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A latent factor analysis (LFA)-based model has outstanding performance in extracting desired patterns from High-dimensional and Sparse (HiDS) data for building a recommender systems. However, they mostly fail in acquiring non-linear features from an HiDS matrix. An AutoEncoder (AE)-based model can address this issue efficiently, but it requires filling unknown data of an HiDS matrix with pre-assumptions that leads to the following limitations: a) prefilling unknown data of an HiDS matrix might skew its known data distribution to generate ridiculous recommendations; and b) incorporating a deep AE-style structure to improve its representative learning ability. Experimental results on three HiDS matrices from real recommender systems show that an FDAE-based model significantly outperforms state-of-the-art recommenders in terms of recommendation accuracy. Meanwhile, its computational efficiency is comparable with the most efficient recommenders with the help of parallelization. [ABSTRACT FROM AUTHOR]