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Twin kernel embedding (TKE) is a powerful non-vectorial data reduction algorithm proposed for advanced applications in clustering and visualization, manifold learning, etc. Due to the requirement of online processing in many cutting edge research problems involving highly structured data like DNA, protein sequences and biometric features that are non-vectorial in nature, learning the out-of-sample (OOS) mapping becomes a necessity. To address this, we propose constrained TKE, which is an OOS extension of TKE capable of learning such a mapping function. This is achieved by including the mapping in the objective function optimized by the TKE algorithm. More broadly, this mapping function can be applied in other data reduction methods as an OOS extension. Furthermore, to improve the accuracy of predictions in case where new samples are presented in batch, a refinement strategy is introduced by exploiting the similarity between new samples which is often ignored by other methods. Experimental results on the Reuters-21578 text collection confirmed the usefulness of the proposed method.