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Structural Correspondence Learning (SCL) is a method for dealing with domain adaptation (different data distributions in the training and testing sets). It was proposed by Blitzer et al. but I am having difficulty understanding exactly how the data is represented in this technique.

SCL deals with Domain Adaptation by choosing m 'pivot features' which are consistent across both domains, then for each one, creating a binary classification task, using the remaining features to predict whether or not a the pivot in question will appear in the instance.

The weight vectors which were learned in this task form W,a mxn matrix , where n is the number of original features. Each element corresponds to the strength of correlation between one original feature with one pivot.

Singular value decomposition is applied to W, factorising it into UDVT. θ is then formed by taking the first h elements of UT.

θ is added to the original feature set; from the paper:

'For training instance t, the augmented feature vector will contain all the original features xt plus the new shared features θxt.

Now, the part which I don't understand:

As far as I can tell, θ has dimensions h x n. The original features have dimensions m x n.

So how can we get θxt for each of the original m instances in the original dataset when θ is hxn?

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Is it not that the original feature vectors, x, are n x 1, so that when we do θx we get a h x 1 vector, which is then appended to the original?

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    $\begingroup$ Welcome to the site, @v90a. Was this intended as an answer to the OP's question, a comment requesting clarification from the OP, or a new question of your own? Please only use the "Your Answer" field to provide answers to the original question. You will be able to comment anywhere when your reputation is >50. If you have a new question, click the gray ASK QUESTION at the top of the page & ask it there, then we can help you properly. Since you're new here, you may want to take our tour, which has information for new users. $\endgroup$ – gung - Reinstate Monica Aug 7 '15 at 15:01
  • $\begingroup$ Just commenting because I recently read the paper: This answer, masked as a question, is actually correct. The only thing amiss here is the form. Stated as an actual answer: "the original feature vectors, x, are n x 1, so that when we do θx we get a h x 1 vector, which is then appended to the original" $\endgroup$ – Wang Tang Jun 9 '16 at 11:58
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for dataSet X,every row of X represent a instance, which can be seen as a row vector,but x is generally a column vector by default. that is, there is a transformation.

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  • $\begingroup$ Hi there. Your question is not clear at this stage. Can you please edit your question to make it clear what your data is, and what is the question you need answering $\endgroup$ – Conor Neilson Jan 3 '18 at 7:21

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