Machine learning has become an important research field in genetics and molecular biology. Survival analysis using machine learning can provide an important computed-aid clinical research scheme for evaluating tumor treatment options. However, the genomic features are high-dimensional, which limits the prediction performance of the survival learning model. Therefore, in this paper, we propose an improved survival prediction model using a deep forest and self-supervised learning. It uses a deep survival forest to perform adaptive learning of high-dimensional genomic data and ensure robustness. In addition, self-supervised learning, as a semi-supervised learning style, is designed to utilize unlabeled samples to improve model performance. Based on four cancer datasets from The Cancer Genome Atlas (TCGA), the experimental results show that our proposed method outperforms four advanced survival analysis methods in terms of the C-index and brier score. The developed prediction model will help doctors rethink patient characteristics’ relevance to survival time and personalize treatment decisions.

In recent years, tumor classification based on the gene expression omnibus has become a continuous attention field in the area of bioinformatics. Integration machine learning techniques are an efficient methods to solve these problems. Generally, in order to obtain good performance in the supervised learning tasks, a large number of labelled samples will be required. However, in many cases, only a few labelled samples and abundant unlabelled samples exist in the training database. The process of labelling these unlabelled samples manually is difficult and expensive. Therefore, semi-supervised learning approaches have been proposed to utilize unlabelled samples to improve the performance of a model. However, noisy samples decrease the robustness of model in semi-supervised learning. We wish training style that samples can be implemented to train by from high- to low-confidence, self-training can meet this requirement, and the deep forest approach with the hyper-parameter settings used in this work can obtain good accuracy. Therefore, in this paper, we present a novel semi-supervised learning approach with a deep forest model to increase the performance of tumor classification, which employs unlabelled samples and minimizes the cost; that is, a updated unlabelled sample mechanism is investigated to expand the number of high-confidence pseudo-labelled samples. Multiple real-world experiments indicate that our proposed approach can obtain results up 0.96 accuracy and F1-Score, and 0.9798 AUCs.

Chebyshev criterion is a powerful tool in the study of limit cycle bifurcations in dynamical systems based on Abelian integrals, but it is difficult when the Abelian integrals involve parameters. In this paper, we consider the Abelian integrals on the periodic annuli of a Hamiltonian with one parameter, arising from the generalized Liénard system, and identify the parameter values such that the Abelian integrals have Chebyshev property. In particular, the bounds on the number of zeros of the Abelian integrals are derived for different parameter intervals. The main mathematical tools are transformations and polynomial boundary theory, which overcome the difficulties in symbolic computations and analysis, arising from large parametric-semi-algebraic systems.