CONDEN-FI: Consistency and Diversity Learning-based Multi-View Unsupervised Feature and In-stance Co-Selection

The objective of multi-view unsupervised feature and instance co-selection is to simultaneously iden-tify the most representative features and samples from multi-view unlabeled data, which aids in mit-igating the curse of dimensionality and reducing instance size to improve the performance of down-stream tasks. However, existing methods treat feature selection and instance selection as two separate processes, failing to leverage the potential interactions between the feature and instance spaces. Addi-tionally, previous co-selection methods for multi-view data require concatenating different views, which overlooks the consistent information among them. In this paper, we propose a CONsistency and DivErsity learNing-based multi-view unsupervised Feature and Instance co-selection (CONDEN-FI) to address the above-mentioned issues. Specifically, CONDEN-FI reconstructs mul-ti-view data from both the sample and feature spaces to learn representations that are consistent across views and specific to each view, enabling the simultaneous selection of the most important features and instances. Moreover, CONDEN-FI adaptively learns a view-consensus similarity graph to help select both dissimilar and similar samples in the reconstructed data space, leading to a more diverse selection of instances. An efficient algorithm is developed to solve the resultant optimization problem, and the comprehensive experimental results on real-world datasets demonstrate that CONDEN-FI is effective compared to state-of-the-art methods.

C$^{2}$IMUFS: Complementary and Consensus Learning-based Incomplete Multi-view Unsupervised Feature Selection

Multi-view unsupervised feature selection (MUFS) has been demonstrated as an effective technique to reduce the dimensionality of multi-view unlabeled data. The existing methods assume that all of views are complete. However, multi-view data are usually incomplete, i.e., a part of instances are presented on some views but not all views. Besides, learning the complete similarity graph, as an important promising technology in existing MUFS methods, cannot achieve due to the missing views. In this paper, we propose a complementary and consensus learning-based incomplete multi-view unsupervised feature selection method (C$^{2}$IMUFS) to address the aforementioned issues. Concretely, C$^{2}$IMUFS integrates feature selection into an extended weighted non-negative matrix factorization model equipped with adaptive learning of view-weights and a sparse $\ell_{2,p}$-norm, which can offer better adaptability and flexibility. By the sparse linear combinations of multiple similarity matrices derived from different views, a complementary learning-guided similarity matrix reconstruction model is presented to obtain the complete similarity graph in each view. Furthermore, C$^{2}$IMUFS learns a consensus clustering indicator matrix across different views and embeds it into a spectral graph term to preserve the local geometric structure. Comprehensive experimental results on real-world datasets demonstrate the effectiveness of C$^{2}$IMUFS compared with state-of-the-art methods.