Latent multi-view subspace clustering has been demonstrated to have desirable clustering performance. However, the original latent representation method vertically concatenates the data matrices from multiple views into a single matrix along the direction of dimensionality to recover the latent representation matrix, which may result in an incomplete information recovery. To fully recover the latent space representation, we in this paper propose an Enhanced Latent Multi-view Subspace Clustering (ELMSC) method. The ELMSC method involves constructing an augmented data matrix that enhances the representation of multi-view data. Specifically, we stack the data matrices from various views into the block-diagonal locations of the augmented matrix to exploit the complementary information. Meanwhile, the non-block-diagonal entries are composed based on the similarity between different views to capture the consistent information. In addition, we enforce a sparse regularization for the non-diagonal blocks of the augmented self-representation matrix to avoid redundant calculations of consistency information. Finally, a novel iterative algorithm based on the framework of Alternating Direction Method of Multipliers (ADMM) is developed to solve the optimization problem for ELMSC. Particularly, we theoretically analyze the convergence of ELMSC in detail. Extensive experiments on real-world datasets show that our proposed ELMSC is able to achieve higher clustering performance than some state-of-art multi-view clustering methods. Moreover, our experiments show that our method remains effective with randomly chosen parameters, demonstrating ELMSC’s practical potential.

As an important category of clustering methods, subspace clustering algorithms have arisen particular attention during the last decade. Most subspace clustering algorithms are designed by first constructing a similarity matrix and then using spectral clustering algorithms to perform clustering. How to learn a suitable representation matrix to construct the similarity matrix is essential to the clustering performance. In most existing algorithms, the representation matrix is solved by norm-minimization, which commonly enforces the error matrix with nuclear norm or sparsity norm. However, these methods may fail to achieve satisfactory performance for real data contaminated by complex noise. To this end, we propose a novel robust subspace clustering method based on the Logarithmic Hyperbolic Cosine Function (LHCF). We theoretically analyze the grouping effect, as well as the convergence behavior, which illustrates that highly correlated samples can be grouped into the same cluster. Experimental results conducted on the Extended Yale B dataset show that the newly proposed algorithm yields better clustering performance compared with some advanced methods.

The low-carbon pilot city policy is an important initiative to explore the path of a win-win situation for both the economy and the environment. Since 2010, China has established 87 low-carbon pilot cities. This policy implementation aims to encourage green technology innovation among listed companies, thereby achieving sustainable corporate growth through the promotion of energy efficiency and renewable energy. This paper aims to unveil the relationship between low-carbon pilot city policies and green technology innovation. This paper explores the impact of policy implementation based on patent data of Chinese listed companies from 2007 to 2019. Empirical results show that the policy can promote green technology innovation among listed companies in the pilot cities. This finding still holds in the parallel trend test and the PSM-Multi-period DID test. Second, the policy has a greater effect on the green-technology innovation of non-state enterprises and can promote more green technology innovation activities of enterprises in the eastern region compared with other areas. Furthermore, in terms of different stock sectors, the low-carbon pilot city policy can significantly promote GEM-affiliated enterprises’ green technology innovation activities. Finally, listed companies with a high degree of digital transformation are more active in green technology innovation in the context of low-carbon pilot city policy.

The maximum correntropy criterion (MCC) algorithm depends upon two fundamental parameters, i.e., step-size and kernel width. Previous studies of parameter optimization in the MCC mainly focus on a single parameter (mainly the kernel width), lacking optimization research concerning both parameters. To this end, this letter investigates a novel optimization scheme simultaneously involving step-size and kernel width. The optimization framework is based on making the power of weight error vector undergo the steepest attenuation. Under the premise of maintaining the same evolutionary trend for time-varying step-size and kernel width, we formulate a constrained parameter optimization problem, where the step-size is subject to a kernel width induced constraint. By taking this approach, the original bivariate optimization can be transformed into a univariate optimization problem, which facilitates optimization solving. We further develop an existing reset scheme to make it suitable for kernel width to ensure a good tracking capability. In addition, we investigate the convergence behavior of the optimized algorithm. Simulation results demonstrate that the developed optimization scheme is beneficial for performance improvement, and the resulting algorithm outperforms some state-of-art MCC-based algorithms.