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We propose to incorporate additional diversity enhancing constraints, in the matrix factorization model for collaborative filtering.
To learn the representation vectors of nodes, we derive the multiplicative updating rules to train the nonnegative matrix factorization model.
The first algorithm merges all the usersʼ data together, and uses a collective matrix factorization model to provide general recommendation (Zheng et al., 2010 [3]).
The third algorithm is a new algorithm which further improves our previous two algorithms by using a ranking-based collective tensor and matrix factorization model.
The second algorithm treats each user differently and uses a collective tensor and matrix factorization model to provide personalized recommendation (Zheng et al., 2010 [4]).
Our approach encodes latent query intents as well as nodes as representation vectors by a novel nonnegative matrix factorization model, and the diversity of the results accounts for the query relevance and the novelty w.r.t.
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Trends in concentrations, source contribution, and incremental excesses across three sites were investigated using the Positive Matrix Factorization model.
Fig. 2 Matrix factorization framework.
It is noted that the multiple nonnegative matrix factorization framework necessitates transforming the two expression matrices into nonnegative matrices.
In this article, we present a Temporal Collective Matrix Factorization (TCMF) model, making the following contributions: (i) we capture preference dynamics through a joint decomposition model that extracts the user temporal patterns, and (ii) co-factorize the temporal patterns with multimodal user-item interactions by minimizing a joint objective function to generate the recommendations.
While it is true that source apportionment studies have been conducted worldwide, this is the first time that the Positive Matrix Factorization (PMF) model is applied in Bogota using full PM10 chemical speciation data, including carbonaceous materials, metals and ions.
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