The success of multiview subspace clustering (MVSC) lies in the efficient integration of consensus and complementary information from subspace structures. However, existing MVSC algorithms often treat these two types of information separately, overlooking the obvious correlations-both positive and negative-that exist between them. To address this issue, we propose a novel method called contrastive-driven diversity and consistency exploration in tensorized MVSC (CD-TMSC). Specifically, our method begins by segmenting self-representations into a consensus representation and a set of specific representations to accurately model both consensus and complementary information. Drawing inspiration from contrastive learning, we introduce a novel fractional regularization term to harness both the positive and negative correlations inherent in consensus and complementary information, where the numerator, employing the Hilbert-Schmidt independence criterion (HSIC), quantifies the negative correlation between the consensus and view-specific representations, as well as among the view-specific representations themselves. Conversely, the denominator, also leveraging HSIC, measures the positive correlation between the original data matrices and their self-representations. Minimizing this term has a dual effect: it reduces the numerator, thereby amplifying the negative correlation, a move that might be seen as counterproductive but, in our innovative approach, it promotes the diversity within representation matrices. Simultaneously, it increases the denominator, reinforcing the positive correlation and bolstering the consistency of the information. Additionally, we incorporate a graph regularization term for the consensus matrix to capture more consistent manifold information. Finally, utilizing the high-quality consensus and view-specific representations derived from our constraints, we reconstruct self-representation matrices and construct a third-order tensor with a low-rank constraint to explore higher order correlations within the self-representations. Our method integrates contrastive-driven regularization, manifold learning, and low-rank tensor learning into a cohesive framework, optimized using an alternating direction minimization strategy. Experimental results on multiple benchmark datasets show that our approach outperforms several state-of-the-art methods.

Late fusion-based algorithms have attracted extensive attention because of their low time and space complexity for handling in-complete multiview data. However, these methods have certain limitations. First, the basic clustering indicator matrices generated by incomplete views are susceptible to low-quality imputation. Second, traditional methods often fail to adequately consider the high-order correlations between these basic clustering indicator matrices, leading to suboptimal performance. Third, conventional methods focus primarily on improving speed, with less emphasis on enhancing clustering performance. To address these issues, we propose two novel models. The first is called tensor-based late fusion incomplete multiview clustering (TLF-IMVC-1). Specifical-ly, TLF-IMVC-1 first seeks a consensus clustering matrix from the basic clustering indicator matrices and subsequently imputes the incomplete portions of these matrices via the learned consen-sus matrix. This approach seamlessly integrates the clustering process with the imputation of missing elements into a unified framework. Furthermore, we construct a third-order tensor from these basic clustering matrices, constrained by the tensor nuclear norm, to capture their high-order correlations. Although this model is effective, it lacks proper guidance in the learning process of the basic clustering indicator matrices, making them susceptible to low-quality imputation. Therefore, we introduce the second novel model, i.e., TLF-IMVC-2, to address this issue. Specifically, TLF-IMVC-2 uses the learned consensus representation matrix as a new component to construct the third-order tensor. This strategy leverages the robust clustering structure inherent in the consensus matrix to guide the learning process of the basic clustering matrices. The experimental results demonstrate that both models outperform state-of-the-art methods in clustering.

In this paper, we present new algorithms for online multicast routing in ad hoc networks where nodes are energy-constrained. The objective is to maximize the total amount of multicast message data routed successfully over the network without any knowledge of future multicast request arrivals and generation rates. Specifically, we first propose an online algorithm for the problem based on an exponential function of energy utilization at each node. The competitive ratio of the proposed algorithm is analyzed if admission control of multicast requests is permitted. We then provide another online algorithm for the problem, which is based on minimizing transmission energy consumption for each multicast request and guaranteeing that the local network lifetime is no less than \gamma times of the optimum, where \gamma is constant with 0 < \gamma\leq 1. We finally conduct extensive experiments by simulations to analyze the performance of the proposed algorithms, in terms of network capacity, network lifetime, and transmission energy consumption for each multicast request. The experimental results clearly indicate that, for online multicast routing in ad hoc wireless networks, the network capacity is proportional to the network lifetime if the transmission energy consumption for each multicast request is at the same time minimized. This is in contrast to the implication by Kar et al. that the network lifetime is proportional to the network capacity when they considered the online unicast routing by devising an algorithm based on the exponential function of energy utilization at each node.

In this paper we consider on-line disjoint path routing in energy-constrained ad hoc networks. The objective is to maximize the network capacity, i.e., maximize the number of messages routed successfully by the network without any knowledge of future disjoint path connection request arrivals and generation rates. We first present two on-line algorithms for the problem. One is based on maximizing the network lifetime and the other is based on an exponential function of energy utilization at nodes. We then conduct extensive experiments by simulations to analyze the performance of the proposed algorithms. The experimental results show that the proposed algorithms outperform those existing algorithms that do not take into account the power load balancing among the nodes.

Networks that are dynamically formed by hundreds or thousands of inexpensive sensors are widely used in environmental monitoring, disaster recovery and the other domains. In this paper, we present a protocol, LM-PB, for on-line broadcast routing in wireless sensor networks where the sensors are energy-constrained. Our protocol is aiming at maximizing the duration before the network becomes inoperative due to the lack of battery energy at sensors. An appropriate selection of transmitting sensors, which cover the rest in the network, is an efficient technique for broadcasting. LM-PB makes such selections by utilizing a novel timing heuristic, called FDL. It does not need any explicit control message and is free of exploring the network topology. Our experimental results demonstrate that LM-PB provides longer network lifetime compared with the existing passive protocols. Meanwhile, we notice that the total number of successfully routed messages, termed as the network capacity, is also maximized by LM-PB. Particularly, the results indicate that the additional delay incurred by LM-PB is much less than the worst case analyzed value, and is acceptable.