Nearest centroid classifier

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In machine learning, a nearest centroid or nearest prototype classifier is a classification model that assigns to observations the label of the class of training samples whose mean (centroid) is closest to the observation.

When applied to text classification using tf*idf vectors to represent documents, the nearest centroid classifier is known as the Rocchio classifier because of its similarity to the Rocchio algorithm for relevance feedback.[1]

An extended version of the nearest centroid classifier has found applications in the medical domain, specifically classification of tumors.[2]

Algorithm

  • Training procedure: given labeled training samples \textstyle \{({\vec {x}}_{1},y_{1}),\dots ,({\vec {x}}_{n},y_{n})\} with class labels y_{i}\in {\mathbf {Y}}, compute the per-class centroids \textstyle {\vec {\mu _{l}}}={\frac {1}{|C_{l}|}}{\underset {i\in C_{l}}{\sum }}{\vec {x}}_{i} where C_{l} is the set of indices of samples belonging to class l\in {\mathbf {Y}}.
  • Prediction function: the class assigned to an observation {\vec {x}} is {\hat {y}}={\arg \min }_{{l\in {\mathbf {Y}}}}\|{\vec {\mu }}_{l}-{\vec {x}}\|

See also

References

  1. ↑ Manning, Christopher; Raghavan, Prabhakar; Schütze, Hinrich (2008). "Vector space classification". Introduction to Information Retrieval. Cambridge University Press. 
  2. ↑ Tibshirani, Robert; Hastie, Trevor; Narasimhan, Balasubramanian; Chu, Gilbert (2002). "Diagnosis of multiple cancer types by shrunken centroids of gene expression". Proceedings of the National Academy of Sciences 99 (10). 
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