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. When applied to text classification using word vectors containing tf*idf weights 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
Given labeled training samples [math]\displaystyle{ \textstyle\{(\vec{x}_1, y_1), \dots, (\vec{x}_n, y_n)\} }[/math] with class labels [math]\displaystyle{ y_i \in \mathbf{Y} }[/math], compute the per-class centroids [math]\displaystyle{ \textstyle\vec{\mu}_\ell = \frac{1}{|C_\ell|}\underset{i \in C_\ell}{\sum} \vec{x}_i }[/math] where [math]\displaystyle{ C_\ell }[/math] is the set of indices of samples belonging to class [math]\displaystyle{ \ell \in \mathbf{Y} }[/math].
Prediction
The class assigned to an observation [math]\displaystyle{ \vec{x} }[/math] is [math]\displaystyle{ \hat{y} = {\arg\min}_{\ell \in \mathbf{Y}} \|\vec{\mu}_\ell - \vec{x}\| }[/math].
See also
References
- ↑ Manning, Christopher; Raghavan, Prabhakar; Schütze, Hinrich (2008). "Vector space classification". Introduction to Information Retrieval. Cambridge University Press. http://nlp.stanford.edu/IR-book/html/htmledition/rocchio-classification-1.html.
- ↑ 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. PMID 12011421.
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