Entropy–Rank Ratio: A Novel Entropy–Based Perspective for DNA Complexity and Classification

Shannon entropy is widely used to measure the complexity of DNA sequences but suffers from saturation effects that limit its discriminative power for long uniform segments. We introduce a novel metric, the entropy rank ratio R, which positions a target sequence within the full distribution of all possible sequences of the same length by computing the proportion of sequences that have an entropyvalue equal to or lower than that of the target. In other words, R expresses the relative position of asequence within the global entropy spectrum, assigning values close to 0 for highly ordered sequencesand close to 1 for highly disordered ones. DNA sequences are partitioned into fixed-length subsequences and non-overlapping n-mer groups; frequency vectors become ordered integer partitionsand a combinatorial framework is used to derive the complete entropy distribution. Unlike classical measures, R captures relative complexity in a scale-free manner, avoiding saturation to log2(4).We integrate R into data augmentation for convolutional neural networks by proposing ratio-guidedcropping techniques and benchmark them against random, entropy-based, and compression-basedmethods. On two independent datasets, viral genes and human genes with polynucleotide expansions, models augmented via R achieve substantial gains in classification accuracy using extremelylightweight architectures.