Single-cell RNA sequencing technologies have enabled us to study tissue heterogeneity at cellular resolution. Fast-developing sequencing platforms like droplet-based sequencing make it feasible to parallel process thousands of single cells effectively. Although a unique molecular identifier (UMI) can remove bias from amplification noise to a certain extent, clustering for such sparse and high-dimensional large-scale discrete data remains intractable and challenging. Most existing deep learning-based clustering methods utilize the mean square error or negative binomial distribution with or without zero inflation to denoise single-cell UMI count data, which may underfit or overfit the gene expression profiles. In addition, neglecting the molecule sampling mechanism and extracting representation by simple linear dimension reduction with a hard clustering algorithm may distort data structure and lead to spurious analytical results. In this paper, we combined the deep autoencoder technique with statistical modeling and developed a novel and effective clustering method, scDMFK, for single-cell transcriptome UMI count data. ScDMFK utilizes multinomial distribution to characterize data structure and draw support from neural network to facilitate model parameter estimation. In the learned low-dimensional latent space, we proposed an adaptive fuzzy k-means algorithm with entropy regularization to perform soft clustering. Various simulation scenarios and the analysis of 10 real datasets have shown that scDMFK outperforms other state-of-the-art methods with respect to data modeling and clustering algorithms. Besides, scDMFK has excellent scalability for large-scale single-cell datasets.
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