The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Support vector machine for elastic planar shape on the linearized space

서포트 벡터 머신을 활용한 일래스틱 평면 형태데이터의 선형공간 속 분류 연구

  • Received : 2024.06.20
  • Accepted : 2024.09.01
  • Published : 2024.12.31
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Abstract

In this paper, we consider a classification model based on support vector machines (SVM) for shape data, which is utilized in various application areas such as computer vision, medical imaging, and so on. When shape is represented as a function, we need a shape distance invariant to translation, scaling, rotation, and reparameterization. We adopt the elastic shape analysis framework based on the square-root velocity function (SRVF) representation. The framework enables us to analyze shape data on a unit hypersphere instead of a Riemannian manifold, the original representation space. The data could be even linearized using a tangent space at the mean of the transformed sample shapes. We apply the SVM to the tangent Euclidean vectors after projection. We design simulation studies for shape classification by generating planar curves from a mixture of von Mises-Fisher distributions. We analyze real data of algal shapes, and compare its performance with other statistical classification methods.

본 논문에서는 컴퓨터 비전, 의학 이미징과 같은 다양한 응용 분야에서 활용되는 형태데이터에 대하여 서포트 벡터 머신 기반의 분류 모형을 제안하고 다른 통계적 모형들과의 분류 성능을 비교한다. 형태를 함수형 데이터로 표현했을 때, 위치이동, 크기조절, 회전, 재매개변수화와 같은 변동 요인에 불변하는 형태 거리를 가지고 분석하기 위하여 최근 활발히 연구되어지고 있는 일래스틱 형태 분석을 기반으로 한다. 이 분석 틀은 형태를 표현하는 곡선을 제곱근속도함수로 변환하여 곡선의 본래 공간인 리마니안 다양체를 단위 초구로 재구성할 수 있다. 초구 위에 변환된 표본 형태데이터의 평균을 중심으로 탄젠트 공간을 만들고, 그 위로 사영시킨 유클리디안 벡터를 통해 서포트 벡터 머신 방법들로 분류한다. 폰 미제스-피셔 혼합분포를 이용하여 생성한 모의실험 형태데이터와 조류 형태를 분석하는 실제 데이터를 통해 제안한 서포트 벡터 머신 방법과 다른 통계적 분류 모형들을 적용하고 그 성능을 비교한다.

Keywords

Acknowledgement

이 성과는 정부(과학기술정보통신부)의 재원으로 한국연구재단의 지원을 받아 수행된 연구임 (RS-2022-00167077). 이 성과는 한국수자원공사(K-water)의 지원을 받아 수행된 연구임.

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