Primal-Dual Algorithms for Non-negative Matrix Factorization with the Kullback-Leibler Divergence

Yanez, Felipe; Bach, Francis

doi:10.48550/arxiv.1412.1788

Cited by 1 publication

(4 citation statements)

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“…( 11). The second model is NMF using KL divergence, labeled NMF [16]. The last model, GNMF [10] described in Sec.…”

Section: Resultsmentioning

confidence: 99%

“…where • is the pointwise multiplication operator and θ A , θ B ∈ R + . We use a weighted Kullback-Leibler (KL) divergence as a distance measure between C and AB, that has been shown to be more accurate than the Frobenius norm for various NMF settings [16]. The second term is the TV of the rows of A on the playlists graph, so penalizing it promotes piecewise constant signals [11].…”

Section: Our Recommendation Algorithmmentioning

confidence: 99%

“…Similarly with the third term for columns of B. Eventually, the proposed model leverages the works of [9,16], and extends them to graphs using the TV seminorm.…”

Section: Our Recommendation Algorithmmentioning

confidence: 99%

“…We describe here the proposed optimization algorithm w.r.t. B for fixed A based on [12,16,18]. The same algorithm can be applied to A for fixed B.…”

Section: Primal-dual Optimization Optimization Problem (1) Is Globall...mentioning

confidence: 99%

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Song recommendation with non-negative matrix factorization and graph total variation

Benzi

Kalofolias

Bresson

2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This work formulates a novel song recommender system 1 as a matrix completion problem that benefits from collaborative filtering through Non-negative Matrix Factorization (NMF) and content-based filtering via total variation (TV) on graphs. The graphs encode both playlist proximity information and song similarity, using a rich combination of audio, meta-data and social features. As we demonstrate, our hybrid recommendation system is very versatile and incorporates several well-known methods while outperforming them. Particularly, we show on real-world data that our model overcomes w.r.t. two evaluation metrics the recommendation of models solely based on low-rank information, graph-based information or a combination of both.

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“…( 11). The second model is NMF using KL divergence, labeled NMF [16]. The last model, GNMF [10] described in Sec.…”

Section: Resultsmentioning

confidence: 99%

Section: Our Recommendation Algorithmmentioning

confidence: 99%

“…Similarly with the third term for columns of B. Eventually, the proposed model leverages the works of [9,16], and extends them to graphs using the TV seminorm.…”

Section: Our Recommendation Algorithmmentioning

confidence: 99%

“…We describe here the proposed optimization algorithm w.r.t. B for fixed A based on [12,16,18]. The same algorithm can be applied to A for fixed B.…”

Section: Primal-dual Optimization Optimization Problem (1) Is Globall...mentioning

confidence: 99%

See 2 more Smart Citations

Song recommendation with non-negative matrix factorization and graph total variation

Benzi

Kalofolias

Bresson

2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

View full text Add to dashboard Cite

show abstract

Primal-Dual Algorithms for Non-negative Matrix Factorization with the Kullback-Leibler Divergence

Cited by 1 publication

References 0 publications

Song recommendation with non-negative matrix factorization and graph total variation

Song recommendation with non-negative matrix factorization and graph total variation

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