Self-paced regularized adaptive multi-view unsupervised feature selection.

Multi-view unsupervised feature selection (MUFS) is an efficient approach for dimensional reduction of heterogeneous data. However, existing MUFS approaches mostly assign the samples the same weight, thus the diversity of samples is not utilized efficiently. Additionally, due to the presence of various regularizations, the resulting MUFS problems are often non-convex, making it difficult to find the optimal solutions.

Distributed Neurodynamic Models for Solving a Class of System of Nonlinear Equations.

This article investigates a class of systems of nonlinear equations (SNEs). Three distributed neurodynamic models (DNMs), namely a two-layer model (DNM-I) and two single-layer models (DNM-II and DNM-III), are proposed to search for such a system's exact solution or a solution in the sense of least-squares. Combining a dynamic positive definite matrix with the primal-dual method, DNM-I is designed and it is proved to be globally convergent.

Neurodynamic optimization approaches with finite/fixed-time convergence for absolute value equations.

This paper proposes three novel accelerated inverse-free neurodynamic approaches to solve absolute value equations (AVEs). The first two are finite-time converging approaches and the third one is a fixed-time converging approach. It is shown that the proposed first two neurodynamic approaches converge to the solution of the concerned AVEs in a finite-time while, under some mild conditions, the third one converges to the solution in a fixed-time.

Self-Guided Partial Graph Propagation for Incomplete Multiview Clustering.

In this work, we study a more realistic challenging scenario in multiview clustering (MVC), referred to as incomplete MVC (IMVC) where some instances in certain views are missing. The key to IMVC is how to adequately exploit complementary and consistency information under the incompleteness of data. However, most existing methods address the incompleteness problem at the instance level and they require sufficient information to perform data recovery.

Segmentation of Brain Tissues from MRI Images Using Multitask Fuzzy Clustering Algorithm.

In recent years, brain magnetic resonance imaging (MRI) image segmentation has drawn considerable attention. MRI image segmentation result provides a basis for medical diagnosis. The segmentation result influences the clinical treatment directly.

Nonconvex low-rank tensor approximation with graph and consistent regularizations for multi-view subspace learning.

Multi-view clustering is widely used to improve clustering performance. Recently, the subspace clustering tensor learning method based on Markov chain is a crucial branch of multi-view clustering. Tensor learning is commonly used to apply tensor low-rank approximation to represent the relationships between data samples.

Sparse signal reconstruction via collaborative neurodynamic optimization.

In this paper, we formulate a mixed-integer problem for sparse signal reconstruction and reformulate it as a global optimization problem with a surrogate objective function subject to underdetermined linear equations. We propose a sparse signal reconstruction method based on collaborative neurodynamic optimization with multiple recurrent neural networks for scattered searches and a particle swarm optimization rule for repeated repositioning. We elaborate on experimental results to demonstrate the outperformance of the proposed approach against ten state-of-the-art algorithms for sparse signal reconstruction.

Cardinality-constrained portfolio selection via two-timescale duplex neurodynamic optimization.

This paper addresses portfolio selection based on neurodynamic optimization. The portfolio selection problem is formulated as a biconvex optimization problem with a variable weight in the Markowitz risk-return framework. In addition, the cardinality-constrained portfolio selection problem is formulated as a mixed-integer optimization problem and reformulated as a biconvex optimization problem.

A Proximal Neurodynamic Network With Fixed-Time Convergence for Equilibrium Problems and Its Applications.

This article proposes a novel fixed-time converging proximal neurodynamic network (FXPNN) via a proximal operator to deal with equilibrium problems (EPs). A distinctive feature of the proposed FXPNN is its better transient performance in comparison to most existing proximal neurodynamic networks. It is shown that the FXPNN converges to the solution of the corresponding EP in fixed-time under some mild conditions.

Bicriteria Sparse Nonnegative Matrix Factorization via Two-Timescale Duplex Neurodynamic Optimization.

In this article, sparse nonnegative matrix factorization (SNMF) is formulated as a mixed-integer bicriteria optimization problem for minimizing matrix factorization errors and maximizing factorized matrix sparsity based on an exact binary representation of l matrix norm. The binary constraints of the problem are then equivalently replaced with bilinear constraints to convert the problem to a biconvex problem. The reformulated biconvex problem is finally solved by using a two-timescale duplex neurodynamic approach consisting of two recurrent neural networks (RNNs) operating collaboratively at two timescales.

Two-timescale neurodynamic approaches to supervised feature selection based on alternative problem formulations.

Feature selection is a crucial step in data processing and machine learning. While many greedy and sequential feature selection approaches are available, a holistic neurodynamics approach to supervised feature selection is recently developed via fractional programming by minimizing feature redundancy and maximizing relevance simultaneously. In view that the gradient of the fractional objective function is also fractional, alternative problem formulations are desirable to obviate the fractional complexity.

A Two-Timescale Duplex Neurodynamic Approach to Mixed-Integer Optimization.

This article presents a two-timescale duplex neurodynamic approach to mixed-integer optimization, based on a biconvex optimization problem reformulation with additional bilinear equality or inequality constraints. The proposed approach employs two recurrent neural networks operating concurrently at two timescales. In addition, particle swarm optimization is used to update the initial neuronal states iteratively to escape from local minima toward better initial states.

Task Assignment for Multivehicle Systems Based on Collaborative Neurodynamic Optimization.

This paper addresses task assignment (TA) for multivehicle systems. Multivehicle TA problems are formulated as a combinatorial optimization problem and further as a global optimization problem. To fulfill heterogeneous tasks, cooperation among heterogeneous vehicles is incorporated in the problem formulations.

A collaborative neurodynamic approach to global and combinatorial optimization.

In this paper, a collaborative neurodynamic optimization approach is proposed for global and combinatorial optimization. First, a combinatorial optimization problem is reformulated as a global optimization problem. Second, a neurodynamic optimization model based on an augmented Lagrangian function is proposed and its states are proven to be asymptotically stable at a strict local minimum in the presence of nonconvexity in objective function or constraints.

A Two-Timescale Duplex Neurodynamic Approach to Biconvex Optimization.

This paper presents a two-timescale duplex neurodynamic system for constrained biconvex optimization. The two-timescale duplex neurodynamic system consists of two recurrent neural networks (RNNs) operating collaboratively at two timescales. By operating on two timescales, RNNs are able to avoid instability.

A nonnegative matrix factorization algorithm based on a discrete-time projection neural network.

This paper presents an algorithm for nonnegative matrix factorization based on a biconvex optimization formulation. First, a discrete-time projection neural network is introduced. An upper bound of its step size is derived to guarantee the stability of the neural network.

A recurrent neural network for adaptive beamforming and array correction.

In this paper, a recurrent neural network (RNN) is proposed for solving adaptive beamforming problem. In order to minimize sidelobe interference, the problem is described as a convex optimization problem based on linear array model. RNN is designed to optimize system's weight values in the feasible region which is derived from arrays' state and plane wave's information.