A double inertial embedded Ishikawa algorithm for two nonexpansive mappings applies to breast cancer detection

Breast cancer remains a major health challenge worldwide, with early detection being crucial for enhancing treatment outcomes and prolonging life. This study introduces innovative machine learning techniques aimed at advancing breast cancer screening models. Specifically, we propose a double inertial embedded Ishikawa algorithm that enhances the traditional Ishikawa algorithm with a double inertial technique for two distinct nonexpansive mappings. We establish a weak convergence theorem in Hilbert spaces, utilizing relaxed real number extrapolation parameters. An example in an infinite-dimensional space corroborates our theoretical findings. The practical application of this algorithm is demonstrated using a real dataset from Phayao Hospital in Northern Thailand, supplemented by data from the UCI website, within an Extreme Learning Machine framework for efficient prediction. Achieving an accuracy of 88.57\%, our algorithm outperforms the well-known FISTA algorithms, highlighting its potential for improving breast cancer diagnostic protocols and outcomes.