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Given a binarily labeled train set, and an unlabeled test set, consider the following two-step classification system:

  • step 1: the train and test data is clustered.
  • step 2: an SVM is fitted for each cluster using the train data and train labels only. Then, if a test data belong to cluster X, we use SVM of cluster X to determine its label.

Can one call such a classification system transductive SVM?

From my understanding: on one side, there is transduction since the unlabeled test set is used in the training phase (to find the clusters). But on the other side, I thought transductive SVM was specifically referring to another kind of classification system, where no clustering was involved (only SVM margins).

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No. A TSVM is an extension of the SVM and is used in semi-supervised learning scenarios (that is, not all the data is labelled, as you pointed out, but for both the train and the test set, meaning that an unlabeled instance, once labeled, may be used in refining the model). You can find some technical information at users.stat.umn.edu/~xshen/paper/tsvm.pdf.

The process you are describing follows the idea of granule computing.

From the Wikipedia page: "information granules are collections of entities that usually originate at the numeric level and are arranged together due to their similarity, functional or physical adjacency, indistinguishability, coherency, or the like."

Grouping data by similarity is the clustering process you are describing.

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