• 제목/요약/키워드: convex points

검색결과 204건 처리시간 0.024초

통계적 기계학습에서의 ADMM 알고리즘의 활용 (ADMM algorithms in statistics and machine learning)

  • 최호식;최현집;박상언
    • Journal of the Korean Data and Information Science Society
    • /
    • 제28권6호
    • /
    • pp.1229-1244
    • /
    • 2017
  • 최근 여러 분야에서 데이터에 근거한 분석방법론에 대한 수요가 증대됨에 따라 이를 처리할 수 있는 최적화 방법이 발전되고 있다. 특히 통계학과 기계학습 분야의 문제들에서 요구되는 다양한 제약 조건은 볼록 최적화 (convex optimization) 방법으로 해결할 수 있다. 본 논문에서 리뷰하는 alternating direction method of multipliers (ADMM) 알고리즘은 선형 제약 조건을 효과적으로 처리할 수 있으며, 합의 방식을 통해 병렬연산을 수행할 수 있어서 범용적인 표준 최적화 툴로 자리매김 되고 있다. ADMM은 원래의 문제보다 최적화가 쉬운 부분문제로 분할하고 이를 취합함으로써 복잡한 원 문제를 해결하는 방식의 근사알고리즘이다. 부드럽지 않거나 복합적인 (composite) 목적 함수를 최적화할 때 유용하며, 쌍대이론과 proximal 작용소 이론을 토대로 체계적으로 알고리즘을 구성할 수 있기 때문에 통계 및 기계학습 분야에서 폭 넓게 활용되고 있다. 본 논문에서는 최근 통계와 관련된 여러 분야에서 ADMM알고리즘의 활용도를 살펴보고자 하며 주요한 두 가지 주제에 중점을 두고자 한다. (1) 목적식의 분할 전략과 증강 라그랑지안 방법 및 쌍대문제의 설명과 (2) proximal 작용소의 역할이다. 알고리즘이 적용된 사례로, 별점화 함수 추정 등의 조정화 (regularization)를 활용한 방법론들을 소개한다. 모의 자료를 활용하여 lasso 문제의 최적화에 대한 실증결과를 제시한다.

이점 대각 이차 근사화 기법을 쌍대기법에 적용한 순차적 근사 최적설계 (Sequential Approximate Optimization by Dual Method Based on Two-Point Diagonal Quadratic Approximation)

  • 박선호;정상진;정승현;최동훈
    • 대한기계학회논문집A
    • /
    • 제35권3호
    • /
    • pp.259-266
    • /
    • 2011
  • 본 논문에서는 SD-TDQAO (Sequential Dual - Two-point Diagonal Quadratic Approximate Optimization)라는 쌍대기법을 이용한 순차적 최적설계 알고리즘을 제안한다. 이 방법은 비선형 목적함수와 제한조건이 포함되어 있는 공학적인 문제를 효과적으로 풀 수 있도록 하는데 목적이 있다. 기존의 볼록성과 분리성이 만족되지 않는 eTDQA2 방법을 이용하여 쌍대기법에 이용할 수 있도록 이차 근사함수의 헤시언 대각요소에 이를 적용하여 쉽게 볼록성과 분리성을 보장할 수 있도록 하였다. 또한 이를 수학적 예제와 위상 최적설계문제를 통해 기존의 쌍대기법 알고리즘인 MMA 와의 비교로 그 성능을 입증하였다.

Underdetermined Blind Source Separation from Time-delayed Mixtures Based on Prior Information Exploitation

  • Zhang, Liangjun;Yang, Jie;Guo, Zhiqiang;Zhou, Yanwei
    • Journal of Electrical Engineering and Technology
    • /
    • 제10권5호
    • /
    • pp.2179-2188
    • /
    • 2015
  • Recently, many researches have been done to solve the challenging problem of Blind Source Separation (BSS) problems in the underdetermined cases, and the “Two-step” method is widely used, which estimates the mixing matrix first and then extracts the sources. To estimate the mixing matrix, conventional algorithms such as Single-Source-Points (SSPs) detection only exploits the sparsity of original signals. This paper proposes a new underdetermined mixing matrix estimation method for time-delayed mixtures based on the receiver prior exploitation. The prior information is extracted from the specific structure of the complex-valued mixing matrix, which is used to derive a special criterion to determine the SSPs. Moreover, after selecting the SSPs, Agglomerative Hierarchical Clustering (AHC) is used to automaticly cluster, suppress, and estimate all the elements of mixing matrix. Finally, a convex-model based subspace method is applied for signal separation. Simulation results show that the proposed algorithm can estimate the mixing matrix and extract the original source signals with higher accuracy especially in low SNR environments, and does not need the number of sources before hand, which is more reliable in the real non-cooperative environment.

Multi-strategy structural damage detection based on included angle of vectors and sparse regularization

  • Liu, Huanlin;Yu, Ling;Luo, Ziwei;Chen, Zexiang
    • Structural Engineering and Mechanics
    • /
    • 제75권4호
    • /
    • pp.415-424
    • /
    • 2020
  • Recently, many structural damage detection (SDD) methods have been proposed to monitor the safety of structures. As an important modal parameter, mode shape has been widely used in SDD, and the difference of vectors was adopted based on sensitivity analysis and mode shapes in the existing studies. However, amplitudes of mode shapes in different measured points are relative values. Therefore, the difference of mode shapes will be influenced by their amplitudes, and the SDD results may be inaccurate. Focus on this deficiency, a multi-strategy SDD method is proposed based on the included angle of vectors and sparse regularization in this study. Firstly, inspired by modal assurance criterion (MAC), a relationship between mode shapes and changes in damage coefficients is established based on the included angle of vectors. Then, frequencies are introduced for multi-strategy SDD by a weighted coefficient. Meanwhile, sparse regularization is applied to improve the ill-posedness of the SDD problem. As a result, a novel convex optimization problem is proposed for effective SDD. To evaluate the effectiveness of the proposed method, numerical simulations in a planar truss and experimental studies in a six-story aluminum alloy frame in laboratory are conducted. The identified results indicate that the proposed method can effectively reduce the influence of noises, and it has good ability in locating structural damages and quantifying damage degrees.

Contour of lingual surface in lower complete denture formed by polished surface impression

  • Heo, Yu-Ri;Kim, Hee-Jung;Son, Mee-Kyoung;Chung, Chae-Heon
    • The Journal of Advanced Prosthodontics
    • /
    • 제8권6호
    • /
    • pp.472-478
    • /
    • 2016
  • PURPOSE. The aim of this study was to analyze the shapes of lingual polished surfaces in lower complete dentures formed by polished surface impressions and to provide reference data for use when manufacturing edentulous trays and lower complete dentures. MATERIALS AND METHODS. Twenty-six patients with mandibular edentulism were studied. After lower wax dentures were fabricated, wax was removed from the lingual side of the wax denture and a lingual polished surface impression was obtained with tissue conditioner. The definitive denture was scanned with a three-dimensional scanner, and scanned images were obtained. At the cross-sections of the lingual frenum, lateral incisors, first premolars, first molars, and anterior border of the retromolar pads, three points were marked and eight measurements were taken. The Kruskal-Wallis test and a post hoc analysis with the Mann-Whitney test were performed. RESULTS. Each patient showed similar values for the same areas on the left and right sides without a statistically significant difference. The height of the contour of the lingual polished surface at the lingual frenum was halfway between the occlusal plane and lingual border, it moved gradually in a downward direction. The angle from the occlusal plane to the height of the contour of the lingual polished surface was increased as it progressed from the lingual frenum towards the retromolar pads. CONCLUSION. The shape of the mandibular lingual polished surface was convex at the lingual frenum, lateral incisors and gradually flattened towards the first molars and retromolar pads.

Hard- and soft-tissue profiles of the midface region in patients with skeletal Class III malocclusion using cone-beam computed tomography multiplanar-reconstructed image analysis

  • Kim, Bomi;Lee, Hyung-Chul;Kim, Seong-Hun;Kim, Yongil;Son, Woosung;Kim, Seong Sik
    • 대한치과교정학회지
    • /
    • 제48권3호
    • /
    • pp.143-152
    • /
    • 2018
  • Objective: This study examined cone-beam computed tomography (CBCT)-derived multiplanar-reconstructed (MPR) cross-sections to clarify the salient characteristics of patients with skeletal class III malocclusion with midface deficiency (MD). Methods: The horizontal and sagittal plane intersection points were identified for middle-third facial analysis in 40 patients in the MD or normal (N) groups. MPR images acquired parallel to each horizontal plane were used for length and angular measurements. Results: A comparison of the MD and N groups revealed significant differences in the zygoma prominence among female patients. The convex zygomatic area in the N group was larger than that in the MD group, and the inferior part of the midface in the N group was smaller than that in the MD group for both male and female patients. A significant difference was observed in the concave middle maxillary area among male patients. Conclusions: This study was conducted to demonstrate the difference between MD and normal face through MPR images derived from CBCT. Male patients in the MD group had a more flattened face than did those in the N group. Female patients in the MD group showed a concave-shaped lower section of the zygoma, which tended to have more severe MD. These findings indicate that orthognathic surgery to improve skeletal discrepancy requires different approaches in male and female patients.

Movement and Home Range of the Red-Tongued Viper Snake (Gloydius ussuriensis) Inhabiting Gapado

  • Kim, Byoung-Soo;Oh, Hong-Shik
    • 한국환경생태학회지
    • /
    • 제29권2호
    • /
    • pp.192-199
    • /
    • 2015
  • This study was conducted to investigate the movement and home range of the red-tongued viper snake (Gloydius ussuriensis) from June 2006 to June 2009. This snake species inhabits an islet on Jeju Island, Gapado. A total of 132 individual snakes were marked during the study. Among the marked individuals, the number of snakes recaptured more than once was 22 (16.8 %) and the number of individuals recaptured more than twice was eight (6.1 %), indicating a relatively low recapture rate. The durations from capture to recapture varied from 1 to 710 days. However, the capture points were not much different, indicating that the moved distance of snakes and the interval between capture-recapture were not correlated. The home ranges of the Red-tongued viper snakes calculated from data of the snakes which were captured more than three times using the MCP(minimum convex polygon) method were $8{\sim}167m^2(64.0{\pm}57.0m^2)$, suggesting that this snake is relatively sedentary. Home range size differences between female ($Mean=62.0m^2$) and male ($Mean=66.0m^2$) snakes were not significant. In the red-tongued viper population of Gapado, there was no statistically significant relationship between body size and home range size although it was positively correlated (r=0.675). Our results provide valuable data to understand life patterns of the red-tongued viper snakes and will be useful when conducting further ecological studies on other snake species.

의료 초음파 영상을 위한 화소단위 집속기법 (Display-Pixel-Based Focusing Method for Ultrasound Imaging)

  • 황재섭;송태경
    • 대한의용생체공학회:의공학회지
    • /
    • 제21권4호
    • /
    • pp.419-431
    • /
    • 2000
  • 본 논문에서는 디지털 스캔 컨버터(DSC, digital scan converter)에 의한 왜곡이 근본적으로 발생하지 않는 새로운 초음파 영상 방법으로서 표시장치의 화소에 직접 수신 집속하는 기법(DPBF, display-pixel-based focusing)과 이를 구현하기 위한 초음파 영상 장치의 구조를 제안한다. 제안한 기법은 극 좌표에 위치하는 샘플링 점들 대신에 직각좌표상의 화소들에 직접 수신 집속 함으로써 DSC의 역할을 제거하였다. DPBF 기법을 적용한 영상에는 DSC에 의한 허상 및 구획화 현상 등이 나타나지 않으며, 일반적인 방법에 의한 영상에 비해 보다 세밀한 영상을 제공한다는 사실을 검증할 수 있었다. 본 논문은 DSC에 의한 보간 효과가 두 개의 비교 영상 A, B 간에 미치는 정도를 정량적으로 평가하기 위해서 영상거침 비(ICRA/B, Image Coarseness Ratio)를 새로운 성능 측정 방법으로 정의하였다. 이 ICRA/B를 이용하여 비교 영상간 거친 정도를 정량적으로 측정하였다.

  • PDF

Ground Penetrating Radar Imaging of a Circular Patterned Ground near King Sejong Station, Antarctica

  • Kim, Kwansoo;Ju, Hyeontae;Lee, Joohan;Chung, Changhyun;Kim, Hyoungkwon;Lee, Sunjoong;Kim, Jisoo
    • 지질공학
    • /
    • 제31권3호
    • /
    • pp.257-267
    • /
    • 2021
  • Constraints on the structure and composition of the active layer are important for understanding permafrost evolution. Soil convection owing to repeated moisture-induced freeze-thaw cycles within the active layer promotes the formation of self-organized patterned ground. Here we present the results of ground penetrating radar (GPR) surveys across a selected sorted circle near King Sejong Station, Antarctica, to better delineate the active layer and its relation to the observed patterned ground structure. We acquire GPR data in both bistatic mode (common mid-points) for precise velocity constraints and monostatic mode (common-offset) for subsurface imaging. Reflections are derived from the active layer-permafrost boundary, organic layer-weathered soil boundary within the active layer, and frozen rock-fracture-filled ice boundary within the permafrost. The base of the imaged sorted circle possesses a convex-down shape in the central silty zone, which is typical for the pattern associated with convection-like soil motion within the active layer. The boundary between the central fine-silty domain and coarse-grained stone border is effectively identified in a radar amplitude contour at the assumed active layer depth, and is further examined in the frequency spectra of the near- and far-offset traces. The far-offset traces and the traces from the lower frequency components dominant on the far-offset traces would be associated with rapid absorption of higher frequency radiowave due to the voids in gravel-rich zone. The presented correlation strategies for analyzing very shallow, thin-layered GPR reflection data can potentially be applied to the various types of patterned ground, particularly for acquiring time-lapse imaging, when electric resistivity tomography is incorporated into the analysis.

협상 해법을 이용한 이더리움 샤드 부하 균형 알고리즘 (Adaptive Load Balancing Algorithm of Ethereum Shard Using Bargaining Solution)

  • 백동환;김승욱
    • 정보처리학회논문지:컴퓨터 및 통신 시스템
    • /
    • 제10권4호
    • /
    • pp.93-100
    • /
    • 2021
  • 블록체인의 확장성 문제를 해결하기 위한 이더리움 샤드 시스템은 부하 균형 문제가 존재하며 이는 그래프 분할 문제로 모델링된다. 본 논문에서는 게임 이론의 협상 해법을 사용하여 이더리움 샤드 시스템의 상반된 효용에 대한 협상이 가능한 적응적 온라인 가중그래프 분할 알고리즘을 제안한다. 게임 이론의 협상 해법은 상반된 효용의 협상점을 공정하게 결정할 수 있는 공리적 해법이다. 제안 알고리즘은 기존 온라인 그래프 분할 알고리즘을 가중그래프에 적용할 수 있도록 개선하였으며 대표적인 교섭 해법인 내쉬 협상 해법을 확장한 확장 내쉬 협상 해법을 사용하여 이더리움 시스템 상황을 고려한 설계를 통해 효과적으로 부하 균형을 수행하였다. 실험 결과, 대표적인 온라인, 오프라인 그래프 분할 알고리즘에 비해 최대 37% 우수한 성능을 보였다.