With a view to overcoming a few shortcomings resulting from the kernel-based SVM models, these kernel-free support vector machine (SVM) models are newly promoted and researched. With the aim of deeply enhancing the classification accuracy of present kernel-free quadratic surface support vector machine (QSSVM) models while avoiding computational complexity, an emerging kernel-free ν-fuzzy reduced QSSVM with L1 norm regularization model is proposed. The model has well-developed sparsity to avoid computational complexity and overfitting and has been simplified as these standard linear models on condition that the data points are (nearly) linearly separable. Computational tests are implemented on several public benchmark datasets for the purpose of showing the better performance of the presented model compared with a few known binary classification models. Similarly, the numerical consequences support the more elevated training effectiveness of the presented model in comparison with those of other kernel-free SVM models. What`s more, the presented model is smoothly employed in lung cancer subtype diagnosis with good performance, by using the gene expression RNAseq-based lung cancer subtype (LUAD/LUSC) dataset in the TCGA database
