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Scalable coordinate descent approaches to parallel matrix factorization for recommender The value DTW ? (?) v N A ,N B (?) can be computed in O(N A N B ) time. Applying the derivations of Section 8.3.3 and Section 8.3.4 to this specific DAG, we can compute ?DTW ? (?), ?DTW ? (?), Z and ? 2 DTW ? (?)Z with the same complexity. The procedures, with appropriate handling of the edge cases, are summarized in Algorithm 9 and 10, respectively. Note that when ? is the negative entropy, DTW ? (?) is known as soft-DTW (Cuturi and Blondel, 2012. ,