Alzheimer's disease (AD) is a progressive and irreversible neurodegenerative disorder. Its etiology may be associated with genetic, environmental, and lifestyle factors. With the advancement of technology, the integration of genomics, transcriptomics, and imaging data related to AD allows simultaneous exploration of molecular information at different levels and their interaction within the organism. This paper proposes a hypergraph-regularized joint deep semi-non-negative matrix factorization (HR-JDSNMF) algorithm to integrate positron emission tomography (PET), single-nucleotide polymorphism (SNP), and gene expression data for AD. The method employs matrix factorization techniques to nonlinearly decompose the original data at multiple layers, extracting deep features from different omics data, and utilizes hypergraph mining to uncover high-order correlations among the three types of data. Experimental results demonstrate that this approach outperforms several matrix factorization-based algorithms and effectively identifies multi-omics biomarkers for AD. Additionally, single-cell RNA sequencing (scRNA-seq) data for AD were collected, and genes within significant modules were used to categorize different types of cell clusters into high and low-risk cell groups. Finally, the study extensively explores the differences in differentiation and communication between these two cell types. The multi-omics biomarkers unearthed in this study can serve as valuable references for the clinical diagnosis and drug target discovery for AD. The realization of the algorithm in this paper code is available at https://github.com/ShubingKong/HR-JDSNMF .