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Centrality of nodes is very useful for understanding the behavior of systems and has recently attracted plenty of attention from researchers. In this paper, we propose a new eigenvector centrality based on node similarity for ranking nodes in multilayer and temporal networks under the framework of tensor computation, referred to as the ECMSim. We define a fourth-order tensor to represent the multilayer and temporal networks. The relationships between different layers(or time stamps) can be depicted by using node similarity. Based on the defined tensor, we establish the tensor equation to obtain nodes centrality values. The nodes centrality values also can be viewed as the Perron eigenvector of a multi-homogeneous map. Furthermore, we show the existence and uniqueness of the proposed centrality measure by existing results. Numerical experiments are carried out to demonstrate that the proposed centrality outperforms some existing ranking methods.INDEX TERMS Network science, multilayer networks, temporal networks, multi-homogeneous map, eigenvector centrality.

Background: In recent years, melanoma is rising at a faster rate compared to other cancers. Although it is the most serious type of skin cancer, the diagnosis at early stages makes it curable. Dermoscopy is a reliable medical technique used to detect melanoma by using a dermoscope to examine the skin. In the last few decades, digital imaging devices have made great progress which allowed capturing and storing high-quality images from these examinations. The stored images are now being standardized and used for the automatic detection of melanoma. However, when the hair covers the skin, this makes the task challenging. Therefore, it is important to eliminate the hair to get accurate results. Methods:In this paper, we propose a simple yet efficient method for hair removal using a variational autoencoder without the need for paired samples. The encoder takes as input a dermoscopy image and builds a latent distribution that ignores hair as it is considered noise, while the decoder reconstructs a hair-free image. Both encoder and decoder use a decent convolutional neural networks architecture that provides high performance. The construction of our model comprises two stages of training. In the first stage, the model has trained on hair-occluded images to output hair-free images, and in the second stage, it is optimized using hair-free images to preserve the image textures. Although the variational autoencoder produces hair-free images, it does not maintain the quality of the generated images. Thus, we explored the use of three-loss functions including the structural similarity index (SSIM), L1-norm, and L2-norm to improve the visual quality of the generated images. Results:The evaluation of the hair-free reconstructed images is carried out using tdistributed stochastic neighbor embedding (SNE) feature mapping by visualizing the distribution of the real hair-free images and the synthesized hair-free images. The conducted experiments on the publicly available dataset HAM10000 show that our method is very efficient.

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