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The collaborative recommendation algorithm based on the Variational Autoencoder (VAE) can help solve the sparsity problem in the recommendation algorithm, but the VAE model's prior is a single Gaussian distribution, which makes the expression tends to be simple and average, and suffers from the problem of underfitting. The Gaussian Mixture Variational Autoencoder (GMVAE) model has a more complex prior, which is more adaptable and effective for nonlinear tasks compared to the original VAE model, and has been widely used for unsupervised clustering and semi-supervised learning. Inspired by this, this paper investigates a collaborative filtering algorithm based on the GMVAE model. In this paper, the authors design experiments based on the Cornac recommender system comparison framework, and use the improved GMVAE for the collaborative recommendation task, the user-item matrix regenerated by the generative model is used for recommendation task. Deep features are extracted with one hidden layer in the inference model and one layer in the generation model to increase model robustness, and an early stop strategy is used to reduce overfitting. In this paper, experiments are conducted on multiple public datasets to compare with other recommendation algorithms in terms of NDCG and recall metrics. The experiments demonstrate that the improved collaborative filtering algorithm based on a GMVAE model performs well in the recommendation task. [ABSTRACT FROM AUTHOR]

To overcome the imprecise shortcomings of keeping low-level outline signal in denoise method based on fractional calculus filtering and losing high-level detail signal in BM3D (block-matching 3D) filtering, this paper proposed a fractional block-matching 3D filtering method. It discussed the basic mathmatic theory of fractional calculus to apply it to the image processing, constructured the fractional integral denoising templates, and discussed the impact of fractional order selection for de-noising results. And it used two standard methods to evaluate result: subjective visual perception and objective peak signal to noise ratio (PSNR). The experiment results show that this method gets better results in reservations high-level details compared with wavelet filtering and nonlocal mean filtering. Through numerical realizing the method and analysing it with some advanced denoise methods today, it proves the correctness and reasonability of the theory and it gets the conclution that this method is better. [ABSTRACT FROM AUTHOR]