Nearest centroid classifier

In machine learning, a nearest centroid classifier 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.

Rocchio Classification

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

See also

• Cluster hypothesis
• k-means clustering
• k-nearest neighbor algorithm
• Linear discriminant analysis

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): 6567–6572. doi:10.1073/pnas.082099299. PMC 124443. PMID 12011421.