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However, dropout events introduces computational challenges and the lack of transparency in methods such as graph neural networks limits their interpretability. This study aimed to decipher disease progression-related spatial domains in breast cancer spatial transcriptomics by developing the three graph regularized non-negative matrix factorization (TGR-NMF). A unitization strategy was proposed to mitigate the impact of dropout events on the computational process, enabling utilization of the complete gene expression count data. By integrating one gene expression neighbor topology and two spatial position neighbor topologies, TGR-NMF was developed for constructing an interpretable low-dimensional representation of spatial transcriptomic data. The progressive lesion area that can reveal the progression of breast cancer was uncovered through heterogeneity analysis. Moreover, several related pathogenic genes and signal pathways on this area were identified by using gene enrichment and cell communication analysis.<\/jats:p>","DOI":"10.1093\/bib\/bbae707","type":"journal-article","created":{"date-parts":[[2025,1,9]],"date-time":"2025-01-09T05:22:21Z","timestamp":1736400141000},"source":"Crossref","is-referenced-by-count":4,"title":["Deciphering progressive lesion areas in breast cancer spatial transcriptomics via TGR-NMF"],"prefix":"10.1093","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3288-4395","authenticated-orcid":false,"given":"Juntao","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Henan Normal University , 46 Jianshe East Road, 453007 Xinxiang,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-8606-798X","authenticated-orcid":false,"given":"Shan","family":"Xiang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Henan Normal University , 46 Jianshe East Road, 453007 Xinxiang,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4200-7502","authenticated-orcid":false,"given":"Dongqing","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Life Sciences and Biotechnology, Shanghai Jiao Tong University , 800 Dongchuan Road, 200240 Shanghai,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2025,1,8]]},"reference":[{"key":"2025010905220581600_ref1","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1186\/s40659-017-0140-9","article-title":"Awareness and current knowledge of breast cancer","volume":"50","author":"Akram","year":"2017","journal-title":"Biol Res"},{"key":"2025010905220581600_ref2","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1186\/s13073-024-01283-x","article-title":"Unsupervised spatially embedded deep representation of spatial transcriptomics","volume":"16","author":"Xu","year":"2024","journal-title":"Genome Med"},{"key":"2025010905220581600_ref3","doi-asserted-by":"publisher","first-page":"23383","DOI":"10.1038\/srep23383","article-title":"Quantification of HER2 heterogeneity in breast cancer-implications for identification of sub-dominant clones for personalised treatment","volume":"6","author":"Buckley","year":"2016","journal-title":"Sci Rep"},{"key":"2025010905220581600_ref4","doi-asserted-by":"crossref","first-page":"bbad500","DOI":"10.1093\/bib\/bbad500","article-title":"stAA: adversarial graph autoencoder for spatial clustering task of spatially resolved transcriptomics","volume":"25","author":"Fang","year":"2024","journal-title":"Brief Bioinform"},{"key":"2025010905220581600_ref5","doi-asserted-by":"publisher","first-page":"1342","DOI":"10.1038\/s41592-021-01255-8","article-title":"SpaGCN: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network","volume":"18","author":"Hu","year":"2021","journal-title":"Nat Methods"},{"key":"2025010905220581600_ref6","doi-asserted-by":"publisher","first-page":"360","DOI":"10.1038\/nmeth.2892","article-title":"Single-cell in situ RNA profiling by sequential hybridization","volume":"11","author":"Lubeck","year":"2014","journal-title":"Nat Methods"},{"key":"2025010905220581600_ref7","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1038\/s41586-019-1049-y","article-title":"Transcriptome-scale super-resolved imaging in tissues by RNA seqFISH","volume":"568","author":"Eng","year":"2019","journal-title":"Eur J Hum Genet"},{"key":"2025010905220581600_ref8","doi-asserted-by":"publisher","DOI":"10.1126\/science.aaa6090","article-title":"RNA imaging. 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