.13 no.6
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    • pp.2485-2492
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    • 2018
  • The rapid development of large-scale integrated circuits has brought great challenges to the circuit testing and diagnosis, and due to the lack of exact fault models, inaccurate analog components tolerance, and some nonlinear factors, the analog circuit fault diagnosis is still regarded as an extremely difficult problem. To cope with the problem that it's difficult to extract fault features effectively from masses of original data of the nonlinear continuous analog circuit output signal, a novel approach of feature extraction and dimension reduction for analog circuit fault diagnosis based on wavelet packet decomposition, local linear embedding algorithm, and clone selection algorithm (WPD-LLE-CSA) is proposed. The proposed method can identify faulty components in complicated analog circuits with a high accuracy above 99%. Compared with the existing feature extraction methods, the proposed method can significantly reduce the quantity of features with less time spent under the premise of maintaining a high level of diagnosing rate, and also the ratio of dimensionality reduction was discussed. Several groups of experiments are conducted to demonstrate the efficiency of the proposed method.

A review on the t-distributed stochastic neighbors embedding (t-SNE에 대한 요약)

  • Kipoong Kim;Choongrak Kim
    • The Korean Journal of Applied Statistics
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    • v.36 no.2
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    • pp.167-173
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    • 2023
  • This paper investigates several methods of visualizing high-dimensional data in a low-dimensional space. At first, principal component analysis and multidimensional scaling are briefly introduced as linear approaches, and then kernel principal component analysis, self-organizing map, locally linear embedding, Isomap, Laplacian Eigenmaps, and local multidimensional scaling are introduced as nonlinear approaches. In particular, t-SNE, which is widely used but relatively unfamiliar in the field of statistics, is described in more detail. We also present a simple example for several methods, including t-SNE. Finally, we provide a review of several recent studies pointing out the limitations of t-SNE and discuss the future research problems presented.

Label Embedding for Improving Classification Accuracy UsingAutoEncoderwithSkip-Connections (다중 레이블 분류의 정확도 향상을 위한 스킵 연결 오토인코더 기반 레이블 임베딩 방법론)

  • Kim, Museong;Kim, Namgyu
    • Journal of Intelligence and Information Systems
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    • v.27 no.3
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    • pp.175-197
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    • 2021
  • Recently, with the development of deep learning technology, research on unstructured data analysis is being actively conducted, and it is showing remarkable results in various fields such as classification, summary, and generation. Among various text analysis fields, text classification is the most widely used technology in academia and industry. Text classification includes binary class classification with one label among two classes, multi-class classification with one label among several classes, and multi-label classification with multiple labels among several classes. In particular, multi-label classification requires a different training method from binary class classification and multi-class classification because of the characteristic of having multiple labels. In addition, since the number of labels to be predicted increases as the number of labels and classes increases, there is a limitation in that performance improvement is difficult due to an increase in prediction difficulty. To overcome these limitations, (i) compressing the initially given high-dimensional label space into a low-dimensional latent label space, (ii) after performing training to predict the compressed label, (iii) restoring the predicted label to the high-dimensional original label space, research on label embedding is being actively conducted. Typical label embedding techniques include Principal Label Space Transformation (PLST), Multi-Label Classification via Boolean Matrix Decomposition (MLC-BMaD), and Bayesian Multi-Label Compressed Sensing (BML-CS). However, since these techniques consider only the linear relationship between labels or compress the labels by random transformation, it is difficult to understand the non-linear relationship between labels, so there is a limitation in that it is not possible to create a latent label space sufficiently containing the information of the original label. Recently, there have been increasing attempts to improve performance by applying deep learning technology to label embedding. Label embedding using an autoencoder, a deep learning model that is effective for data compression and restoration, is representative. However, the traditional autoencoder-based label embedding has a limitation in that a large amount of information loss occurs when compressing a high-dimensional label space having a myriad of classes into a low-dimensional latent label space. This can be found in the gradient loss problem that occurs in the backpropagation process of learning. To solve this problem, skip connection was devised, and by adding the input of the layer to the output to prevent gradient loss during backpropagation, efficient learning is possible even when the layer is deep. Skip connection is mainly used for image feature extraction in convolutional neural networks, but studies using skip connection in autoencoder or label embedding process are still lacking. Therefore, in this study, we propose an autoencoder-based label embedding methodology in which skip connections are added to each of the encoder and decoder to form a low-dimensional latent label space that reflects the information of the high-dimensional label space well. In addition, the proposed methodology was applied to actual paper keywords to derive the high-dimensional keyword label space and the low-dimensional latent label space. Using this, we conducted an experiment to predict the compressed keyword vector existing in the latent label space from the paper abstract and to evaluate the multi-label classification by restoring the predicted keyword vector back to the original label space. As a result, the accuracy, precision, recall, and F1 score used as performance indicators showed far superior performance in multi-label classification based on the proposed methodology compared to traditional multi-label classification methods. This can be seen that the low-dimensional latent label space derived through the proposed methodology well reflected the information of the high-dimensional label space, which ultimately led to the improvement of the performance of the multi-label classification itself. In addition, the utility of the proposed methodology was identified by comparing the performance of the proposed methodology according to the domain characteristics and the number of dimensions of the latent label space.

A NOTE ON CERTAIN QUOTIENT SPACES OF BOUNDED LINEAR OPERATORS

  • Cho, Chong-Man;Ju, Seong-Jin
    • Communications of the Korean Mathematical Society
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    • v.19 no.4
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    • pp.715-720
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    • 2004
  • Suppose X is a closed subspace of Z = ${({{\Sigma}^{\infty}}_{n=1}Z_{n})}_{p}$ (1 < p < ${\infty}$, dim $Z_{n}$ < ${\infty}$). We investigate an isometrically isomorphic embedding of L(X)/K(X) into L(X, Z)/K(X, Z), where L(X, Z) (resp. L(X)) is the space of the bounded linear operators from X to Z (resp. from X to X) and K(X, Z) (resp. K(X)) is the space of the compact linear operators from X to Z (resp. from X to X).

Domain-Specific Terminology Mapping Methodology Using Supervised Autoencoders (지도학습 오토인코더를 이용한 전문어의 범용어 공간 매핑 방법론)

  • Byung Ho Yoon;Junwoo Kim;Namgyu Kim
    • Information Systems Review
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    • v.25 no.1
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    • pp.93-110
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    • 2023
  • Recently, attempts have been made to convert unstructured text into vectors and to analyze vast amounts of natural language for various purposes. In particular, the demand for analyzing texts in specialized domains is rapidly increasing. Therefore, studies are being conducted to analyze specialized and general-purpose documents simultaneously. To analyze specific terms with general terms, it is necessary to align the embedding space of the specific terms with the embedding space of the general terms. So far, attempts have been made to align the embedding of specific terms into the embedding space of general terms through a transformation matrix or mapping function. However, the linear transformation based on the transformation matrix showed a limitation in that it only works well in a local range. To overcome this limitation, various types of nonlinear vector alignment methods have been recently proposed. We propose a vector alignment model that matches the embedding space of specific terms to the embedding space of general terms through end-to-end learning that simultaneously learns the autoencoder and regression model. As a result of experiments with R&D documents in the "Healthcare" field, we confirmed the proposed methodology showed superior performance in terms of accuracy compared to the traditional model.

Chaotic Behaviour of Vibration signal in Rolling Mill Bearing (압연기 베어링 진동 신호의 카오스적 거동)

  • 배영철;김이곤;최남섭;김경민;정양희;최홍준;김서영
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 2000.10a
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    • pp.634-637
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    • 2000
  • A diagnosis system that provides early warnings regarding machine malfunction is very important for rolling mill so as to avoid great losses resulting from unexpected shutdown of the production line. But it is very difficult to provide early warnings in rolling mill. Because dynamics of rolling mill is non-linear. This paper shows a chaotic behaviour of vibration signal in rolling mill using embedding method. Not only phase plane and Poincare map are implemented but also FFT and histogram of vibration signal in rolling mill is presented by embedding method.

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Korean Dependency Parsing using Deep Learning (딥 러닝을 이용한 한국어 의존 구문 분석)

  • Lee, Changki;Kim, Junseok;Kim, Jeonghee
    • Annual Conference on Human and Language Technology
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    • 2014.10a
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    • pp.87-91
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    • 2014
  • 일반적인 기계학습 기반의 자연어처리 모듈의 개발에서 자질의 설계와 최적의 자질 조합을 구하는 작업은 많은 시간과 노력이 필요하다. 본 논문에서는 딥 러닝 기술을 전이 기반 방식의 한국어 의존 구문 분석에 적용하여 자질 튜닝 작업에 들어가는 많은 시간과 노력을 줄일 수 있음을 보인다. 또한 딥 러닝을 적용하기 위해 필요한 다양한 단어 표현(word embedding) 모델을 적용하여 최적의 단어 표현 모델을 알아내고, 성능 향상을 위해 최근에 개발된 Drop-out 및 Rectified Linear hidden Unit(ReLU) 기술을 적용한다. 실험결과, 기존 한국어 의존 구문 분석 연구들보다 높은 UAS 90.37%의 성능을 보였다.

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