Multi-view clustering has attracted increasing attention in data mining communities. Despite superior clustering performance, we observe that existing multi-view subspace clustering methods directly fuse multi-view information in the similarity level by merging noisy affinity matrices; and isolate the processes of affinity learning, multiple information fusion and clustering. Both factors may cause insufficient utilization of multi-view information, leading to unsatisfying clustering performance. This paper proposes a novel consensus one-step multi-view subspace clustering (COMVSC) method to address these issues. Instead of directly fusing affinity matrices, COMVSC optimally integrates discriminative partition-level information, which is helpful in eliminating noise among data. Moreover, the affinity matrices, consensus representation and final clustering labels are learned simultaneously in a unified framework. Extensive experiment results on benchmark datasets demonstrate the superiority of our method over other state-of-the-art approaches.

Albeit great success has been achieved in image defocus blur detection, there are still several unsolved challenges, e.g., interference of background clutter, scale sensitivity and missing boundary details of blur regions. To deal with these issues, we propose a deep neural network which recurrently fuses and refines multi-scale deep features (DeFusionNet) for defocus blur detection. We first fuse the features from different layers of FCN as shallow features and semantic features, respectively. Then, the fused shallow features are propagated to deep layers for refining the details of detected defocus blur regions, and the fused semantic features are propagated to shallow layers to assist in better locating blur regions. The fusion and refinement are carried out recurrently. In order to narrow the gap between low-level and high-level features, we embed a feature adaptation module before feature propagating to exploit the complementary information as well as reduce the contradictory response of different feature layers. Since different feature channels are with different extents of discrimination for detecting blur regions, we design a channel attention module to select discriminative features for feature refinement. Finally, the output of each layer at last recurrent step are fused to obtain the final result. We collect a new dataset consists of various challenging images and their pixel-wise annotations for promoting further study. Extensive experiments on two commonly used datasets and our newly collected one are conducted to demonstrate both the efficacy and efficiency of DeFusionNet.

Classic portfolio selection problems mainly focus on high-risk financial markets with tradeoffs between returns and risk. However, more risk-averse investors pursue long-term portfolio planning with the objectives of maximizing final returns and maximizing flexibility. This article addresses a new type of the portfolio problem, called periodic investment portfolio selection problems (PIPSPs), in which investors periodically allocate resources to financial products with different periods. A multiobjective model for PIPSPs is first presented. With a mechanism for utilizing the data generated during the implementation of multiobjective evolutionary algorithms (MOEAs), a data-assisted MOEA (DA-MOEA) is proposed to solve PIPSPs. The main idea of a DA-MOEA is to combine a MOEA with a data-assisted process that consists of three components: 1) feature construction; 2) data fusion model development; and 3) obtained information utilization. To solve the addressed PIPSPs, two versions of DA-MOEAs with baselines of nondominated sorting and decomposition-based mechanisms are implemented, namely, the data-assisted NSGA-II (DA-NSGA-II) and data-assisted MOEA/D (DA-MOEA/D). In the developed DA-MOEAs for PIPSPs, a feature construction process and a data fusion model are well designed for mining data with different formats. To validate the algorithms, two sets of test instances are generated. The experimental results demonstrate the efficacy of the data-assisted process. Furthermore, the effects of the algorithm components, such as the data source sizes, information types, and information utilization strategies, are investigated.

Multi-view spectral clustering can effectively reveal the intrinsic cluster structure among data by performing clustering on the learned optimal embedding across views. Though demonstrating promising performance in various applications, most of existing methods usually linearly combine a group of pre-specified first-order Laplacian matrices to construct the optimal Laplacian matrix, which may result in limited representation capability and insufficient information exploitation. Also, storing and implementing complex operations on the{$n\times n}$Laplacian matrices incurs intensive storage and computation complexity. To address these issues, this paper first proposes a multi-view spectral clustering algorithm that learns a high-order optimal neighborhood Laplacian matrix, and then extends it to the late fusion version for accurate and efficient multi-view clustering. Specifically, our proposed algorithm generates the optimal Laplacian matrix by searching the neighborhood of the linear combination of both the first-order and high-order base Laplacian matrices simultaneously. By this way, the representative capacity of the learned optimal Laplacian matrix is enhanced, which is helpful to better utilize the hidden high-order connection information among data, leading to improved clustering performance. We design an efficient algorithm with proved convergence to solve the resultant optimization problem. Extensive experimental results on nine datasets demonstrate the superiority of the proposed algorithm

Multiple kernel clustering (MKC) algorithm aims to group data into different categories by optimally integrating information from a group of pre-specified kernels. Though demonstrating superiorities in various applications, we observe that existing MKC algorithms usuallydo not sufficiently consider the local density around individual data samplesandexcessively limit the representation capacity of the learned optimal kernel, leading to unsatisfying performance. In this paper, we propose an algorithm, called optimal neighborhood MKC with adaptive local kernels (ON-ALK), to address the two issues. In specific, we construct adaptive local kernels to sufficiently consider the local density around individual data samples, where different numbers of neighbors are discriminatingly selected on each sample. Further, the proposed ON-ALK algorithm boosts the representation of the learned optimal kernel via relaxing it into the neighborhood area of weighted combination of the pre-specified kernels. To solve the resultant optimization problem, a three-step iterative algorithm is designed and theoretically proven to be convergent. After that, we also study the generalization bound of the proposed algorithm. Extensive experiments have been conducted to evaluate the clustering performance. As indicated, the algorithm significantly outperforms state-of-the-art methods in recent literatures on six challenging benchmark datasets, verifying its advantages and effectiveness.

Although demonstrating great success, previous multi-view unsupervised feature selection (MV-UFS) methods often construct a view-specific similarity graph and characterize the local structure of data within each single view. In such a way, the cross-view information could be ignored. In addition, they usually assume that different feature views are projected from a latent feature space while the diversity of different views cannot be fully captured. In this work, we resent a MV-UFS model via cross-view local structure preserved diversity and consensus learning, referred to as CvLP-DCL briefly. In order to exploit both the shared and distinguishing information across different views, we project each view into a label space, which consists of a consensus part and a view-specific part. Therefore, we regularize the fact that different views represent same samples. Meanwhile, a cross-view similarity graph learning term with matrix-induced regularization is embedded to preserve the local structure of data in the label space. By imposing the$l_{2,1}$-norm on the feature projection matrices for constraining row sparsity, discriminative features can be selected from different views. An efficient algorithm is designed to solve the resultant optimization problem and extensive experiments on six publicly datasets are conducted to validate the effectiveness of the proposed CvLP-DCL.

Multi-view clustering has attracted increasing attention in multimedia, machine learning and data mining communities. As one kind of the essential multi-view clustering algorithm, multi-view subspace clustering (MVSC) becomes more and more popular due to its strong ability to reveal the intrinsic low dimensional clustering structure hidden across views. Despite superior clustering performance in various applications, we observe that existing MVSC methodsdirectly fuse multi-view information in the similarity level by merging noisy affinity matrices; andisolate the processes of affinity learning, multi-view information fusion and clustering. Both factors may cause insufficient utilization of multi-view information, leading to unsatisfying clustering performance. This paper proposes a novel consensus one-step multi-view subspace clustering (COMVSC) method to address these issues. Instead of directly fusing multiple affinity matrices, COMVSC optimally integrates discriminative partition-level information, which is helpful to eliminate noise among data. Moreover, the affinity matrices, consensus representation and final clustering labels matrix are learned simultaneously in a unified framework. By doing so, the three steps can negotiate with each other to best serve the clustering task, leading to improved performance. Accordingly, we propose an iterative algorithm to solve the resulting optimization problem. Extensive experiment results on benchmark datasets demonstrate the superiority of our method against other state-of-the-art approaches.

Incomplete multi-view clustering (IMVC) optimally combines multiple pre-specified incomplete views to improve clustering performance. Among various excellent solutions, the recently proposed multiple kernel k-means with incomplete kernels (MKKM-IK) forms a benchmark, which redefines IMVC as a joint optimization problem where the clustering and kernel matrix imputation tasks are alternately performed until convergence. Though demonstrating promising performance in various applications, we observe that the manner of kernel matrix imputation in MKKM-IK would incur intensive computational and storage complexities, over-complicated optimization and limitedly improved clustering performance. In this paper, we first propose an Efficient and Effective Incomplete Multi-view Clustering (EE-IMVC) algorithm to address these issues. Instead of completing the incomplete kernel matrices, EE-IMVC proposes to impute each incomplete base matrix generated by incomplete views with a learned consensus clustering matrix. Moreover, we further improve this algorithm by incorporating prior knowledge to regularize the learned consensus clustering matrix. Two three-step iterative algorithms are carefully developed to solve the resultant optimization problems with linear computational complexity, and their convergence is theoretically proven. After that, we theoretically study the generalization bound of the proposed algorithms. Furthermore, we conduct comprehensive experiments to study the proposed algorithms in terms of clustering accuracy, evolution of the learned consensus clustering matrix and the convergence. As indicated, our algorithms deliver their effectiveness by significantly and consistently outperforming some state-of-the-art ones.

Feature extraction and feature selection have been regarded as two independent dimensionality reduction methods in most of the existing literature. In this paper, we propose to integrate both approaches into a unified framework and design an unsupervised linear feature selective projection (FSP) for feature extraction with low-rank embedding and dual Laplacian regularization, with the aim to exploit the intrinsic relationship among data and suppress the impact of noise. Specifically, a projection matrix with an l2,1-norm regularization is introduced to project original high dimensional data points into a new subspace with lower dimension, where the l2,1-norm regularization can endow the projection with good interpretability. We deploy a coefficient matrix with low rank constraint to reconstruct the data points and the l2,1-norm is imposed to regularize the data reconstruction errors in the low-dimensional subspace and make FSP robust to noise. Furthermore, a dual graph Laplacian regularization term is imposed on the low dimensional data and data reconstruction matrix for preserving the local manifold geometrical structure of data. Finally, an alternatively iterative algorithm is carefully designed for solving the proposed optimization model. Theoretical convergence and computational complexity analysis of the algorithm are also provided. Comprehensive experiments on various benchmark datasets have been carried out to evaluate the performance of the proposed FSP. As indicated, our algorithm significantly outperforms other state-of-the-art methods for feature extraction.

Satellite Imaging Scheduling, Satellite Downlinking Scheduling and Ground Resources Scheduling are important components in satellites daily management. Considering the highly interlinking of these three types of scheduling, an Integrated Satellite Scheduling model is formulated and proved NP-complete in this paper. To address the large scale and oversubscription of the Integrated Satellite Scheduling in an actual background, an evolvable real-time system of Integrated Satellite Scheduling is constructed based on Cooperative Neuro Evolution of Augmenting Topologies (C-NEAT). With the help of the C-NEAT, the system learns from historical scheduling data and adaptively assigns each request to the satellite or the ground antenna which is most likely to fulfill this request. Moreover, the real-time scheduling function of the system is actualized by the windowed scheduling framework. Experimental results indicate that the system greatly reduces the problem size of Integrated Satellite Scheduling and improves the scheduling efficiency, where daily and emergent requests are arranged over time.

The problem of network disintegration has broad applications and recently has received growing attention, such as network confrontation and disintegration of harmful networks. This paper presents an optimized disintegration strategy model for complex networks and introduces the GA optimization method into the network disintegration problem to identify the optimal disintegration strategy, which is a heuristic optimization algorithm and rarely applied to the study of network robustness. The efficiency of the proposed solution was verified by comparing it with other disintegration strategies used in a ER network with multi-edges. Numerical experiments suggest that our solution can improve the effect of network disintegration and that the “best” choice for edge failure disintegration can be identified through global searches. Our understanding of the optimal disintegration strategy may also shed light on a new property of the edges within network disintegration and deserves additional study.

Planning problems, such as mission capability planning in defense, can traditionally be modeled as a resource investment project scheduling problem (RIPSP) with unconstrained resources and cost. This formulation is too abstract in some real-world applications. In these applications, the durations of tasks depend on the allocated resources. In this paper, we first propose a new version of RIPSPs, namely extended RIPSPs (ERIPSPs), in which the durations of tasks are a function of allocated resources. Moreover, we introduce a resource proportion coefficient to manifest the contribution degree of various resources to activities. Since the more realistic nature of projects in practice implies that the circumstances under which the plan will be executed are stochastic in nature, we present a stochastic version of ERIPSPs, namely stochastic extended RIPSPs (SERIPSPs). To solve SERIPSPs, we first use scenarios to capture the space of possibilities (i.e., stochastic elements of the problem). We focus on three sources of uncertainty: duration perturbation, resource breakdown, and precedence alteration. We propose a robustness measure for the solutions of SEPIPSPs when uncertainties interact. We then formulate an SERIPSP as a multiobjective optimization model with three optimization objectives: makespan, cost, and robustness. A knowledge-based multiobjective evolutionary algorithm (K-MOEA) is proposed to solve the problem. The mechanism of K-MOEA is simple and time efficient. The algorithm has two main characteristics. The first is that useful information (knowledge) contained in the obtained approximated nondominated solutions is extracted during the evolutionary process. The second is that extracted knowledge is utilized by updating the population periodically to guide subsequent search. The approach is illustrated using a synthetic case study. Randomly generated benchmark instances are used to analyze the performance of the proposed K-MOEA. The experimental results illustrate the effectiveness of the proposed algorithm and its potential for solving SERIPSPs.

Optimization problems under uncertainty have received considerable attention in recent years due to their practical implications. In real-world applications, a problem is usually confronted with multiple types of uncertainties that are incommensurable with each other. Decision makers in the real-world do not trade-off objectives alone, but also and more importantly trade-off different uncertainties. The contemporary optimization techniques that deal with uncertainty generally treat different types of uncertainties by aggregating them into a single form. In this paper, we introduce a new type of optimization problems which are characterized by multiple conflicting uncertainties. We term them as multi-uncertainty optimization problems. Modeling multiple conflicting uncertainties as an optimization problem can provide analysts a powerful tool to search non-dominated solutions in a risk space in addition to the objective space. This is particularly useful since sources of uncertainties are usually uncontrollable and cannot be optimized as objectives. The concept of a risk operating curve is introduced which provides a unique perspective of the problem to the decision makers allowing them to opt for solutions based on their risk attitude toward different sources of uncertainties. The application of these concepts is demonstrated through a test problem in the resource-constrained project scheduling domain.

Many planning problems, such as mission capability planning, can be modelled as project scheduling problems. Unlike conventional deterministic project scheduling problems, project scheduling problems involve uncertainty and the execution of the plan is very likely to be perturbed by many factors. In other words, the circumstances under which the plan will be executed are changing and stochastic. In this paper, we first use scenarios to represent the stochastic elements in the problem; these are: perturbation strength and perturbation occurrence time. We define and explain the Stochastic Resource Investment Project Scheduling (SRIPS) problem. A multi-objective optimization model of SRIPS is proposed where three optimization objectives are considered simultaneously: makespan, cost, and robustness. A multi-objective genetic algorithm is employed to solve the problem. Finally, we generate two test problems with 30 and 60 non-dummy activities to validate the performance of the proposed approach and analyze the sensitivity of the results to different parameter settings.