Bladder cancer prognosis is a critical factor in determining optimal treatment strategies. However, the heterogeneity of multi-omics data and the high dimensionality of gene features pose significant challenges for accurate survival prediction. Traditional single-omics or naive integration methods often struggle to capture complex inter-omics relationships and are vulnerable to noise from redundant genes. To address these issues, a novel deep learning framework--AAE-Cox-M, is proposed to integrate mRNA, miRNA, DNA methylation, and CNV data for survival analysis. This method features a two-stage integration strategy based on Cross-omics Pre-training, which first pretrains on one omics type and then incorporates additional omics data to enhance cross-layer feature learning. Additionally, a differential expression-based feature selection module is employed to reduce dimensionality, eliminate irrelevant signals, and highlight biologically meaningful genes. To improve representation robustness, an adversarial autoencoder is employed, combining survival loss with adversarial regularization to better model the underlying data distribution while resisting overfitting. Experiments conducted on the TCGA-BLCA dataset and four independent GEO datasets demonstrate that AAE-Cox-M consistently outperforms existing linear and deep models. Ablation studies further verify the contributions of each module.

Sparse large-scale multiobjective optimization problems (SLSMOPs) frequently emerge in diverse artificial intelligence applications. They are characterized by a high-dimensional search space where only a small subset of decision variables are non-zero. Many existing algorithms aim to concurrently identify zero-valued variables and optimize the non-zero subset within a reduced search space. However, striking an effective balance between these two aspects often proves elusive. To address this, we propose turning SLSMOPs into evolutionary multitasking, culminating in the development of a novel optimization framework, SparseEMT. This framework organizes the optimization process into three interrelated tasks based on the importance of variables. The first auxiliary task emphasizes fine-grained exploration of both zero and non-zero variables within a low-dimensional space. The second auxiliary task narrows the focus to a detailed search of only non-zero variables in an even lower-dimensional space. Finally, the main task concentrates on searching within the original high-dimensional space. In this framework, the entire population is divided into three segments, each dedicated to a specific task. Individuals undergo crossover and mutation both within their assigned tasks and across different tasks, facilitated by a specialized knowledge transfer strategy. Extensive empirical studies show that SparseEMT outperforms state-of-the-art algorithms on both the benchmark test suite and real-world applications, making it an effective solution for SLSMOPs.

Deep learning advances neural decoding in functional magnetic resonance imaging (fMRI) tasks with convolution and attention-based methods. However, these methods struggle with capturing global spatiotemporal information due to high dimensionality, noise and inter-individual difference of fMRI, which also increase computational complexity and prior bias. To this end, a novel causal state space model, Causal fMRI-Mamba, is proposed for neural decoding and task state mapping. It effectively captures global spatiotemporal information via eliminating local redundancies and capturing long-distance dependencies. Meanwhile, a causal representation framework is designed to extract invariant high-order features and disentangle related causal features, enhancing model performance. Furthermore, a dense connection module is expanded to prevent significant causal information loss in hidden states of inter layers. On the HCP brain task state classification task, Causal fMRI-Mamba achieves better performance and generalization than comparison methods.

In practical medical diagnosis, small sample sizes in gene expression profiling data can lead to overfitting. Addressing this, we leverage the potential of the Conditional Wasserstein Generative Adversarial Network with Gradient Penalty (CWGAN-GP) to amplify data volumes. However, it lacks control over the locations of generated samples and struggles to get a better balance between discriminators and generators during training. To overcome these hurdles, we propose the Improved CWGAN-GP, implementing two critical improvements. The first involves the adoption of a data segmentation strategy based on sample influence scores. By calculating the influence score for each sample, we prioritize samples at decision boundaries and outside the distributions as the training set, thus yielding more explicit decision boundaries. The second enhancement is that a depth feature constraint based on the Pearson correlation coefficient is proposed. Here, an encoder extracts the deep features, applying a constraint between the noise and deep features guided by the Pearson correlation coefficient. This strategy navigates the model closer to a Nash equilibrium. Empirical evaluations conducted on six publicly available gene expression profiling datasets validate our approach, demonstrating that it not only generates higher quality samples but also showcases superior stability compared to existing methods.

The utilization of both constrained and unconstrained-based optimization for solving constrained multi-objective optimization problems (CMOPs) has become prevalent among recently proposed constrained multiobjective evolutionary algorithms (CMOEAs). However, the constrained-based optimization which adopted by many CMOEAs typically gives priority to feasible solutions over infeasible ones regardless of their objective values, potentially leading to degraded performance due to the elimination of promising infeasible solutions with strong convergence and diversity. Furthermore, many existing CMOEAs have difficulty in maintaining diversity while focusing on feasibility, thereby hindering their ability to effectively address CMOPs characterized by complex feasible regions. To tackle these challenges, a constraint-Pareto dominance relationship is proposed in this paper to evaluate solutions based on both objectives and feasibility, to improve the optimization potential by reduce the elimination probability of promising infeasible solutions. A diversity enhancement strategy is also designed to enable simultaneously focus on both diversity and feasibility, thus effectively ensuring the diversity of the feasible solutions obtained. Empirical results from benchmark suites and real-world problems demonstrate that our proposed algorithm surpasses state-of-the-art CMOEAs.

Gene selection and cancer classification are inherently multi-objective tasks that require balancing competing objectives, such as maximizing classification accuracy while minimizing irrelevant or redundant genes. Existing methods often optimize a single objective or treat gene selection and classification independently, limiting their overall effectiveness. This study proposes a unified framework, MORPSO_ECD+ELM, which formulates gene selection and classification as a multimodal multi-objective optimization problem (MMOP) to optimize both objectives simultaneously. The framework introduces two key innovations: (1) an enhanced crowding distance (ECD) metric to improve diversity preservation and (2) an advanced multi-objective particle swarm optimization variant (MORPSO_ECD) that incorporates ECD and ring topography to effectively explore the MMOP solution space. Integrated with the Extreme Learning Machine (ELM), this framework achieves robust and efficient cancer classification. Extensive experimental validations demonstrate that the proposed approach achieves high classification accuracy while identifying biologically meaningful gene subsets, providing a powerful solution to bridge the gap between gene selection and cancer classification.

Radial basis function (RBF) neural networks for Multi-Instance Multi-Label (MIML) directly can exploit the connections between instances and labels so that they can preserve useful prior information, but they only adopt Gaussian radial basis function as their RBF whose parameters are difficult to determine. In this paper, parameters can be obtained by multi-objective optimization methods with multi performance measures treated as objectives, specifically, parameter estimation of different RBFs by an improved multi-objective particle swarm optimization (MOPSO) is proposed where Recall rate and Precision rate are chosen to obtain the most desirable Pareto optimal solution set. Furthermore, share-learning factor is proposed to modify the particle velocity in standard MOPSO to improve the global search ability and group cooperative ability. It is experimentally demonstrated that the proposed method can estimate the reliable parameters of different RBFs, and it is also very competitive with the state of art MIML methods.

Particle swarm optimisation algorithm (PSO) possesses a strong exploitation capability due to its fast search speed. It, however, suffers from an early convergence leading to its inability to preserve diversity. An improved particle swarm optimiser is proposed based on a constriction factor and Gravitational Search Algorithm to overcome premature convergence. The constriction factor ensures an appropriately controlled transition from exploration into exploitation, leading to an enhanced diversity and appropriate learning rate adjustment throughout the search process. We introduce Gravitational Search Algorithm to enhance the exploratory ability of PSO. An adaptive response strategy is incorporated to activate stagnated particles to curtail the high tendency to get trapped in a local optimum. To verify the efficacy of the improvement strategies, we employ the proposed algorithm in training a Single Layer Feedforward neural network to classify real-world data ranging from binary to multi-class datasets of which our proposed algorithm outperforms the others.

Multi-leader comprehensive learning particle swarm optimiser possesses strong exploitation ability, by randomly selecting and assigning best-ranked particles as leaders during optimisation. However, it lacks the ability to preserve diversity by mainly focusing on exploitation, and adopting random selection to choose leaders also hinders its performance. To overcome these deficiencies, an improved multi-leader comprehensive learning particle swarm optimiser is proposed based on Karush-Kuhn-Tucker proximity measure and Gravitational Search Algorithm. Karush-Kuhn-Tucker proximity measure is employed to determine the best-ranked particles’ contribution to the swarm’s convergence to influence their selection as guides for other particles. Gravitational Search Algorithm is introduced to preserve the algorithm’s ability to maintain diversity. To curb premature convergence and particles getting trapped in a local optimum, an adaptive reset velocity strategy is incorporated to activate stagnated particles. Some benchmark test functions are employed to compare the proposed algorithm with seven other peer algorithms. The results verify that our proposed algorithm possesses a better capability to elude local optima with faster convergence than other algorithms. Furthermore, to prove the efficacy of the application of our proposed algorithm in real-life, the algorithms are used to train a Feedforward neural network for epilepsy detection, of which our proposed algorithm outperforms the others.

The diversity of the population is a key factor for particle swarm optimisation (PSO) when dealing with most optimisation problems. The best previously visited positions of each particle are the exemplar in PSO to guide particle swarm to search, and the diversity of the population can be controlled by these best previously visited positions. Base on this idea of to control the diversity of population to improve the performance of PSO, this paper proposes a novel PSO with mutation breeding (MBPSO), which performs a mutation breeding operation periodically, to control the diversity of the population to improve the global optimisation ability. The mutation breeding operation can be divided into two steps: breeding and mutation. The breeding step is to replace all of best previously visited positions of each particle with the global best previously visited position, and the mutation step is to perform a mutation operation for those new generated best previously visited positions. In addition, we adopt a new updating mechanism of the global best previously position to avoid falling into local optimum. The experimental results on a suit of benchmark functions verifies that the proposed PSO is a competitive algorithm when compare with other PSO variants.

Feature selection is an important task to improve the classifier’s accuracy and to decrease the problem size. A number of methodologies have been presented for feature selection problems using metaheuristic algorithms. In this paper, an improved self-adaptive inertia weight particle swarm optimisation with local search and combined with C4.5 classifiers for feature selection algorithm is proposed. In this proposed algorithm, the gradient base local search with its capacity of helping to explore the feature space and an improved self-adaptive inertia weight particle swarm optimisation with its ability to converge a best global solution in the search space. Experimental results have verified that the SIW-APSO-LS performed well compared with other state of art feature selection techniques on a suit of 16 standard data sets.

BACKGROUND: Gene selection is one of the critical steps in the course of the classification of microarray data. Since particle swarm optimization has no complicated evolutionary operators and fewer parameters need to be adjusted, it has been used increasingly as an effective technique for gene selection. Since particle swarm optimization is apt to converge to local minima which lead to premature convergence, some particle swarm optimization based gene selection methods may select non-optimal genes with high probability. To select predictive genes with low redundancy as well as not filtering out key genes is still a challenge. RESULTS: To obtain predictive genes with lower redundancy as well as overcome the deficiencies of traditional particle swarm optimization based gene selection methods, a hybrid gene selection method based on gene scoring strategy and improved particle swarm optimization is proposed in this paper. To select the genes highly related to out samples' classes, a gene scoring strategy based on randomization and extreme learning machine is proposed to filter much irrelevant genes. With the third-level gene pool established by multiple filter strategy, an improved particle swarm optimization is proposed to perform gene selection. In the improved particle swarm optimization, to decrease the likelihood of the premature of the swarm the Metropolis criterion of simulated annealing algorithm is introduced to update the particles, and the half of the swarm are reinitialized when the swarm is trapped into local minima. CONCLUSIONS: Combining the gene scoring strategy with the improved particle swarm optimization, the new method could select functional gene subsets which are significantly sensitive to the samples' classes. With the few discriminative genes selected by the proposed method, extreme learning machine and support vector machine classifiers achieve much high prediction accuracy on several public microarray data, which in turn verifies the efficiency and effectiveness of the proposed gene selection method.

BACKGROUND: The main goal of successful gene selection for microarray data is to find compact and predictive gene subsets which could improve the accuracy. Though a large pool of available methods exists, selecting the optimal gene subset for accurate classification is still very challenging for the diagnosis and treatment of cancer. RESULTS: To obtain the most predictive genes subsets without filtering out critical genes, a gene selection method based on least absolute shrinkage and selection operator (LASSO) and an improved binary particle swarm optimization (BPSO) is proposed in this paper. To avoid overfitting of LASSO, the initial gene pool is divided into clusters based on their structure. LASSO is then employed to select high predictive genes and further calculate the contribution value which indicates the genes' sensitivity to samples' classes. With the second-level gene pool established by double filter strategy, the BPSO encoding the contribution information obtained from LASSO is improved to perform gene selection. Moreover, from the perspective of the bit change probability, a new mapping function is defined to guide the updating of the particle to select the more predictive genes in the improved BPSO. CONCLUSIONS: With the compact gene pool obtained by double filter strategies, the improved BPSO could select the optimal gene subsets with high probability. The experimental results on several public microarray data with extreme learning machine verify the effectiveness of the proposed method compared to the relevant methods.

Low-rank matrix completion aims to recover matrices with missing entries and has attracted considerable attention from machine learning researchers. Most of the existing methods, such as weighted nuclear-norm-minimization-based methods and Qatar Riyal (QR)-decomposition-based methods, cannot provide both convergence accuracy and convergence speed. To investigate a fast and accurate completion method, an iterative QR-decomposition-based method is proposed for computing an approximate singular value decomposition. This method can compute the largest r(r > 0) singular values of a matrix by iterative QR decomposition. Then, under the framework of matrix trifactorization, a method for computing an approximate SVD based on QR decomposition (CSVDQR)-based L2,1-norm minimization method (LNM-QR) is proposed for fast matrix completion. Theoretical analysis shows that this QR-decomposition-based method can obtain the same optimal solution as a nuclear norm minimization method, i.e., the L2,1-norm of a submatrix can converge to its nuclear norm. Consequently, an LNM-QR-based iteratively reweighted L2,1-norm minimization method (IRLNM-QR) is proposed to improve the accuracy of LNM-QR. Theoretical analysis shows that IRLNM-QR is as accurate as an iteratively reweighted nuclear norm minimization method, which is much more accurate than the traditional QR-decomposition-based matrix completion methods. Experimental results obtained on both synthetic and real-world visual data sets show that our methods are much faster and more accurate than the state-of-the-art methods.

Traditional gene selection methods for microarray data mainly considered the features' relevance by evaluating their utility for achieving accurate predication or exploiting data variance and distribution, and the selected genes were usually poorly explicable. To improve the interpretability of the selected genes as well as prediction accuracy, an improved gene selection method based on binary particle swarm optimization (BPSO) and prior information is proposed in this paper. In the proposed method, BPSO encoding gene-to-class sensitivity (GCS) information is used to perform gene selection. The gene-to-class sensitivity information, extracted from the samples by extreme learning machine (ELM), is encoded into the selection process in four aspects: initializing particles, updating the particles, modifying maximum velocity, and adopting mutation operation adaptively. Constrained by the gene-to-class sensitivity information, the new method can select functional gene subsets which are significantly sensitive to the samples' classes. With the few discriminative genes selected by the proposed method, ELM, K-nearest neighbor and support vector machine classifiers achieve much high prediction accuracy on five public microarray data, which in turn verifies the efficiency and effectiveness of the proposed gene selection method.

Extreme learning machine (ELM) is one of suitable base-classifiers for ensemble learning systems because of its fast learning speed, good generalization performance and simple setting. For the ensemble learning, how to select the base classifiers is a key issue which influences the performance of the ensemble system dramatically. To obtain a compact ensemble system with improved generalization performance, a diversity guided ensemble of ELMs based on attractive and repulsive particle swarm optimization (ARPSO) is proposed in this paper. In the proposed method, ARPSO considers both the convergence accuracy on the validation data and the diversity of the ensemble system. To effectively weigh the diversity of the ensemble system, a new diversity based on the Euclidean distance among the candidate ELMs is defined in this study. Experimental results on function approximation and benchmark classification problems verify that the proposed method could build more compact ensemble of ELMs with better generalization performance than some classical ensemble of ELMs.

Extreme learning machines (ELMs) for generalized single-hidden-layer feedforward networks which perform well in both regression and classification applications have caused a lot of attention. To obtain compact network architecture with better generalization performance, an improved ELM with adaptive growth of hidden nodes (AG-ELM) combined with particle swarm optimization (PSO) is proposed in this study. PSO is used to select the optimal weights and biases to overcome the deficiency of the standard AG-ELM. All parameters in one network are represented by one particle in PSO, and the dimension of the particle increases in the training process. Simulation results on various test problems verify that the proposed algorithm achieves more compact network architecture and has better generalization performance with less steps than classical AG-ELM.

Traditional particle swarm optimization (PSO) has good global search ability, but it easily loses its diversity and thus leads to premature convergence. Gradient descent methods such as backpropagation (BP) algorithm have good performance in searching local minima, whereas they are apt to converge to local minima. To improve search ability, two hybrid algorithms combining two improved PSOs individually with BP are proposed to train single-hidden-layer feedforward neural networks in this paper. In the two improved PSOs, other than the phases of repulsion and attraction, a new phase named as a mixed phase is introduced, in which the particles are attracting and repelling simultaneously to prevent premature convergence. Moreover, a modified mutation operation is performed to help particles jump out of local minima in the improved PSOs. The proposed hybrid methods achieve better convergence performance with faster convergence rate than some commonly used PSO–BP approaches and purely global or local search methods. The experiments results on function approximation and benchmark classification problems are given to verify the effectiveness and efficiency of the proposed hybrid algorithms.

In this paper, a new effective model is proposed to forecast how long the postoperative patients suffered from non-small cell lung cancer will survive. The new effective model which is based on the extreme learning machine (ELM) and principal component analysis (PCA) can forecast successfully the postoperative patients' survival time. The new model obtains better prediction accuracy and faster convergence rate which the model using backpropagation (BP) algorithm and the Levenberg-Marquardt (LM) algorithm to forecast the postoperative patients' survival time can not achieve. Finally, simulation results are given to verify the efficiency and effectiveness of our proposed new model.

In this paper, a modified learning algorithm to obtain better generalization performance is proposed. The cost terms of this new algorithm are selected based on the second-order derivatives of the neural activation at the hidden layers and the first-order derivatives of the neural activation at the output layer. It can be guaranteed that in the course of training, the additional cost terms for this algorithm can penalize both the input-to-output mapping sensitivity and the high frequency components to obtain better generalization performance. Finally, theoretical justifications and simulation results are given to verify the efficiency and effectiveness of the proposed learning algorithm.