• Title/Summary/Keyword: similarity dimension

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Crack Growth Behaviors of Cement Composites by Fractal Analysis

  • Won, Jong-Pil;Kim, Sung-Ae
    • KCI Concrete Journal
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    • v.14 no.1
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    • pp.30-35
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    • 2002
  • The fractal geometry is a non-Euclidean geometry which describes the naturally irregular or fragmented shapes, so that it can be applied to fracture behavior of materials to investigate the fracture process. Fractal curves have a characteristic that represents a self-similarity as an invariant based on the fractal dimension. This fractal geometry was applied to the crack growth of cementitious composites in order to correlate the fracture behavior to microstructures of cementitious composites. The purpose of this study was to find relationships between fractal dimensions and fracture energy. Fracture test was carried out in order to investigate the fracture behavior of plain and fiber reinforced cement composites. The load-CMOD curve and fracture energy of the beams were observed under the three point loading system. The crack profiles were obtained by the image processing system. Box counting method was used to determine the fractal dimension, D$_{f}$. It was known that the linear correlation exists between fractal dimension and fracture energy of the cement composites. The implications of the fractal nature for the crack growth behavior on the fracture energy, G$_{f}$ is apparent.ent.

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Application of Fractal Geometry to Architectural Design

  • Lee, Myung-Sik
    • Architectural research
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    • v.16 no.4
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    • pp.175-183
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    • 2014
  • Contemporary architecture tends to deconstruct modern architecture based on rationalization just like reductionism and functionalism and secedes from it. It means change from mechanical to organic and ecological view of the world. According to these changes, consideration of a compositive relationship presented variety and complexity in architecture. Thus, the modern speculation based on rationalism cannot provide an alternative interpretation about complicated architectural phenomena. At this point in time, the purpose of this study is to investigate the possibilities of the fractal as an alternative tool of analysis and design in contemporary architecture. In this study, two major aspects are discussed. First, the fractal concepts just like 'fractal dimension', 'box-counting dimension' and 'fractal rhythm' can be applied to analysis in architecture. Second, the fractal formative principles just like 'scaling', 'superimposition trace', 'distortion' and 'repetition' can be applied to design in architecture. Fractal geometry similar to nature's patterned order can provide endless possibilities for analysis and design in architecture. Therefore further study of fractal geometry should be conducted synthetically from now on.

Fractal Structure of the Stock Markets of Leading Asian Countries

  • Gunay, Samet
    • East Asian Economic Review
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    • v.18 no.4
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    • pp.367-394
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    • 2014
  • In this study, we examined the fractal structure of the Nikkei225, HangSeng, Shanghai Stock Exchange and Straits Times Index of Singapore. Empirical analysis was performed via non-parametric, semi-parametric long memory tests and also fractal dimension calculations. In order to avoid spurious long memory features, besides the Detrended Fluctuations Analysis (DFA), we also used Smith's (2005) modified GPH method. As for fractal dimension calculations, they were conducted via Box-Counting and Variation (p=1) tests. According to the results, while there is no long memory property in log returns of any index, we found evidence for long memory properties in the volatility of the HangSeng, the Shanghai Stock Exchange and the Straits Times Index. However, we could not find any sign of long memory in the volatility of Nikkei225 index using either the DFA or modified GPH test. Fractal dimension analysis also demonstrated that all raw index prices have fractal structure properties except for the Nikkei225 index. These findings showed that the Nikkei225 index has the most efficient market properties among these markets.

Gated Recurrent Unit Architecture for Context-Aware Recommendations with improved Similarity Measures

  • Kala, K.U.;Nandhini, M.
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.14 no.2
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    • pp.538-561
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    • 2020
  • Recommender Systems (RecSys) have a major role in e-commerce for recommending products, which they may like for every user and thus improve their business aspects. Although many types of RecSyss are there in the research field, the state of the art RecSys has focused on finding the user similarity based on sequence (e.g. purchase history, movie-watching history) analyzing and prediction techniques like Recurrent Neural Network in Deep learning. That is RecSys has considered as a sequence prediction problem. However, evaluation of similarities among the customers is challenging while considering temporal aspects, context and multi-component ratings of the item-records in the customer sequences. For addressing this issue, we are proposing a Deep Learning based model which learns customer similarity directly from the sequence to sequence similarity as well as item to item similarity by considering all features of the item, contexts, and rating components using Dynamic Temporal Warping(DTW) distance measure for dynamic temporal matching and 2D-GRU (Two Dimensional-Gated Recurrent Unit) architecture. This will overcome the limitation of non-linearity in the time dimension while measuring the similarity, and the find patterns more accurately and speedily from temporal and spatial contexts. Experiment on the real world movie data set LDOS-CoMoDa demonstrates the efficacy and promising utility of the proposed personalized RecSys architecture.

Fractal Analysis of Urban Morphology Considering Distributed Situation of Buildings (건물분포를 고려한 도시형태의 프랙털(Fractal) 해석)

  • Moon, Tae-Heon
    • Journal of the Korean Association of Geographic Information Studies
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    • v.8 no.3
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    • pp.1-10
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    • 2005
  • The purpose of this paper is to conduct an experimental measurement and analysis of cities' morphology. Fractal theory that is an effective tool for evaluating self-similarity and complexity of objects was applied. For the comparative analysis of fractailities and computational verification, two totally different cities in Japan were selected. They are Kitakyushu City, which is a big and fully developed city, and Jinguu Machi of which almost all the area is covered with agricultural land use. After converting vector data to raster data within GIS, fractal dimensions of two cases in Kitakyushu City and one case in Jinguu Machi were calculated. The calculation showed that two parts of Kitakyushu City were already fractal. Jinguu Machi, however, was difficult to find fractality. As a conclusion, fractal was proved to be an useful tool to estimate the shape of cities reflecting their internal spatial structure, that is self-similarity and complexity.

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The New Estimation Methods for Outdoor Equipment using Fractal Mathematics (프랙탈 수학을 이용한 옥외용 설비의 정량적 평가법 제안)

  • Park, Beom-Su;Lim, Jang-Seob;So, Soon-Youl;Lee, Jin;Song, Il-Keun;Lee, Jae-Bong
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.20 no.2
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    • pp.183-187
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    • 2007
  • Fractal mathematics is being highlighted as a research method for classification of image. But the application of Fractal dimension(FD) has been requited the complicated calculation method because of its complex repetition progressing. In this paper, it has been developed the new approach method to express the Fractal Dimension(FD) for aging level calculation and estimation system of outside insulator using special image processing algorithm. As a result after FD testing, the recognized aging estimation of FD has a very characteristics compared to the conventional visual inspection.

A Study on the Post-Industrial Design and the Trends (후기 산업주의 디자인과 그 트렌드에 관한 연구)

  • 윤영화
    • Archives of design research
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    • v.17 no.1
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    • pp.191-200
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    • 2004
  • After the Industrialism, long-lasting issues about Post-Industrialism have closely been associated with our daily lives. The keyword of Post-Industrialism could be regarded as Immateriality, which is represented by service, Information and knowledge. In the Post-Industrial society, the major role of Post-Industrial design trend is a mediator to deliver the immateriality to users. Additionally, the maturity of technologies and product life cycle have leaded users to the design trend that is free from the technologies and functions of products. In this context, the most powerful trend of the Post-Industrial design could be "metaphor design" and "poetic dimension". The similarity of these two styles is situated in the romanticism -reflection of symbol and metaphor. However, the appearance of Apple's iMac in 1998, poetic dimension, which uses transparent plastic and colourful, pleasurable 'blobjects' has dominated the post-industrial design trend.

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Performance Improvement of Deep Clustering Networks for Multi Dimensional Data (다차원 데이터에 대한 심층 군집 네트워크의 성능향상 방법)

  • Lee, Hyunjin
    • Journal of Korea Multimedia Society
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    • v.21 no.8
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    • pp.952-959
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    • 2018
  • Clustering is one of the most fundamental algorithms in machine learning. The performance of clustering is affected by the distribution of data, and when there are more data or more dimensions, the performance is degraded. For this reason, we use a stacked auto encoder, one of the deep learning algorithms, to reduce the dimension of data which generate a feature vector that best represents the input data. We use k-means, which is a famous algorithm, as a clustering. Sine the feature vector which reduced dimensions are also multi dimensional, we use the Euclidean distance as well as the cosine similarity to increase the performance which calculating the similarity between the center of the cluster and the data as a vector. A deep clustering networks combining a stacked auto encoder and k-means re-trains the networks when the k-means result changes. When re-training the networks, the loss function of the stacked auto encoder and the loss function of the k-means are combined to improve the performance and the stability of the network. Experiments of benchmark image ad document dataset empirically validated the power of the proposed algorithm.

Analysis of Intellectual Structure of Subject Specialty through Author Co-citation (전문영역의 주제구조분석 - 저자공인용에 근거하여 -)

  • Cho Myeung-Hee
    • Journal of the Korean Society for Library and Information Science
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    • v.22
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    • pp.331-360
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    • 1992
  • This research presents author co-citation analysis of the subject area in the humanities - Korean history. Three approaches to multivariate analyses were used to display the inter-author relationships in the similarity matrix. Data on co-citation of sixty seven authors for the period of 1980­1989 were extracted from the database constructed by author. The author's name, here refers to a body of writings by a person, is the unit of analysis. The data were subjected to non-metric multidimensional scaling program create two-dimensional map of authors. Authors with similarity are clustered using hierarchical agglomerative procedure and it is found that five clusters in Korean history represent primarily research specializations. Author map of Korean history reveals the first dimension corresponding to subject orientation of authors and the second dimension corresponds to research method or research style. In factor analysis, each factor reflects research specialty made up of authors, and factor locadings demonstrate the breadth or concentration of sixty seven authors' scholarly contributions on Korean history. It is demonstrated that the· specific methodology employed by this research, author co-citation analysis, is useful to represent the intellectual structure of Korean history.

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Analysis of Characteristics in Ara River Basin Using Fractal Dimension (프랙탈 차원을 이용한 아라천 유역특성 분석)

  • Hwang, Eui-Ho;Lee, Eul-Rae;Lim, Kwang-Suop;Jung, Kwan-Sue
    • Journal of Korea Water Resources Association
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    • v.44 no.10
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    • pp.831-841
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    • 2011
  • In this study, with the assumption that the geographical characteristics of the river basin have selfsimilarity, fractal dimensions are used to quantify the complexity of the terrain. For this, Area exponent and hurst exponent was applied to estimate the fractal dimension by using spatial analysis. The result shows that the value of area exponent and hurst exponent calculated by the fractal dimension are 2.008~2.074 and 2.132~2.268 respectively. Also the $R^2$ of area exponent and hurst exponent are 94.9% and 87.1% respectively too. It shows that the $R^2$ is relatively high. After analyzing the spatial self-similarity parameter, it is shown that traditional urban area's moderate slope geographical characteristic closed to 2D fractal in Ara water way. In addition, the relation between fractal dimension and geographical elements are identified. With these results, fractal dimension is the representative value of basin characteristics.