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Background Numerous essential algorithms and methods, including entropy-based quantitative methods, have been developed to analyze complex DNA sequences since the last decade. Exons and introns are the most notable components of DNA and their identification and prediction are always the focus of state-of-the-art research. Results In this study, we designed an integrated entropy-based analysis approach, which involves modified topological entropy calculation, genomic signal processing (GSP) method and singular value decomposition (SVD), to investigate exons and introns in DNA sequences. We optimized and implemented the topological entropy and the generalized topological entropy to calculate the complexity of DNA sequences, highlighting the characteristics of repetition sequences. By comparing digitalizing entropy values of exons and introns, we observed that they are significantly different. After we converted DNA data to numerical topological entropy value, we applied SVD method to effectively investigate exon and intron regions on a single gene sequence. Additionally, several genes across five species are used for exon predictions. Conclusions Our approach not only helps to explore the complexity of DNA sequence and its functional elements, but also provides an entropy-based GSP method to analyze exon and intron regions. Our work is feasible across different species and extendable to analyze other components in both coding and noncoding region of DNA sequences. Electronic supplementary material The online version of this article (10.1186/s12859-019-2772-y) contains supplementary material, which is available to authorized users.

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Background The prediction of long non-coding RNA (lncRNA) has attracted great attention from researchers, as more and more evidence indicate that various complex human diseases are closely related to lncRNAs. In the era of bio-med big data, in addition to the prediction of lncRNAs by biological experimental methods, many computational methods based on machine learning have been proposed to make better use of the sequence resources of lncRNAs. Results We developed the lncRNA prediction method by integrating information-entropy-based features and machine learning algorithms. We calculate generalized topological entropy and generate 6 novel features for lncRNA sequences. By employing these 6 features and other features such as open reading frame, we apply supporting vector machine, XGBoost and random forest algorithms to distinguish human lncRNAs. We compare our method with the one which has more K-mer features and results show that our method has higher area under the curve up to 99.7905%. Conclusions We develop an accurate and efficient method which has novel information entropy features to analyze and classify lncRNAs. Our method is also extendable for research on the other functional elements in DNA sequences.