‎The high-dimensional data analysis using classical regression approaches is not applicable, and the consequences may need to be more accurate.
This study tried to analyze such data by introducing new and powerful approaches such as support vector regression, functional regression, LASSO and ridge regression. On this subject, by investigating two high-dimensional data sets  (riboflavin and simulated data sets) using the suggested approaches, it is progressed to derive the most efficient model based on three criteria (correlation squared, mean squared error and mean absolute error percentage deviation) according to the type of data.

‎Modeling and efficient estimation of the trend function is of great importance in the estimation of variogram and prediction of spatial data. In this article, the support vector regression method is used to model the trend function. Then the data is de-trended and the estimation of variogram and prediction is done. On a real data set, the prediction results obtained from the proposed method have been compared with Spline and kriging prediction methods through cross-validation.  The criterion for choosing the appropriate method for prediction is to minimize the root mean square of the error. The prediction results for several positions with known values were left out of the data set (for some reason) and were obtained for new positions. The results show the high accuracy of prediction (for all positions and elimination positions) with the proposed method compared to kriging and spline.

‎With the advancement of biological sciences and modern technologies‎, ‎high-dimensional data‎, ‎in which the number of independent variables exceeds the number of observations‎, ‎have become increasingly prevalent in various fields‎. ‎Gene expression data associated with riboflavin or vitamin $B_2$ production represent an important example of such datasets‎. ‎Riboflavin‎, ‎as an essential micronutrient‎, ‎plays a crucial role in metabolic reactions and vital biological processes through its coenzyme forms‎, ‎$mathit{FAD}$ and $mathit{FMN}$‎. ‎Therefore‎, ‎the biological production of this vitamin using microorganisms as a sustainable and economical approach has gained considerable importance in the food‎, ‎pharmaceutical‎, ‎and animal feed industries‎. ‎The presence of a large number of variables and multicollinearity among them presents major obstacles to classical regression methods‎. ‎Consequently‎, ‎regularisation and dimensionality reduction approaches‎, ‎including Ridge regression‎, ‎Lasso‎, ‎Elastic Net and Partial Least Squares (PLS)‎, ‎have been developed to improve model stability and predictive performance‎. ‎Moreover‎, ‎machine learning methods such as Support Vector Machines (SVM) and Support Vector Regression (SVR) have been widely applied in high-dimensional data analysis due to their ability to capture complex and nonlinear relationships‎. ‎In this study‎, ‎regression and machine learning methods‎, ‎including Ridge‎, ‎Lasso‎, ‎Elastic Net‎, ‎PLS‎, ‎SVM‎, ‎and SVR‎, ‎are implemented and compared using real riboflavin production data and simulated datasets to evaluate their performance in handling multicollinearity‎, ‎dimensionality reduction‎, ‎and prediction of production levels.}