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Such a model can be derived by building on the notion of the maximum margin matrix factorization [27].
Such a set of mappings is obtained, building on the notion of the maximum margin matrix factorization, by minimizing a weighted sum of nuclear norms.
Since the dimensionality of the R latent feature spaces (i.e., p r ) is unknown, inspired by maximum margin matrix factorization [27], we can allow the unknown matrices C r) to have an unbounded number of columns and F r), r=1,2,…,R to have an unbounded number of rows.
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Based on the framework, we propose three solutions by specifying three state-of-the-art collaborative filtering methods, namely Maximum-Margin Matrix Factorization, Regularized Low-rank Matrix Factorization, and Probabilistic Matrix Factorization.
Let A φ denotes a n ' × m φ -dimensional transformation matrix, namely orthogonal kernel maximum margin projection subspace; then, φ(x ij ) is projected into m φ dimensional space as follow {mathbf{y}}_{ij}^{varphi }={mathbf{A}}_{varphi}^Tvarphi left({mathbf{x}}_{ij}right) (19).
where a r is the column vector of matrix A, i.e., A = [a 1, a 2 … a m], namely orthogonal maximum margin projection subspace (OMMPS).
However, the coordinate axes of MMC subspace are not optimal in meaning of maximum margin due to the fact that they are solved by (SVD) on the difference between the between-class scatter matrix and within-class scatter matrix without exerting the constraints.
The poll has a maximum margin of sampling error of plus or minus three points.
maximum margin criterion.
orthogonal maximum margin projection subspace.
The maximum margin is around 21%%.
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