The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Use of Minimal Spanning Trees on Self-Organizing Maps

자기조직도에서 최소생성나무의 활용

  • Jang, Yoo-Jin (Department of Statistics, Korea University) ;
  • Huh, Myung-Hoe (Department of Statistics, Korea University) ;
  • Park, Mi-Ra (Department of Preventive Medicine, Eulji University)
  • Published : 2009.04.30
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Abstract

As one of the unsupervised learning neural network methods, self-organizing maps(SOM) are applied to various fields. It reduces the dimension of multidimensional data by representing observations on the low dimensional manifold. On the other hand, the minimal spanning tree(MST) of a graph that achieves the most economic subset of edges connecting all components by a single open loop. In this study, we apply the MST technique to SOM with subnodes. We propose SOM's with embedded MST and a distance measure for optimum choice of the size and shape of the map. We demonstrate the method with Fisher's Iris data and a real gene expression data. Simulated data sets are also analyzed to check the validity of the proposed method.

비지도 학습 신경망모형의 한 종류인 자기조직도(self-organizing map: SOM)는 고차원 자료를 차원축소하고 저차원지도를 통해 유사한 개체를 군집화하는 방법이며 다양한 분야의 데이터에 적용되고 있다. 한편 최소생성나무(minimal spanning tree: MST)는 개체점들을 닫힌 루프 없이 가장 짧게 선분으로 연결하는 그래프 방법이다. 본 연구에서는 부노드 자기조직도에 최소생성나무를 적용하여 부노드 간 거리를 근사적으로 나타내는 자료 시각화 방법과 자기조직도의 최적 형태와 크기를 결정하기 위한 거리 측도를 제안하였다. 또한 피서의 붓꽃자료와 실제 유전자발현자료 및 모의생성 자료에 적용하여 이 방법의 유용성을 살펴보았다.

Keywords

References

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