Multiview Tensor Spectral Clustering via Co-Regularization.

Graph-based multi-view clustering encodes multi-view data into sample affinities to find consensus representation, effectively overcoming heterogeneity across different views. However, traditional affinity measures tend to collapse as the feature dimension expands, posing challenges in estimating a unified alignment that reveals both cross-view and inner relationships. To tackle this challenge, we propose to achieve multi-view uniform clustering via consensus representation co-regularization. First, the sample affinities are encoded by both popular dyadic affinity and recent high-order affinities to comprehensively characterize spatial distributions of the HDLSS data. Second, a fused consensus representation is learned through aligning the multi-view low-dimensional representation by co-regularization. The learning of the fused representation is modeled by a high-order eigenvalue problem within manifold space to preserve the intrinsic connections and complementary correlations of original data. A numerical scheme via manifold minimization is designed to solve the high-order eigenvalue problem efficaciously. Experiments on eight HDLSS datasets demonstrate the effectiveness of our proposed method in comparison with the recent thirteen benchmark methods.

Design and optimization of an innovative lanthanum/chitosan bead for efficient phosphate removal and study of process performance and mechanisms.

Presence of excessive phosphorus in surface waters is the main cause for eutrophication. In this study, a lanthanum/chitosan (La/CS) bead was prepared so as to provide a cost-effective solution to the problem. The optimization of bead for the treatment was conducted, leading to the optimal condition: 30 wt% La/CS bead at a dosage of 30 g L-1 (wet weight). A higher phosphate removal around 90% was obtained in pH 4.0-10.0. Most of uptake occurred in the first 2 h and the equilibrium was reached in about 6 h. Coexisting ions of Cl-, [Formula: see text] , [Formula: see text] , and [Formula: see text] had negligible effects on the treatment, while the presence of F- reduced the uptake by 10.39%. The maximum adsorption capacity of 261.1 mg-PO4·g-1 (dried weight) at pH 5.0 was achieved, which is much better than many reported La-based adsorbents. The adsorbed phosphate can be effectively recovered with an alkaline solution. A multi-cycle regeneration-reuse study illustrated that the treated water still met the phosphorus discharge standard. The characterization results demonstrated the disappearance of La(OH)3 and La2(CO3)3 on the bead and the formation of NH3+ … P and La-P groups after the adsorption, indicating the significant roles of ion exchange and electrostatic attraction on the uptake. The excellent performance found in this study clearly indicates that the optimized La/CS bead is promising in the treatment of phosphate and perhaps its recovery for industrial use.