Sparse-regularized symmetric nonnegative matrix factorization for adaptive sequence encoding

Yanfen Lin

doi:10.1016/j.engappai.2026.115019

Sparse-regularized symmetric nonnegative matrix factorization for adaptive sequence encoding

2026-05-15

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DOI：10.1016/j.engappai.2026.115019

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Sequence encoding has been a crucial component in many engineering applications, such as biological sequence classification. However, adaptive learning of compact representations for symbolic sequences, especially in scenarios with limited data, remains a challenging problem. In this paper, an HMM (hidden Markov model) based encoder is proposed, which is an adaptive learning framework centered on sparse factorization of the co-occurrence matrices for sequences. We propose a spare-regularized symmetric NMF (nonnegative matrix factorization) algorithm as the HMM learner, with the regularization strength adaptively estimated according to the symbolic distribution of different sequence sets. A rigorous convergence proof is provided, and a new model-reduction approach is proposed to automatically determine the optimal number of HMM states, based on the state distribution in sequence representations. The proposed method is experimentally evaluated on commonly used sequence sets from three real-world domains, with results demonstrating its effectiveness and efficiency compared with various methods including neural network-based encoders.

Keywords:

HMM

sequence encoding

sparse regularization

nonnegative matrix factorization

adaptive learning

Sparse-regularized symmetric nonnegative matrix factorization for adaptive sequence encoding

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