Authors: R. K. Mishra, Devender Singh, S. D. Iyer
Abstract: High-dimensional data analysis has become a central topic in modern scientific research due to rapid advances in data acquisition technologies. In many contemporary applications, the number of variables or features is extremely large compared to the number of observations, leading to unique analytical and computational challenges. Traditional statistical and machine learning techniques often fail or perform poorly in such settings due to issues like the curse of dimensionality, overfitting, and interpretability problems. This paper presents a comprehensive review of high-dimensional data analysis, focusing on theoretical foundations, dimensionality reduction techniques, feature selection methods, and modern machine learning approaches. We also discuss practical challenges, including computational complexity and data sparsity, and highlight applications in fields such as bioinformatics, image processing, finance, and social network analysis. The paper aims to provide a balanced overview that is accessible to researchers from mathematics, statistics, and engineering backgrounds, while also identifying open research directions in this rapidly evolving field.
Keywords: High-dimensional data, curse of dimensionality, dimensionality reduction, feature selection, machine learning, big data analytics
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