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The random feature method (RFM) has demonstrated great potential in bridging traditional numerical methods and machine learning techniques for solving partial differential equations (PDEs). It retains the advantages of mesh-free approaches…

We study the Frank-Wolfe algorithm for constrained optimization problems with relatively smooth objectives. Building upon our previous work, we propose a fully adaptive variant of the Frank-Wolfe method that dynamically adjusts the step…

We study the problem of evaluating the excess risk of large-scale empirical risk minimization under the square loss. Leveraging the idea of wild refitting and resampling, we assume only black-box access to the training algorithm and develop…

Majorization-minimization (MM) is a family of optimization methods that iteratively reduce a loss by minimizing a locally-tight upper bound, called a majorizer. Traditionally, majorizers were derived by hand, and MM was only applicable to a…

An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…

This letter proposes a novel adaptive reduced-rank filtering scheme based on joint iterative optimization of adaptive filters. The novel scheme consists of a joint iterative optimization of a bank of full-rank adaptive filters that forms…

Fluorescence Molecular Tomography (FMT) is a widely used non-invasive optical imaging technology in biomedical research. It usually faces significant accuracy challenges in depth reconstruction, and conventional iterative methods struggle…

Federated clustering, an integral aspect of federated machine learning, enables multiple data sources to collaboratively cluster their data, maintaining decentralization and preserving privacy. In this paper, we introduce a novel federated…

This paper concerns iterative reconstruction for low-dose and few-view CT by minimizing a data-fidelity term regularized with the Total Variation (TV) penalty. We propose a very fast iterative algorithm to solve this problem. The algorithm…

This paper presents an original method of fuzzy approximate reasoning that can open a new direction of research in the uncertainty inference of Artificial Intelligence(AI) and Computational Intelligence(CI). Fuzzy modus ponens (FMP) and…

G-images refer to image data defined on irregular graph domains. This work elaborates a similarity-preserving Fuzzy C-Means (FCM) algorithm for G-image segmentation and aims to develop techniques and tools for segmenting G-images. To…

Inverse problems of partial differential equations are ubiquitous across various scientific disciplines and can be formulated as statistical inference problems using Bayes' theorem. To address large-scale problems, it is crucial to develop…

Nonnegative matrix factorization (NMF) has been widely used to dimensionality reduction in machine learning. However, the traditional NMF does not properly handle outliers, so that it is sensitive to noise. In order to improve the…

Model merging aims to combine multiple fine-tuned models into a single set of weights that performs well across all source tasks. While prior work has shown that merging can approximate the performance of individual fine-tuned models for…

Many applications of generalised linear models (GLMs) can be improved by applying constraints that impose assumptions on the associations or improve consistency of the estimators. Yet, there are still barriers to the implementation and…

This paper proposes Inverse Gram Matrix (IGM) methods to prioritize the Pairwise Reciprocal Matrix (PRM) in the Analytic Hierarchy Process. The IGM methods include Pseudo-IGM, Normalized-IGM, and Lagrange-IGM. Interestingly, the proposed…

Image downscaling and upscaling are two basic rescaling operations. Once the image is downscaled, it is difficult to be reconstructed via upscaling due to the loss of information. To make these two processes more compatible and improve the…

In this paper we present a fast and efficient method for the reconstruction of Magnetic Resonance Images (MRI) from severely under-sampled data. From the Compressed Sensing theory we have mathematically modeled the problem as a constrained…

Unimodular/Phase only sequence having impulse like aperiodic auto-correlation function plays a central role in the applications of RADAR, SONAR, Cryptography, and Wireless (CDMA) Communication Systems. In this paper, we propose a fast…

This paper proposes a reduced-rank scheme for adaptive beamforming based on the constrained joint iterative optimization of filters. We employ this scheme to devise two novel reduced-rank adaptive algorithms according to the constant…