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Low-rank tensor representation (LRTR) has become a significant method for achieving improved multi-view clustering (MVC) performance. Generally, most LRTR methods impose a tensor low-rank constraint (TLRC) on a tensor, which is spliced by the representation matrix of each view, to explore the low-rank prior hidden in these representation matrices. However, two problems remain unsolved. On the one hand, these representation matrices still contain noise since the raw data usually possess noise; on the other hand, and more importantly, is there any other prior information that can be explored among these representation matrices? Since samples located in the same cluster are similar, the coefficients of their representation matrices should exhibit similar. That is, these representation matrices should be local smoothness (LS), which is also verified by our numerical tests. In addition, the use of the LS prior helps to denoise the noise contain in the data. Then, in this paper, we propose a joint LS and LRTR for robust MVC method (LS-LRTR), which can simultaneously exploit the low-rank and LS priors. Specifically, we utilize a TLRC to explore the low-rank prior in the representation matrices. Subsequently, to mine the LS prior and further reduce the influence of noise, we introduce the Total Variation (TV) norm to the constraint representation matrices. Then, we fuse the TLRC and TV norm into a unified framework. Additionally, we apply an Augmented Lagrange Multiplier to solve the optimization problem of LS-LRTR. Experiments conducted on several datasets indicate that LS-LRTR outperforms the state-of-the-art clustering methods. • Our model integrates local smoothness and low-rank tensor representation for clustering. • Our model applies TV norm to explore the local smoothness and denoise. • Our model is the first to leverage both low-rank and local smoothness. • Experimental results outperform other state-of-the-art clustering methods. [ABSTRACT FROM AUTHOR]

Low-rank representation (LRR) is a classic subspace clustering (SC) algorithm, and many LRR-based methods have been proposed. Generally, LRR-based methods use denoized data as dictionaries for data reconstruction purpose. However, the dictionaries used in LRR-based algorithms are fixed, leading to poor clustering performance. In addition, most of these methods assume that the input data are linearly correlated. However, in practice, data are mostly nonlinearly correlated. To address these problems, we propose a novel adaptive kernel dictionary-based LRR (AKDLRR) method for SC. Specifically, to explore nonlinear information, the given data are mapped to the Hilbert space via the kernel technique. The dictionary in AKDLRR is not fixed; it adaptively learns from the data in the kernel space, making AKDLRR robust to noise and yielding good clustering performance. To solve the AKDLRR model, an efficient procedure including an alternative optimization strategy is proposed. In addition, a theoretical analysis of the convergence performance of AKDLRR is presented, which reveals that AKDLRR can converge in at most three iterations under certain conditions. The experimental results show that AKDLRR can achieve the best clustering performance and has excellent speed in comparison with other algorithms. [ABSTRACT FROM AUTHOR]

Driven by the global goal of "carbon neutrality", energy conservation, emission reduction and low-carbon development have become important research directions. Transparent thermal insulation materials can effectively shield near-infrared radiation while maintaining high visible light transmittance, making them widely applicable in building energy conservation. In this paper, antimony-doped tin oxide (ATO) and cesium tungsten bronze (Cs x WO 3 , or CWO) are chosen to be composited in order to solve the problems of the poor shielding effect of ATO for short-wavelength near-infrared (NIR) light and the unsatisfactory shielding effect of CWO for long-wavelength NIR light. Therefore, in this study, we employed a one-step hydrothermal method to form a novel CWO@ATO core-shell structure to combine the advantages of both ATO and CWO. By adjusting the composite ratio of ATO and CWO, both the physical and electronic stucutres are effectively tuned to promote the optical modulation in a broad bandwidth. Enventually, the core-shell structured composite exhibit an excellent near-infrared blocking property, surpassing the pure ATO by 27.8 % in the wavelength region of 780∼1500 nm while improving by 14.9 % compared to CWO in the long wavelength between 1500 and 2500 nm. Furthermore, the prepared CWO@ATO core-shell structure repesents near-infrared shielding rate as high as 93.1 % in the full NIR spectrum, and possesses an overall thermal insulation coefficiency (THI) of 9.33 in the full range from 780 nm to 2500 nm, which is substantially larger than that of pure ATO and CWO by a factor of 2.37 and 3.05, respectively. This core-shell structure engineering realizes the utilization of complementary advantages of ATO and Cs 0·33 WO 3 materials, providing a new method to improve the near-infrared performance of energy-saving glass coating, and having broad application prospects in the field of low-carbon buildings. [ABSTRACT FROM AUTHOR]

Incomplete multi-view clustering (IMVC) methods have attracted extensive attention in the field of clustering due to their superior performance in addressing incomplete multi-view data. However, existing IMVC methods often address balanced incomplete multi-view data, i.e., the missing rate of each view is the same, which does not match reality. In real life, the missing rate of each view in incomplete multi-view data is often different; these are referred to as unbalanced incomplete multi-view data. However, few articles consider the processing of unbalanced incomplete multi-view data. Therefore, we propose an innovative method, unbalanced incomplete multi-view clustering based on low-rank tensor graph learning (UIMVC/LTGL), to handle unbalanced incomplete multi-view data. Specifically, we first use the adjacency relationship between views to adaptively complete similarity graph matrices. To explore the consistency and high-order correlation among views, we further introduce a consensus representation learning term and low-rank tensor constraint into UIMVC/LTGL. In practical applications, each view's contribution to clustering should be different, especially for UIMVC problems. Therefore, we also apply the adaptive weight strategy to each view, which makes reasonable use of the information of each view. The abovementioned steps are integrated into a unified framework to obtain the optimal clustering effect. The augmented Lagrange multiplier (ALM) method is employed to solve the optimization problem. The experimental results on seven well-known datasets fully demonstrate the superiority of the proposed method. [ABSTRACT FROM AUTHOR]