The analysis of cancer data from multi-omics can effectively promote cancer research. The main focus of this article is to cluster cancer samples and identify feature genes to reveal the correlation between cancers and genes, with the primary approach being the analysis of multi-view cancer omics data. Our proposed solution, the Multi-View Enhanced Tensor Nuclear Norm and Local Constraint (MVET-LC) model, aims to utilize the consistency and complementarity of omics data to support biological research. The model is designed to maximize the utilization of multi-view data and incorporates a nuclear norm and local constraint to achieve this goal. The first step involves introducing the concept of enhanced partial sum of tensor nuclear norm, which significantly enhances the flexibility of the tensor nuclear norm. After that, we incorporate total variation regularization into the MVET-LC model to further augment its performance. It enables MVET-LC to make use of the relationship between tensor data structures and sparse data while paying attention to the feature details of the tensor data. To tackle the iterative optimization problem of MVET-LC, the alternating direction method of multipliers is utilized. Through experimental validation, it is demonstrated that our proposed model outperforms other comparison models.

中文翻译：

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用于癌症聚类和特征基因选择的多视图增强张量核范数和局部约束模型。

多组学癌症数据分析可以有效促进癌症研究。本文的主要内容是对癌症样本进行聚类并识别特征基因，以揭示癌症与基因之间的相关性，主要方法是多视图癌症组学数​​据的分析。我们提出的解决方案，多视图增强张量核范数和局部约束（MVET-LC）模型，旨在利用组学数据的一致性和互补性来支持生物学研究。该模型旨在最大限度地利用多视图数据，并结合核规范和局部约束来实现这一目标。第一步引入张量核范数增强部分和的概念，这显着增强了张量核范数的灵活性。之后，我们将全变分正则化纳入 MVET-LC 模型中，以进一步增强其性能。它使得MVET-LC能够利用张量数据结构和稀疏数据之间的关系，同时关注张量数据的特征细节。为了解决 MVET-LC 的迭代优化问题，采用了乘法器交替方向法。通过实验验证，证明我们提出的模型优于其他比较模型。