This survey paper provides a comprehensive analysis of big data algorithms in recommendation systems, addressing the lack of depth and precision in existing literature. It proposes a two-pronged approach: a thorough analysis of current algorithms and a novel, hierarchical taxonomy for precise categorization. The taxonomy is based on a tri-level hierarchy, starting with the methodology category and narrowing down to specific techniques. Such a framework allows for a structured and comprehensive classification of algorithms, assisting researchers in understanding the interrelationships among diverse algorithms and techniques. Covering a wide range of algorithms, this taxonomy first categorizes algorithms into four main analysis types: user and item similarity based methods, hybrid and combined approaches, deep learning and algorithmic methods, and mathematical modeling methods, with further subdivisions into sub-categories and techniques. The paper incorporates both empirical and experimental evaluations to differentiate between the techniques. The empirical evaluation ranks the techniques based on four criteria. The experimental assessments rank the algorithms that belong to the same category, sub-category, technique, and sub-technique. Also, the paper illuminates the future prospects of big data techniques in recommendation systems, underscoring potential advancements and opportunities for further research in this fields.