Federated Multi-View Clustering has gained increasing attention for its ability to discover complementary clustering structures of distributed multi-view data while preserving data privacy. However, real-world clients often only have access to partial views, and the view incompleteness poses great challenges to federated multi-view feature fusion to exploit consistent and complementary information. Moreover, efficiency is highly expected in federated scenarios due to the limited resources of each client. To alleviate these issues, we propose Federated Incomplete Multi-View Clustering with Tensorized Low-Rank Constraint (FIMVC-TLRC), which incorporates anchors to improve efficiency and is able to address prevalent view incompleteness issue in federated scenarios. FIMVC-TLRC aligns the local anchor graphs and employs a tensorized low-rank constraint based on the tensor Schatten p-norm to enforce the consistency of the data representations learned by each client. Besides, a federated optimization framework is developed to jointly optimize the construction and alignment of anchor graphs, thus enabling collaborative and privacy-preserving training. Experimental results on multiple datasets demonstrate its effectiveness.

Marginal Fisher Analysis (MFA) is a classical dimensionality reduction (DR) method that leverages dual graphs to capture intra-class compactness and inter-class separability. However, MFA’s reliance on high-quality labels limits its practical application. For another, existing unsupervised DR methods neglect data’s local manifold relationship, resulting in poor discriminativeness. To address these limitations, we propose a novel DR method named Discriminative Graph Embedding Framework (DGEF) via Label-Free Marginal Fisher Analysis. Our approach uses the adjacency matrix and cluster indicator matrix derived from centerless K-Means to construct intrinsic graph and penalty graph, which preserve the local manifold structure of the data. Additionally, we have derived the convertible relationship between centerless K-Means and Manifold learning and unified them within a graph embedding framework. By adopting the intrinsic graph and penalty graph, our DGEF avoids centroid initialization and ensures robustness and discriminativeness. This method achieves dimensionality reduction adaptively without relying on labeled data. Extensive experiments on benchmark datasets show that our approach outperforms conventional methods in clustering performance.

Locality Preserving Projections (LPP) aims to find a projection matrix to map the high-dimensional data into a low-dimensional subspace while preserving the local manifold structure, which is a classical unsupervised subspace learning method. However, the lack of label guidance makes LPP not able to fully exploit the discriminative information of the data. To solve the problem, we propose a Self-Guided Discriminative LPP algorithm employing pseudo labels learned by K-Means to guide the subspace learning. In this way, it facilitates the discovery of discriminative cluster information while preserving inherent manifold structure. Besides, considering K-Means' sensitivity to selection of cluster centroids, we introduce a centerless K-Means method to improve robustness by eliminating the need of centroid initialization. We also discuss the internal relationship between K-Means and LPP, and prove that K-Means can be written in the form of LPP under certain conditions. Experiments on seven benchmark datasets demonstrate that our method greatly improves the clustering performance.

K-Means clustering is a classical and effective unsupervised learning method attributed to its simplicity and efficiency. However, it faces notable challenges, including sensitivity to random initial centroid selection, a limited ability to discover the intrinsic manifold structures within nonlinear datasets, and difficulty in achieving balanced clustering in practical scenarios. To overcome these weaknesses, we introduce a novel framework for K-Means that leverages manifold learning. This approach eliminates the need for centroid calculation and utilizes a cluster indicator matrix to align the manifold structures, thereby enhancing clustering accuracy. Beyond the traditional Euclidean distance, our model incorporates Gaussian kernel distance, K-nearest neighbor distance, and low-pass filtering distance to effectively manage data that is not linearly separable. Furthermore, we introduce a balanced regularizer to achieve balanced clustering results. The detailed experimental results demonstrate the efficacy of our proposed methodology.

Linear Discriminant Analysis (LDA) is a classical supervised dimensionality reduction algorithm. However, LDA focuses more on global structure and overly depends on reliable data labels. For data with outliers and nonlinear structures, LDA cannot effectively capture the true structure of the data. Moreover, the subspace dimension learned by LDA must be smaller than cluster number, which limits its practical applications. To address these issues, we propose a novel unsupervised LDA method that combines centerless K-means and LDA. This method eliminates the need to calculate cluster centroids and improves model robustness. By fusing centerless K-means and LDA into a unified framework and deducing the connection between K-means and manifold learning, this method captures the local manifold structure and discriminative structure. Additionally, the dimensionality of the subspace is not restricted. This method not only overcomes the limitations of traditional LDA but also improves the model’s adaptability to complex data. Extensive experiments on seven datasets demonstrate the effectiveness of the proposed method.

Recent advances in cancer immunotherapy have highlighted the potential of neoantigen-based vaccines. However, the design of such vaccines is hindered by the possibility of weak binding affinity between the peptides and the patient's specific human leukocyte antigen (HLA) alleles, which may not elicit a robust adaptive immune response. Triggering cross-immunity by utilizing peptide mutations that have enhanced binding affinity to target HLA molecules, while preserving their homology with the original one, can be a promising avenue for neoantigen vaccine design. In this study, we introduced UltraMutate, a novel algorithm that combines Reinforcement Learning and Monte Carlo Tree Search, which identifies peptide mutations that not only exhibit enhanced binding affinities to target HLA molecules but also retains a high degree of homology with the original neoantigen. UltraMutate outperformed existing state-of-the-art methods in identifying affinity-enhancing mutations in an independent test set consisting of 3660 peptide-HLA pairs. UltraMutate further showed its applicability in the design of peptide vaccines for Human Papillomavirus and Human Cytomegalovirus, demonstrating its potential as a promising tool in the advancement of personalized immunotherapy.