  DNA sequences encode vital genetic and biological information, yet these
unfixed-length sequences cannot serve as the input of common data mining
algorithms. Hence, various representation schemes have been developed to
transform DNA sequences into fixed-length numerical representations. However,
these schemes face difficulties in learning high-quality representations due to
the complexity and sparsity of DNA data. Additionally, DNA sequences are
inherently noisy because of mutations. While several schemes have been proposed
for their effectiveness, they often lack semantic structure, making it
difficult for biologists to validate and leverage the results. To address these
challenges, we propose \textbf{Dy-mer}, an explainable and robust DNA
representation scheme based on sparse recovery. Leveraging the underlying
semantic structure of DNA, we modify the traditional sparse recovery to capture
recurring patterns indicative of biological functions by representing frequent
K-mers as basis vectors and reconstructing each DNA sequence through simple
concatenation. Experimental results demonstrate that \textbf{Dy-mer} achieves
state-of-the-art performance in DNA promoter classification, yielding a
remarkable \textbf{13\%} increase in accuracy. Moreover, its inherent
explainability facilitates DNA clustering and motif detection, enhancing its
utility in biological research.
