Tsallis statistics enhanced logistic regression for gene expression classification

Two kinds of Tsallis statistics-enhanced sigmoid functions are introduced based on $q$-deformed exponents for $q<1$ that are free of empirically chosen cutoffs. These generalizations of the classical sigmoid enables a more flexible and robust fitting method in the context of classification problems, particularly when dealing with complex, non-linear dependencies in data. The $q$-deformed classifiers are applied to four cancer datasets, demonstrating its robustness, noise resistance, and stability. In the simulated experiments, the improved algorithm outperforms traditional methods such as Logistic Regression, SVM, and Random Forest, with significantly smaller standard deviation. On real cancer datasets, Tsallis enhanced method achieves substantial improvements, particularly outperforming Logistic Regression with traditional sigmoid function with breast cancer data. These results demonstrate the exceptional robustness, noise resistance and stability of Tsallis statistics-enhanced method, making it a reliable solution for complex and noisy data environments.