Linear Convergence of Adaptively Iterative Thresholding Algorithms for Compressed Sensing

This paper studies the convergence of the adaptively iterative thresholding (AIT) algorithm for compressed sensing. We first introduce a generalized restricted isometry property (gRIP). Then we prove that the AIT algorithm converges to the original sparse solution at a linear rate under a certain gRIP condition in the noise free case. While in the noisy case, its convergence rate is also linear until attaining a certain error bound. Moreover, as by-products, we also provide some sufficient conditions for the convergence of the AIT algorithm based on the two well-known properties, i.e., the coherence property and the restricted isometry property (RIP), respectively. It should be pointed out that such two properties are special cases of gRIP. The solid improvements on the theoretical results are demonstrated and compared with the known results. Finally, we provide a series of simulations to verify the correctness of the theoretical assertions as well as the effectiveness of the AIT algorithm.Comment: 15 pages, 5 figure

Graph Partitioning Algorithms and Applications on CyTOF Experiments

Graph partitioning is a fundamental problem in computer science and engineering with diverse applications in fields such as circuit design, network analysis, and data mining [6]. The goal of graph partitioning is to divide a given graph into multiple clusters, with the aim of minimizing certain criteria, such as the number of edges between clusters. Numerous algorithms are available for graph partitioning, ranging from simple heuristics to sophisticated optimization techniques. Due to the NP-hard nature of graph partitioning problems, finding efficient algorithms for large-scale graphs partitioning is crucial. This thesis comprehensively studies existing graph partitioning algorithms, including a recently proposed novel algorithm [1]. The performance of these algorithms is compared in terms of accuracy and timing on various datasets. The accuracy of the partitioning results is compared with the true partitioning groups by using the Normalized Mutual Information (NMI) value and the purity measurement. Additionally, these partitioning algorithms are applied to data from a CyTOF experiment, a significant field in biostatistics. The results demonstrate that the proposed algorithm generally outperforms the spectral partitioning algorithm from k-means in terms of partitioning quality, but it requires more time to converge, resulting in higher computational costs. Overall, the proposed algorithm shows promise for producing improved partitioning results, but further optimization for computational efficiency is needed. This work contributes to the understanding of graph partitioning algorithms and their performance, providing insights for future research in this area.Bachelor of Scienc

Modeling and Applied Research in Sustainable Development

We develop an algebraic polynomial model to measure and compare the sustainability in 4 countries after studying existing sustainable development index systems. The model consists of three facets of indicators: natural resources reserve, environment carrying capacity and social welfare level. We use recursive least-squares method (RLS) to determine the parameters of the fitted model and apply this model to design a sustainable development plan for Tanzania. Considering the country profile and model testing results, the plan comprises of five programs: producing clean water, generating electricity, improving transport conditions, developing tourism industry and advancing medical and health services. Finally we predict the change of each indicator in the next two decades and compare the results under natural state, finding that the sustainability of Tanzania will increase

Afghanistan and Regional Security: Implications for China

[The United States is going to start off the well-publicized withdrawal of coalition forces from Afghanistan. This will signify a major shift of US strategic designs in the region: from short-time tactical operation to long-term strategic presence. The US forces in Afghanistan will likely be further reduced in due time, but the US efforts for transforming Afghanistan into a strategic stronghold will be enhanced. Such a shift will undoubtedly bring about a major implication for China, as a neutral and stable Afghanistan is in its interest. It is thus recommended to make joint efforts with like-minded countries to prevent Afghanistan from sliding into chaos and thus jeopardizing China, and to prevent the perpetualization of US strategic presence in Afghanistan.] </p

Federated Knowledge Graph Completion via Latent Embedding Sharing and Tensor Factorization

Knowledge graphs (KGs), which consist of triples, are inherently incomplete and always require completion procedure to predict missing triples. In real-world scenarios, KGs are distributed across clients, complicating completion tasks due to privacy restrictions. Many frameworks have been proposed to address the issue of federated knowledge graph completion. However, the existing frameworks, including FedE, FedR, and FEKG, have certain limitations. = FedE poses a risk of information leakage, FedR's optimization efficacy diminishes when there is minimal overlap among relations, and FKGE suffers from computational costs and mode collapse issues. To address these issues, we propose a novel method, i.e., Federated Latent Embedding Sharing Tensor factorization (FLEST), which is a novel approach using federated tensor factorization for KG completion. FLEST decompose the embedding matrix and enables sharing of latent dictionary embeddings to lower privacy risks. Empirical results demonstrate FLEST's effectiveness and efficiency, offering a balanced solution between performance and privacy. FLEST expands the application of federated tensor factorization in KG completion tasks.Comment: Accepted by ICDM 202

Spatiotemporal Attention Enhances Lidar-Based Robot Navigation in Dynamic Environments

Foresighted robot navigation in dynamic indoor environments with cost-efficient hardware necessitates the use of a lightweight yet dependable controller. So inferring the scene dynamics from sensor readings without explicit object tracking is a pivotal aspect of foresighted navigation among pedestrians. In this paper, we introduce a spatiotemporal attention pipeline for enhanced navigation based on 2D lidar sensor readings. This pipeline is complemented by a novel lidar-state representation that emphasizes dynamic obstacles over static ones. Subsequently, the attention mechanism enables selective scene perception across both space and time, resulting in improved overall navigation performance within dynamic scenarios. We thoroughly evaluated the approach in different scenarios and simulators, finding good generalization to unseen environments. The results demonstrate outstanding performance compared to state-of-the-art methods, thereby enabling the seamless deployment of the learned controller on a real robot