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自組織映射圖 Self-Organizing Maps

SOM (Self-Organizing Maps/Kohonen map, 自組織映射圖)是一種分群演算法(非監督式演算法),屬於類神經一類。與其他分群演算法的最大不同在於,SOM有一個拓樸空間(Topological map),此拓樸圖用來表達每個輸出值(output/cluster)的分布狀況。因此,SOM可透過視覺化的低維度空間來表達原本的高維度空間的資料,視覺化後的結果亦能有效說明分群後的結果,研究者不至於難以說明為何如此的分群(黑箱問題)。

來源、作者

  • Kohonen, T. (1982). Self-organized formation of topologically correct feature maps. Biological Cybernetics, 43:59-69.

基本概念

典型SOM採用二維的拓樸空間,其網路架構如圖所示。
  1. 對於每一筆資料(X)來說,
  2. 首先會根據權重(Weight)去拓樸空間計算資料(X)與輸出單元(Y)的差距量,
  3. 並找出最佳的優勝單元(Winner)(圖例中為Y(0,1)),即差距量最小
  4. 最後根據資料(X)與輸出單元(Y)的差距量,以及輸出單元(Y)與優勝單元(Winner)的距離,來修正權重(Weight)

應用

  • Dieter Merkl, Text classification with self-organizing maps: Some lessons learned, Neurocomputing, Volume 21, Issues 1-3, 6 November 1998, Pages 61-77, ISSN 0925-2312, DOI: 10.1016/S0925-2312(98)00032-0.
  • Linda K. Dow, Sandeep Kalelkar, Ernst R. Dow, Self-organizing maps for the analysis of NMR spectra, Drug Discovery Today: BIOSILICO, Volume 2, Issue 4, July 2004, Pages 157-163, ISSN 1741-8364, DOI: 10.1016/S1741-8364(04)02409-6.
  • Kun Chang Lee, Hyung Rae Cho, Jin Sung Kim, A self-organizing feature map-driven approach to fuzzy approximate reasoning, Expert Systems with Applications, Volume 33, Issue 2, August 2007, Pages 509-521, ISSN 0957-4174, DOI: 10.1016/j.eswa.2006.05.031.
  • Markus Hagenbuchner, Ah Chung Tsoi, A supervised training algorithm for self-organizing maps for structures, Pattern Recognition Letters, Volume 26, Issue 12, Artificial Neural Networks in Pattern Recognition, September 2005, Pages 1874-1884, ISSN 0167-8655, DOI: 10.1016/j.patrec.2005.03.009.

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