A review on clustering algorithms for large-scale data sets

Abstract

We extend the celebrated sliced inverse regression to address the challenges of decentralized data, prioritizing privacy and communication efficiency. Our approach, federated sliced inverse regression (FSIR), facilitates collaborative estimation of the sufficient dimension reduction subspace among multiple clients, solely sharing local estimates to protect sensitive datasets from exposure. To guard against potential adversary attacks, FSIR further employs diverse perturbation strategies, including a novel multivariate Gaussian mechanism that guarantees differential privacy at a low cost of statistical accuracy. Additionally, FSIR naturally incorporates a collaborative variable screening step, enabling effective handling of high-dimensional client data. Theoretical properties of FSIR are established for both low-dimensional and high-dimensional settings, supported by extensive numerical experiments and real data analysis.

Research on Trade Protectionism from the Perspective of a Community with a Shared Future for Mankind

“…First, the seemingly favourable domestic environment created by the United States only briefly provided limited job opportunities. However, once Chinese products led by Huawei are unable to enter the U.S. market, and the cost of producing similar products in the U.S. is extremely high, the increased spending will once again have a negative impact on American consumers, thus subjecting the American people to even more adverse effects [4]. As the prices of imported goods rise and costeffective foreign products like Huawei's cannot enter the country, resources cannot be effectively allocated, thereby affecting the healthy development of the domestic economy.…”