# Consensus Guided Multi-View Unsupervised Feature Selection with Hybrid Regularization
###### Abstract  
Multi-source heterogeneous data has been widely adopted in developing artificial intelligence systems in recent years. In real-world scenarios, raw multi-source data are generally unlabeled and inherently contain multi-view noise and feature redundancy, leading to extensive research on unsupervised multi-view feature selection. However, existing approaches mainly utilize the local adjacency relationships and the \(L_{2,1}\)-norm to guide the feature selection process, which may lead to instability in performance. To address these problems, this paper proposes a Consensus Guided Multi-view Unsupervised Feature Selection with Hybrid Regularization (CGMvFS). Specifically, CGMvFS integrates multiple view-specific basic partitions into a unified consensus matrix, which is constructed to guide the feature selection process by preserving comprehensive pairwise constraints across diverse views. A hybrid regularization strategy incorporating the \(L_{2,1}\)-norm and the Frobenius norm is introduced into the feature selection objective function, which not only promotes feature sparsity but also effectively prevents overfitting, thereby improving the stability of the model. Extensive empirical evaluations demonstrate that CGMVFS outperforms state-of-the-art comparison approaches across diverse multi-view datasets. unsupervised feature selection; consensus clustering; heterogeneous data +
Footnote †: journal: Medicalparadigm, operating without labeled data, employs intrinsic data structures to identify important features, rendering it particularly prevalent in real-world applications where annotated multi-source heterogeneous data are often unavailable. In general, this paper focuses on the research on unsupervised multi-view feature selection. In unsupervised learning, feature selection algorithms' performance is highly contingent on the design paradigms of guidance information. Current methods showcase diverse innovations in guidance mechanisms, which can be broadly grouped into two principal paradigms according to their underlying strategies: (1) Graph-structured regularization approaches; representative works include the multi-view feature selection framework proposed by [PERSON] et al. [14], which integrated adaptive graph similarity learning with view weight co-optimization. Additionally, [PERSON] et al. [15] achieved cross-view complementary information mining by constructing multi-graph orthogonal constraints alongside clustering consistency objective functions. (2) Non-negative orthogonal decomposition frameworks: notable implementations encompass [PERSON] et al. 's [16] extended weighted non-negative matrix factorization (WNMF) architecture, which utilized a complementary-consensus dual-module collaborative mechanism for feature selection. Another innovative study [17; 18; 19] introduced shared subspace embedding techniques into multi-view learning, thereby establishing low-dimensional representations for high-dimensional data. Despite methodological progress, persistent limitations warrant attention. Current methods mainly focus on the local adjacency relationship of samples, while the global cluster structures between samples can be further used as pseudo-constraints to guide the feature selection process. In addition, only applying \(L_{2,1}\)-norm regularization can ensure sparsity in feature selection, but it may lead to overfitting problems. To address these problems, this paper presents a Consensus Guided Multi-view Unsupervised Feature Selection with Hybrid Regularization (CGMvFS). Specifically, CGMvFS employs consensus clustering across individual views to capture view-specific intrinsic data structures. The resulting view-specific co-association matrices are aggregated to construct a unified co-association matrix that establishes comprehensive pairwise constraints across all views. A novel hybrid-regularized objective function is then formulated to simultaneously learn view-specific feature projection matrices while preserving the cross-view pairwise constraints.