• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권4호
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• pp.296-311
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• 2021

Topological Data Analysis (TDA), a relatively new field of data analysis, has proved very useful in a variety of applications. The main persistence tool from TDA is persistent homology in which data structure is examined at many scales. Representations of persistent homology include persistence barcodes and persistence diagrams, both of which are not straightforward to reconcile with traditional machine learning algorithms as they are sets of intervals or multisets. The problem of faithfully representing barcodes and persistent diagrams has been pursued along two main avenues: kernel methods and vectorizations. One vectorization is the Betti sequence, or Betti curve, derived from the persistence barcode. While the Betti sequence has been used in classification problems in various applications, to our knowledge, the stability of the sequence has never before been discussed. In this paper we show that the Betti sequence is unstable under the 1-Wasserstein metric with regards to small perturbations in the barcode from which it is calculated. In addition, we propose a novel stabilized version of the Betti sequence based on the Gaussian smoothing seen in the Stable Persistence Bag of Words for persistent homology. We then introduce the normalized cumulative Betti sequence and provide numerical examples that support the main statement of the paper.

• 한국압력기기공학회 논문집
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• 제19권2호
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• pp.146-154
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• 2023

In nuclear power plants, ultrasonic test for pipe wall thickness measurement is used during periodic inspections to prevent pipe rupture due to pipe wall thinning. However, when measuring pipe wall thickness using ultrasonic test, a significant amount of measurement error occurs due to the on-site conditions of the nuclear power plant. If the maximum pipe wall thinning rate is decided by the measured pipe wall thickness containing a significant error, the pipe wall thinning rate data have significant uncertainty and systematic overestimation. This study proposes preprocessing of pipe wall thinning measurement data using support vector machine regression algorithm. By using support vector machine, pipe wall thinning measurement data can be smoothened and accordingly uncertainty and systematic overestimation of the estimated pipe wall thinning rate data can be reduced.

• 한국통신학회논문지
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• 제41권11호
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• pp.1507-1514
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• 2016

Full-image guided filter는 커널 윈도우 영역만 필터링에 반영되는 기존의 커널 윈도우 기반 가이드 필터와 달리 가중치 전파 도식과 양방향 모델이 적용되어 영상의 모든 픽셀이 필터링에 반영된다. 이로써 가이드 필터의 경계 보존과 평활화 등의 가이드 이미지 필터의 특성을 유지하면서도 계산 복잡도를 개선할 수 있다. 본 논문에서는 full-image guided filter의 더 빠른 처리가 필요한 스테레오 비전 및 각종 실시간 시스템 분야에 적용될 수 있도록 효율적인 하드웨어 구조를 제안하였다. 필터링 프로세스에서 발생하는 각종 데이터의 종속성 분석과 영상의 PSNR 분석, 데이터 빈도 분석 등을 통하여 적합한 하드웨어 구조를 제안하였다. 또한 양방향 모델이 적용된 가중치 연산 모듈의 휴식 구간이 최소화되도록 효율적인 스케줄링을 하였고 실시간 처리가 가능하게 하였다. 제안한 하드웨어 구조는 동부하이텍 0.11um 표준셀 라이브러리로 합성하였을 경우 최대 동작주파수 214MHz(384*288 영상: 965 fps)와 76K(내부 메모리 제외) 게이트의 하드웨어 복잡도를 나타냈다.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2023년도 학술발표회
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• pp.174-174
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• 2023

The impact of global warming on the south Asian summer monsoon is of critical importance for the large population of this region. This study aims to investigate the future changes of the precipitation extremes during pre-monsoon and monsoon, across this region in a more organized regional structure. The study area is divided into six major divisions based on the Köppen-Geiger's climate structure and 10 sub-divisions considering the geographical locations. The future changes of extreme precipitation indices are analyzed for each zone separately using five indices from ETCCDI (Expert Team on Climate Change Detection and Indices); R10mm, Rx1day, Rx5day, R95pTOT and PRCPTOT. 10 global climate model (GCM) outputs from the latest CMIP6 under four combinations of SSP-RCP scenarios (SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5) are used. The GCMs are bias corrected using nonparametric quantile transformation based on the smoothing spline method. The future period is divided into near future (2031-2065) and far future (2066-2100) and then the changes are compared based on the historical period (1980-2014). The analysis is carried out separately for pre-monsoon (March, April, May) and monsoon (June, July, August, September). The methodology used to compare the changes is probability distribution functions (PDF). Kernel density estimation is used to plot the PDFs. For this study we did not use a multi-model ensemble output and the changes in each extreme precipitation index are analyzed GCM wise. From the results it can be observed that the performance of the GCMs vary depending on the sub-zone as well as on the precipitation index. Final conclusions are made by removing the poor performing GCMs and by analyzing the overall changes in the PDFs of the remaining GCMs.