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A Hilbert space operator T belongs to * -class

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Background Breast cancer is one of the most common cancers in women. It is necessary to classify breast cancer subtypes because different subtypes need specific treatment. Identifying biomarkers and classifying breast cancer subtypes is essential for developing appropriate treatment methods for patients. MiRNAs can be easily detected in tumor biopsy and play an inhibitory or promoting role in breast cancer, which are considered promising biomarkers for distinguishing subtypes. Results A new method combing ensemble regularized multinomial logistic regression and Cox regression was proposed for identifying miRNA biomarkers in breast cancer. After adopting stratified sampling and bootstrap sampling, the most suitable sample subset for miRNA feature screening was determined via ensemble 100 regularized multinomial logistic regression models. 124 miRNAs that participated in the classification of at least 3 subtypes and appeared at least 50 times in 100 integrations were screened as features. 22 miRNAs from the proposed feature set were further identified as the biomarkers for breast cancer by using Cox regression based on survival analysis. The accuracy of 5 methods on the proposed feature set was significantly higher than on the other two feature sets. The results of 7 biological analyses illustrated the rationality of the identified biomarkers. Conclusions The screened features can better distinguish breast cancer subtypes. Notably, the genes and proteins related to the proposed 22 miRNAs were considered oncogenes or inhibitors of breast cancer. 9 of the 22 miRNAs have been proved to be markers of breast cancer. Therefore, our results can be considered in future related research.