Data and dimensionality reduction are essential in data analysis and system modeling. As data sets grow in size and complexity, reduction techniques become necessary. Data reduction focuses on reducing the number of data points, revealing underlying structures through clustering. Dimensionality reduction reduces the number of features, often transforming data into a lower-dimensional space. These processes are guided by optimization criteria and can be classified into filters and wrappers. Filters evaluate features based on statistical properties, while wrappers assess their effectiveness in classification tasks. Dimensionality reduction has been a long-standing challenge in computer science, with techniques like principal component analysis and Fisher analysis being widely used. Recent advancements include biologically-inspired optimization methods, such as genetic algorithms and particle swarm optimization, which help in finding optimal feature subsets. The study explores information granularity and granular computing, emphasizing the role of clustering and fuzzy clustering in data reduction. It also discusses linear and nonlinear feature transformations, including PCA, and the use of biologically-inspired optimization in feature selection. The paper outlines a general roadmap for dimensionality reduction, highlighting the importance of optimization criteria and formal frameworks of information granules. It covers data reduction, dimensionality reduction, and co-joint data and dimensionality reduction, discussing biclustering as a key technique. The study emphasizes the need for effective and computationally feasible algorithms to combat the curse of dimensionality, ensuring that data analysis remains meaningful and efficient.Data and dimensionality reduction are essential in data analysis and system modeling. As data sets grow in size and complexity, reduction techniques become necessary. Data reduction focuses on reducing the number of data points, revealing underlying structures through clustering. Dimensionality reduction reduces the number of features, often transforming data into a lower-dimensional space. These processes are guided by optimization criteria and can be classified into filters and wrappers. Filters evaluate features based on statistical properties, while wrappers assess their effectiveness in classification tasks. Dimensionality reduction has been a long-standing challenge in computer science, with techniques like principal component analysis and Fisher analysis being widely used. Recent advancements include biologically-inspired optimization methods, such as genetic algorithms and particle swarm optimization, which help in finding optimal feature subsets. The study explores information granularity and granular computing, emphasizing the role of clustering and fuzzy clustering in data reduction. It also discusses linear and nonlinear feature transformations, including PCA, and the use of biologically-inspired optimization in feature selection. The paper outlines a general roadmap for dimensionality reduction, highlighting the importance of optimization criteria and formal frameworks of information granules. It covers data reduction, dimensionality reduction, and co-joint data and dimensionality reduction, discussing biclustering as a key technique. The study emphasizes the need for effective and computationally feasible algorithms to combat the curse of dimensionality, ensuring that data analysis remains meaningful and efficient.