The study of influence propagation over networks has received increasing attention in many scientific domains. In particular, the linear threshold model is widely studied due to its ability to capture the mechanism by which multiple sources of exposure are required for nodes in the network to take action. Most existing research on influence propagation concentrate on asingletopic spreading in isolation over the network. However, real-life social contagions often involvemultipletopics spreading simultaneously in acorrelatedmanner; e.g., different conspiracy theories, political opinions on taxes, immigration, gun control, etc. In this work, we propose amulti-dimensional threshold model with correlated influencesas an extension of the classical linear threshold model to incorporate multiple correlated topics spreading simultaneously over networks. We provide analytical results that accurately predict the threshold, probability, and expected size ofglobalcascades, i.e., cases where asignificantfraction of the population getsinfluenced. Through extensive simulations, we demonstrate that our analytical results match the numerical results near-perfectly in the finite node regime. These results reveal the interplay between the underlying network structure, the correlation among spreading topics, and the heterogeneous thresholds on thefinalresults of the propagation.

The study of complex contagions over networks has been receiving increasing attention across many scientific domains. Especially, linear threshold models are widely studied due to the ability to capture the mechanism that multiple sources of exposure are required for nodes in the network to take action. Most related works on influence propagation only concentrate on a single content spreading over networks. However, complex contagions usually involve multiple correlated contents spreading simultaneously, demonstrating significant implications for many real-life systems. In this work, we propose a multi-dimensional threshold model as an extension of the classical linear threshold model to incorporate multiple correlated contents spreading simultaneously over networks. We also provide analytical results that accurately predict probability of emergence of global cascades for correlated contents. These results reveal the interplay between the underlying network structure and contents' correlation on the spreading processes. Thus, our work advances analysis, prediction and control strategies for complex contagions over networks,

Modeling spreading processes over complex networks has been receiving increasing attention. For example, bond percolation models considering population heterogeneity have been used to derive insights into disease spread and misinformation control. However, most works on spreading processes with population heterogeneity only concentrate on single-layer contact networks. To study how the course of a spreading process changes due to multiple layers of contact networks (e.g., neighborhood vs. schools or Twitter vs. Facebook) while considering population heterogeneity from a principled, mathematical lens, we propose the Multi-layer Mask model based on SIR dynamics. We derive analytical expressions for three fundamental epidemiological quantities: the probability of emergence, the epidemic threshold, and the expected epidemic size. Analytical results are shown to be in near-perfect agreement with the numerical results obtained through extensive simulations. These results reveal the impact of the structure of the multi-layer contact network, viral transmission dynamics, and population heterogeneity on the final state of the spreading process. Thus, they might help develop mitigation and control strategies for disease spread and information diffusion.

In this paper, we address the problem of estimating scale factors between images. We formulate the scale estimation problem as a prediction of a probability distribution over scale factors. We design a new architecture, SealeNet, that exploits dilated convolutions as well as self- and cross-correlation layers to predict the scale between images. We demonstrate that rectifying images with estimated scales leads to significant performance improvements for various tasks and methods. Specifically, we show how ScaleNet can be combined with sparse local features and dense correspondence networks to improve camera pose estimation, 3D reconstruction, or dense geometric matching in different benchmarks and datasets. We provide an extensive evaluation on several tasks, and analyze the computational overhead of SealeNet. The code, evaluation protocols, and trained models are publicly available at https://github.com/axelBarroso/ScaleNet.

In this paper, we investigate how L2 normalisation affects the back-propagated descriptor gradients during training. Based on our observations, we propose HyNet, a new local descriptor that leads to state-of-the-art results in matching. HyNet introduces a hybrid similarity measure for triplet margin loss, a regularisation term constraining the descriptor norm, and a new network architecture that performs L2 normalisation of all intermediate feature maps and the output descriptors. HyNet surpasses previous methods by a significant margin on standard benchmarks that include patch matching, verification, and retrieval, as well as outperforming full end-to-end methods on 3D reconstruction tasks.

Despite the fact that Second Order Similarity (SOS) has been used with significant success in tasks such as graph matching and clustering, it has not been exploited for learning local descriptors. In this work, we explore the potential of \sos in the field of descriptor learning by building upon the intuition that a positive pair of matching points should exhibit similar distances with respect to other points in the embedding space. Thus, we propose a novel regularization term, named Second Order Similarity Regularization (SOSR), that follows this principle. By incorporating SOSR into training, our learned descriptor achieves state-of-the-art performance on several challenging benchmarks containing distinct tasks ranging from local patch retrieval to structure from motion. Furthermore, by designing a von Mises-Fischer distribution based evaluation method, we link the utilization of the descriptor space to the matching performance, thus demonstrating the effectiveness of our proposed SOSR. Extensive experimental results, empirical evidence, and in-depth analysis are provided, indicating that SOSR can significantly boost the matching performance of the learned descriptor.

The research focus of designing local patch descriptors has gradually shifted from handcrafted ones (e.g., SIFT) to learned ones. In this paper, we propose to learn high performance descriptor in Euclidean space via the Convolutional Neural Network (CNN). Our method is distinctive in four aspects: (i) We propose a progressive sampling strategy which enables the network to access billions of training samples in a few epochs. (ii) Derived from the basic concept of local patch matching problem, we empha-size the relative distance between descriptors. (iii) Extra supervision is imposed on the intermediate feature maps. (iv) Compactness of the descriptor is taken into account. The proposed network is named as L2-Net since the output descriptor can be matched in Euclidean space by L2 distance. L2-Net achieves state-of-the-art performance on the Brown datasets [16], Oxford dataset [18] and the newly proposed Hpatches dataset [11]. The good generalization ability shown by experiments indicates that L2-Net can serve as a direct substitution of the existing handcrafted descriptors. The pre-trained L2-Net is publicly available.

In this paper, an unsupervised classification for compact polarimetry SAR (C-PolSAR) image is proposed by combining the H/α decomposition with the Wishart classifier. Firstly, H/α decomposition method is applied to the compact polarimetry (CP) data. By analyzing the different (H, a) values corresponding to the three compact polarimetry mode: the π/4, CL, and CC modes, we find that only in the CC mode, different scattering targets are distinguished well by (H, α) values. The decomposition results are used as the initial classification. Then the maximum likelihood classifier based on the complex Wishart distribution is adopted to classify the image iteratively. After four iterations, the classification results are much improved, and the classification details can be identified clearly. We use the AirSAR of San Francisco L-band data to illustrate the effectiveness of the proposed classification method.