MOTIVATION: Spatial multi-omics technologies jointly profile transcriptomes, proteins and chromatin accessibility in situ, enabling integrative analysis of tissue organization across molecular layers. However, most existing graph-based integration methods rely on independently constructed modality-specific k-nearest-neighbor graphs. When auxiliary modalities are sparse or noisy, these graphs can become topologically discordant, propagate spurious edges, weaken cross-modal alignment, and reduce spatial domain resolution. RESULTS: We present Anchored RNA for Integrated Spatial Embedding (ARISE), an RNA expression anchored framework for spatial multi-omics integration. ARISE defines a shared-edge topology by intersecting RNA feature-similarity and spatial-proximity graphs, encodes auxiliary modalities on this common scaffold, and integrates them through inside-out hierarchical fusion. We further show theoretically that graph intersection minimizes false-positive edges within a broad class of k-of-r graph fusion rules, providing a principled basis for topology anchoring. Across various spatial multi-omics benchmarks spanning simulated and real datasets in bi-modal and tri-modal settings, ARISE improves spatial domain identification, cross-modal consistency, and preservation of tissue structure relative to existing methods. Furthermore, the learned representation supports biologically meaningful downstream analyses, including marker-based domain annotation, pathway enrichment, and cis-regulatory inference, indicating that ARISE yields a robust and interpretable framework for spatial multi-omics integration. AVAILABILITY AND IMPLEMENTATION: The source code is available at https://github.com/XiangxiangWang-code/ARISE. The archived version used in this study is available at https://doi.org/10.6084/m9.figshare.32686137.v2.

Biological age is a more direct reflection of physiological status than chronological age, serving as a vital measure to evaluate health risks and aging interventions. While steroid metabolomics offers rich information for exploring aging mechanisms, the complex and nonlinear interactions within metabolic networks remain challenging in modeling. Here, we propose and describe METRON as a deep learning framework to predict biological ages from steroid metabolomics. Specifically, a Metabolite Interaction Perception Module (MIPM) is proposed to capture the interactions. Subsequently, a Group-Rational Kolmogorov-Arnold Network is also integrated to capture intricate dependencies and enhance the representation capability. We demonstrate that METRON achieves promising performance as compared to other machine learning and deep learning methods. Beyond performance, METRON offers interpretability by recovering the established markers such as Dehydroepiandrosterone (DHEA) and identifying 17-hydroxyprogesterone (17-OH-P4) as the key signature linked to hypothalamic-pituitary-adrenal axis dynamics. These results support the capacity of METRON not only to estimate biological age but also to uncover underappreciated metabolic drivers behind aging.

Large Language Models (LLMs) demonstrate promising capabilities in natural language understanding and reasoning with enormous parameter spaces and vast amounts of training data. These attributes have facilitated their deployment into diverse application domains. However, the underlying parameters implicitly assume decision-making boundaries, resulting in a significant number of decision spaces not covered by training data. This makes them susceptible to adversarial manipulations through carefully crafted inputs. To illuminate the vulnerabilities of LLMs, we propose a unified token-level jailbreaking attack that makes victim models generate responses for potentially harmful queries. Specifically, we propose an evolutionary algorithm to evolve perturbation sets, utilizing gradient-based and crossover-based operators to enhance performance under multiple scenarios. Furthermore, we develop a repository for reusing past perturbations and conduct an analysis of token sensitivity within LLMs, facilitating zero-shot attacks with convergence. Extensive benchmark experiments validate the effectiveness of our method on three different models, achieving increases of 62.36%, 57.89%, and 64.81% in attack success rates compared to baseline methods under white-box scenarios. In addition, the evaluation experiments demonstrate our method is effective for multiple scenarios and different size of models. This research reveals vulnerabilities of LLMs, provides theoretical foundations for developing more robust defense strategies, and contributes to building more reliable AI systems.

Despite the popularity of graph neural networks, perturbed graph data is still a serious threat towards its inherent vulnerabilities. Adversarial examples can still easily manipulate the output of graph neural networks across various attack scenarios. Meanwhile, attacks on graph networks also appear to be crucial, as it can help model designers enhance the robustness of their models. In this study, we propose a sensitivity-oriented poisoning attack for self-supervised graph embedding models through bilevel optimization, which employs different optimization methods at each level. In addition, in order to improve attack effectiveness, we analyze graph structure to identify sensitive nodes and edges that guide attack directions, combining gradient-based and query-based methods to target both edge connections and node attributes. Besides, according to the defects of existing graph masked auto-encoders models, we design the feature sensitivity and feature variance to reduce the feature differentiability, which impairs the performance of the downstream model. Ablation studies validate our operator is effective on three citation datasets. And benchmark-based experiments support the effectiveness of our method on three different graph tasks. Specifically, our approach can achieve an average reduction of 3% in the accuracy of node classification compared to existing methods for attacking neural structures alone. For attacking both graph structures and attributes, our model has even achieved an average reduction of 4.5% for the node classification task, outperforming the existing methods.

Cellular responses to genetic perturbations are prevalent in wide contexts from the fundamental understandings on pathology to the development of clinical therapies and the discovery of novel drug targets. Nonetheless, the substantial amount of possible perturbation combinations renders wet-lab experiments prohibitively expensive and time-consuming. To address it, the BRNET model is proposed for predicting non-linear transcriptional outcomes where multiple perturbations exist. BRNET integrates prior knowledge with advanced embeddings into a non-stacked neural structure to predict transcriptional responses to both individual and multiple genetic perturbations. For unseen scenarios, BRNET also generalizes well under the corresponding perturbations. Experimental results highlight the capabilities of BRNET, demonstrating promising performance as compared to established deep learning models.

Accurate cancer subtype identification is crucial for personalized medicine, as it enables precise diagnosis based on molecular characteristics. With the advent of large-scale multi-omics data from various resources, researchers now have unprecedented opportunities to explore cancer subtypes comprehensively. However, the inherent complexity, high dimensionality, and heterogeneity of these datasets present significant statistical and computational challenges, often leading to suboptimal clustering performance when inter-omics heterogeneity is overlooked. To address these challenges, we propose a novel method called the Hierarchical Multi-view Graph Diffusion Weighted (HMGDW) model for cancer subtype identification. Our approach begins with the generation of multiple base clusterings through random feature sampling, effectively mitigating the impact of high dimensionality. These base clusterings are subsequently integrated via a late integration strategy to yield the consensus clustering result. Then, we introduce a graph diffusion weighted mechanism that prioritizes views with the most significant contributions to the unified graph representation. Lastly, we conducted extensive experiments on both generic multi-view datasets and multi-omics cancer multi-omics datasets. The experimental results demonstrate that HMGDW consistently outperforms several state-of-the-art methods, achieving robust and accurate clustering. Additionally, a case study on the acute myeloid leukemia (AML) dataset validates the practical efficacy of our model in identifying clinically relevant subtypes.

Drug combination therapy plays a vital role in disease treatment, including cancer, as it contributes to treatment efficacy and can alleviate the effect of drug resistance. Although clinical trials and screening may provide valuable information about synergistic drug combinations, they suffer from challenging combinatorial space. Multiple methods are proposed to address those issues. However, they still fail in making full use of global and local triplet context relationships of known synergistic combinations. To this end, a deep learning model which leverages dual view hypergraph representation fusion for synergistic drug combinations identification is proposed, namely DVHSyn. It first extracts the transcriptome features of cancer cell lines and molecular structures of drugs. Subsequently, by modeling the synergistic effect on a hypergraph, DVHSyn simultaneously learns the local and global context of the sample triplets via a hypergraph view and its expanded heterogeneous graph view. Finally, the learned representations of the above two branches are fused selectively to predict synergistic drug combinations. Experiment results demonstrate that DVHSyn surpasses six other competing methods. One case study also reflects that DVHSyn has the potential to predict novel synergistic drug combinations. Overall, our method is effective in identifying synergistic drug combinations and provides new insights for novel drug development.

Spatial transcriptomics (ST) complements scRNA-seq by enabling in situ gene-expression profiling while preserving native tissue architecture and histomorphology. Yet ST data are inherently noisy, high-dimensional, and multimodal, complicating robust clustering. Many existing approaches define neighbor-hoods solely by spatial proximity and aggregate features via naive averaging, which blurs tissue boundaries and underrepre-sents biologically salient heterogeneity and microenvironmental interactions. In this study, we propose MuSACL, a Multimodal Spatially Adaptive Contrastive Learning model that integrates gene expression, spatial coordinates, and histological images to accurately identify spatial domains in ST data. Specifically, MuSACL introduces a Multimodal Proximity Subgraph (MPS) to construct biologically informed graph structures. Furthermore, MuSACL employs heterogeneous modalities using a Graph Attention Network (GAT) and proposes a novel Spatially Adaptive Attention Readout (SAAR) mechanism to enhance contrastive learning with spatial adaptivity. This approach overcomes the limitations of naive feature averaging, yielding more expressive, spatially aware representations. On two public ST datasets, MuSACL significantly surpasses state-of-the-art baselines. Ablations attribute the gains to MPS and SAAR, which enhance representation quality and spatial resolution.

Single-cell RNA sequencing (scRNA-seq) technology has made significant breakthroughs in genomics research in recent years, enabling in-depth analysis of gene expression profiles at the single-cell level. A key step in analyzing scRNA-seq data is clustering cells into subpopulations, which facilitates subsequent downstream analysis. Unfortunately, the rapid growth of scRNAseq data and the prevalence of dropout events pose challenges in cell type annotation. In this paper, we develop a hybrid model, Single-cell Multi-hop Autoencoder (scMAE), based on deep graph embedding clustering. This model combines multi-hop graph convolutional networks (GCNs) to capture cell neighbor information and uses deep graph convolutional networks to identify cell clusters. Additionally, the model integrates a zero-inflated negative binomial (ZINB) model into a topologically adaptive graph convolutional autoencoder to learn low-dimensional latent representations and applies Kullback-Leibler (KL) divergence for the clustering task. By jointly training on the adjacency matrix and gene expression data, the model simultaneously optimizes the clustering results and the generative model. Specifically, the loss function combines four components: adjacency matrix reconstruction loss, ZINB loss, generator loss, and clustering loss, and an alternating training strategy is employed to enhance clustering performance. Extensive experiments on 15 scRNA-seq datasets from different yet representative single-cell sequencing platforms demonstrate that scMAE outperforms various state-of-the-art clustering methods.

MOTIVATION: Predicting RNA-binding proteins (RBPs) is central to understanding post-transcriptional regulatory mechanisms. Here, we introduce EnrichRBP, an automated and interpretable computational platform specifically designed for the comprehensive analysis of RBP interactions with RNA. RESULTS: EnrichRBP is a web service that enables researchers to develop original deep learning and machine learning architectures to explore the complex dynamics of RBPs. The platform supports 70 deep learning algorithms, covering feature representation, selection, model training, comparison, optimization, and evaluation, all integrated within an automated pipeline. EnrichRBP is adept at providing comprehensive visualizations, enhancing model interpretability, and facilitating the discovery of functionally significant sequence regions crucial for RBP interactions. In addition, EnrichRBP supports base-level functional annotation tasks, offering explanations and graphical visualizations that confirm the reliability of the predicted RNA-binding sites. Leveraging high-performance computing, EnrichRBP provides ultra-fast predictions ranging from seconds to hours, applicable to both pre-trained and custom model scenarios, thus proving its utility in real-world applications. Case studies highlight that EnrichRBP provides robust and interpretable predictions, demonstrating the power of deep learning in the functional analysis of RBP interactions. Finally, EnrichRBP aims to enhance the reproducibility of computational method analyses for RBP sequences, as well as reduce the programming and hardware requirements for biologists, thereby offering meaningful functional insights. AVAILABILITY AND IMPLEMENTATION: EnrichRBP is available at https://airbp.aibio-lab.com/. The source code is available at https://github.com/wangyb97/EnrichRBP, and detailed online documentation can be found at https://enrichrbp.readthedocs.io/en/latest/.

High-throughput sequencing such as Hi-C captures spatiotemporal chromatin interactions, revealing the intricate interplays within transcriptional regulation and chromatin dynamics during cellular reprogramming and developmental processes. However, the forecast on chromatin dynamics in successive developmental stages remains challenging due to the inherent complexity of spatial and temporal patterns in Hi-C data across developmental stages. Towards such a direction, we present StarMie, a deep learning framework that integrates the spatiotemporal-aware module and the multi-stage differential variation module to predict high-throughput chromatin interactions in next developmental stages. Our comprehensive evaluation demonstrates that StarMie outperforms existing methods and sufficiently captures discriminative spatial and temporal dependencies as well as inter-stage-level variations of chromatin interactions. Moreover, the dual importance of both spatial and temporal information in Hi-C data is observed in parameter analysis. Ablation studies also confirm the essential role of each component in StarMie. Furthermore, five cross-species case studies support StarMie's cross-species generalizability and its capability to extract universal chromatin interaction patterns in different developmental stages. In-depth analysis demonstrates that StarMie uncovers conserved genomic logic in cardiac development and disease. Overall, this work paves a new approach for exploring genome reprogramming and development through predictive modeling of Hi-C dynamics.

Drug combination therapy is a promising strategy for managing complex and co-existing diseases. However, drug-drug interactions (DDIs) can result in unexpected adverse effects, making it crucial to understand such interactions to prevent adverse drug reactions and develop new therapeutic strategies. Current DDI annotation methods heavily rely on atom-level graph structural features, overlooking valuable drug contextual representations within medical literature. Additionally, these methods are typically designed for a specific task, limiting their scalability to diverse medical scenarios. To address these limitations, we propose TEmbed-DDI, a novel framework that leverages contextual representations and pre-trained large language model embeddings to enhance feature extraction for DDI annotations. Specifically, we retrieve meaningful contextual texts for each drug to enrich semantic features and adopt pre-trained large language model embeddings to capture rich features from these long-range contextual representations. TEmbed-DDI is the first framework to incorporate LLM-powered embeddings for medical interaction annotations. Furthermore, a bidirectional neural network is integrated into TEmbed-DDI for the integrative Western and traditional Chinese medicine DDI annotation tasks. Comparative results demonstrate that TEmbed-DDI achieves state-of-the-art performance, with the highest AUC scores of 0.992 and 0.95 on the Western CHCH and DEEP interaction annotation benchmarks. Even for the newly constructed Traditional Chinese Medicine (TCM) DDI annotation benchmark, TEmbed-DDI consistently exhibits outstanding generalization capability, achieving an AUC of 0.956. Moreover, case studies further validate TEmbed-DDI's capability to annotate previously unknown interactions. These findings suggest that TEmbed-DDI can serve as a valuable tool in annotating previously unknown drug combinations for real-world applications, facilitating the development of efficacious therapies. Furthermore, as the first framework combining traditional Chinese medicine into DDI annotation tasks, its adaptability highlights the potential in supporting cross-domain medical research. TEmbed-DDI's design principles can inspire the development of flexible LLM-powered frameworks for drug combination discovery in the future.

Despite the remarkable process in the field of arbitrary image style transfer (AST), inconsistent evaluation continues to plague style transfer research. Existing methods often suffer from limited objective evaluation and inconsistent subjective feedback, hindering reliable comparisons among AST variants. In this study, we propose a multi-granularity assessment system that combines standardized objective and subjective evaluations. We collect a fine-grained dataset considering a range of image contexts such as different scenes, object complexities, and rich parsing information from multiple sources. Objective and subjective studies are conducted using the collected dataset. Specifically, we innovate on traditional subjective studies by developing an online evaluation system utilizing a combination of point-wise, pair-wise, and group-wise questionnaires. Finally, we bridge the gap between objective and subjective evaluations by examining the consistency between the results from the two studies. We experimentally evaluate CNN-based, flow-based, transformer-based, and diffusion-based AST methods by the proposed multi-granularity assessment system, which lays the foundation for a reliable and robust evaluation. Providing standardized measures, objective data, and detailed subjective feedback empowers researchers to make informed comparisons and drive innovation in this rapidly evolving field.

Cell type identification plays a vital role in single-cell RNA sequencing (scRNA-seq) data analysis. Although many deep embedded methods to cluster scRNA-seq data have been proposed, they still fail in elucidating the intrinsic properties of cells and genes. Here, we present a novel end-to-end deep graph clustering model for single-cell transcriptomics data based on unsupervised Gene-Cell Collective representation learning and Optimal Transport (scGCOT) which integrates both cell and gene correlations. Specifically, scGCOT learns the latent embedding of cells and genes simultaneously and reconstructs the cell graph, the gene graph, and the gene expression count matrix. A zero-inflated negative binomial (ZINB) model is estimated via the reconstructed count matrix to capture the essential properties of scRNA-seq data. By leveraging the optimal transport-based joint representation alignment, scGCOT learns the clustering process and the latent representations through a mutually supervised self optimization strategy. Extensive experiments with 14 competing methods on 15 real scRNA-seq datasets demonstrate the competitive edges of scGCOT.

Bioactive peptide therapeutics has been a long-standing research topic. Notably, the antimicrobial peptides (AMPs) have been extensively studied for its therapeutic potential. Meanwhile, the demand for annotating other therapeutic peptides, such as antiviral peptides (AVPs) and anticancer peptides (ACPs), also witnessed an increase in recent years. However, we conceive that the structure of peptide chains and the intrinsic information between the amino acids is not fully investigated among the existing protocols. Therefore, we develop a new graph deep learning model, namely TP-LMMSG, which offers lightweight and easy-to-deploy advantages while improving the annotation performance in a generalizable manner. The results indicate that our model can accurately predict the properties of different peptides. The model surpasses the other state-of-the-art models on AMP, AVP and ACP prediction across multiple experimental validated datasets. Moreover, TP-LMMSG also addresses the challenges of time-consuming pre-processing in graph neural network frameworks. With its flexibility in integrating heterogeneous peptide features, our model can provide substantial impacts on the screening and discovery of therapeutic peptides. The source code is available at https://github.com/NanjunChen37/TP_LMMSG.

MOTIVATION: The annotation of cell types from single-cell transcriptomics is essential for understanding the biological identity and functionality of cellular populations. Although manual annotation remains the gold standard, the advent of automatic pipelines has become crucial for scalable, unbiased, and cost-effective annotations. Nonetheless, the effectiveness of these automatic methods, particularly those employing deep learning, significantly depends on the architecture of the classifier and the quality and diversity of the training datasets. RESULTS: To address these limitations, we present a Pruning-enabled Gene-Cell Net (PredGCN) incorporating a Coupled Gene-Cell Net (CGCN) to enable representation learning and information storage. PredGCN integrates a Gene Splicing Net (GSN) and a Cell Stratification Net (CSN), employing a pruning operation (PrO) to dynamically tackle the complexity of heterogeneous cell identification. Among them, GSN leverages multiple statistical and hypothesis-driven feature extraction methods to selectively assemble genes with specificity for scRNA-seq data while CSN unifies elements based on diverse region demarcation principles, exploiting the representations from GSN and precise identification from different regional homogeneity perspectives. Furthermore, we develop a multi-objective Pareto pruning operation (Pareto PrO) to expand the dynamic capabilities of CGCN, optimizing the sub-network structure for accurate cell type annotation. Multiple comparison experiments on real scRNA-seq datasets from various species have demonstrated that PredGCN surpasses existing state-of-the-art methods, including its scalability to cross-species datasets. Moreover, PredGCN can uncover unknown cell types and provide functional genomic analysis by quantifying the influence of genes on cell clusters, bringing new insights into cell type identification and characterizing scRNA-seq data from different perspectives. AVAILABILITY AND IMPLEMENTATION: The source code is available at https://github.com/IrisQi7/PredGCN and test data is available at https://figshare.com/articles/dataset/PredGCN/25251163.

MOTIVATION: Spatial transcriptomics can quantify gene expression and its spatial distribution in tissues, thus revealing molecular mechanisms of cellular interactions underlying tissue heterogeneity, tissue regeneration, and spatially localized disease mechanisms. However, existing spatial clustering methods often fail to exploit the full potential of spatial information, resulting in inaccurate identification of spatial domains. RESULTS: In this article, we develop a deep graph contrastive clustering framework, stDGCC, that accurately uncovers underlying spatial domains via explicitly modeling spatial information and gene expression profiles from spatial transcriptomics data. The stDGCC framework proposes a spatially informed graph node embedding model to preserve the topological information of spots and to learn the informative and discriminative characterization of spatial transcriptomics data through self-supervised contrastive learning. By simultaneously optimizing the contrastive learning loss, reconstruction loss, and Kullback-Leibler divergence loss, stDGCC achieves joint optimization of feature learning and topology structure preservation in an end-to-end manner. We validate the effectiveness of stDGCC on various spatial transcriptomics datasets acquired from different platforms, each with varying spatial resolutions. Our extensive experiments demonstrate the superiority of stDGCC over various state-of-the-art clustering methods in accurately identifying cellular-level biological structures. AVAILABILITY AND IMPLEMENTATION: Code and data are available from https://github.com/TimE9527/stDGCC and https://figshare.com/projects/stDGCC/186525.

Accurate screening of cancer types is crucial for effective cancer detection and precise treatment selection. However, the association between gene expression profiles and tumors is often limited to a small number of biomarker genes. While computational methods using nature-inspired algorithms have shown promise in selecting predictive genes, existing techniques are limited by inefficient search and poor generalization across diverse datasets. This study presents a framework termed Evolutionary Optimized Diverse Ensemble Learning (EODE) to improve ensemble learning for cancer classification from gene expression data. The EODE methodology combines an intelligent grey wolf optimization algorithm for selective feature space reduction, guided random injection modeling for ensemble diversity enhancement, and subset model optimization for synergistic classifier combinations. Extensive experiments were conducted across 35 gene expression benchmark datasets encompassing varied cancer types. Results demonstrated that EODE obtained significantly improved screening accuracy over individual and conventionally aggregated models. The integrated optimization of advanced feature selection, directed specialized modeling, and cooperative classifier ensembles helps address key challenges in current nature-inspired approaches. This provides an effective framework for robust and generalized ensemble learning with gene expression biomarkers.

Cell clustering is a critical step in analyzing single-cell RNA sequencing (scRNA-seq) data, which allows us to characterize the cellular heterogeneity of transcriptional profiling at the single-cell level. Single-cell deep embedded representation models have recently become popular since they can learn feature representation and clustering simultaneously. However, the model still suffers from a variety of significant challenges, including the massive amount of data, pervasive dropout events, and complicated noise patterns in transcriptional profiling. Here, we propose a Single-Cell Deep Embedding Fusion Representation (scDEFR) model, which develop a deep embedded fusion representation to learn fused heterogeneous latent embedding that contains both the transcriptome gene-level information and the cell topology information. We first fuse them layer by layer to obtain compressed representations of intercellular relationships and transcriptome information. After that, the zero-inflated negative binomial model (ZINB)-based decoder is proposed to capture the global probabilistic structure of the data and reconstruct the final gene expression information and cell graph. Finally, by simultaneously integrating the clustering loss, crossentropy loss, ZINB loss, and the cell graph reconstruction loss, scDEFR can optimize clustering performance and learn the latent representation in fused information under a joint mutual supervised strategy. We conducted extensive and comprehensive experiments on 15 single-cell RNA-seq datasets from different sequencing platforms to demonstrate the superiority of scDEFR over a variety of state-of-the-art methods.

The rapid growth of omics-based data has revolutionized biomedical research and precision medicine, allowing machine learning models to be developed for cutting-edge performance. However, despite the wealth of high-throughput data available, the performance of these models is hindered by the lack of sufficient training data, particularly in clinical research (in vivo experiments). As a result, translating this knowledge into clinical practice, such as predicting drug responses, remains a challenging task. Transfer learning is a promising tool that bridges the gap between data domains by transferring knowledge from the source to the target domain. Researchers have proposed transfer learning to predict clinical outcomes by leveraging pre-clinical data (mouse, zebrafish), highlighting its vast potential. In this work, we present a comprehensive literature review of deep transfer learning methods for health informatics and clinical decision-making, focusing on high-throughput molecular data. Previous reviews mostly covered image-based transfer learning works, while we present a more detailed analysis of transfer learning papers. Furthermore, we evaluated original studies based on different evaluation settings across cross-validations, data splits and model architectures. The result shows that those transfer learning methods have great potential; high-throughput sequencing data and state-of-the-art deep learning models lead to significant insights and conclusions. Additionally, we explored various datasets in transfer learning papers with statistics and visualization.

MOTIVATION: Recent frameworks based on deep learning have been developed to identify cancer subtypes from high-throughput gene expression profiles. Unfortunately, the performance of deep learning is highly dependent on its neural network architectures which are often hand-crafted with expertise in deep neural networks, meanwhile, the optimization and adjustment of the network are usually costly and time consuming. RESULTS: To address such limitations, we proposed a fully automated deep neural architecture search model for diagnosing consensus molecular subtypes from gene expression data (DNAS). The proposed model uses ant colony algorithm, one of the heuristic swarm intelligence algorithms, to search and optimize neural network architecture, and it can automatically find the optimal deep learning model architecture for cancer diagnosis in its search space. We validated DNAS on eight colorectal cancer datasets, achieving the average accuracy of 95.48%, the average specificity of 98.07%, and the average sensitivity of 96.24%, respectively. Without the loss of generality, we investigated the general applicability of DNAS further on other cancer types from different platforms including lung cancer and breast cancer, and DNAS achieved an area under the curve of 95% and 96%, respectively. In addition, we conducted gene ontology enrichment and pathological analysis to reveal interesting insights into cancer subtype identification and characterization across multiple cancer types. AVAILABILITY AND IMPLEMENTATION: The source code and data can be downloaded from https://github.com/userd113/DNAS-main. And the web server of DNAS is publicly accessible at 119.45.145.120:5001.

MOTIVATION: Single-cell RNA sequencing (scRNA-seq) is an increasingly popular technique for transcriptomic analysis of gene expression at the single-cell level. Cell-type clustering is the first crucial task in the analysis of scRNA-seq data that facilitates accurate identification of cell types and the study of the characteristics of their transcripts. Recently, several computational models based on a deep autoencoder and the ensemble clustering have been developed to analyze scRNA-seq data. However, current deep autoencoders are not sufficient to learn the latent representations of scRNA-seq data, and obtaining consensus partitions from these feature representations remains under-explored. RESULTS: To address this challenge, we propose a single-cell deep clustering model via a dual denoising autoencoder with bipartite graph ensemble clustering called scBGEDA, to identify specific cell populations in single-cell transcriptome profiles. First, a single-cell dual denoising autoencoder network is proposed to project the data into a compressed low-dimensional space and that can learn feature representation via explicit modeling of synergistic optimization of the zero-inflated negative binomial reconstruction loss and denoising reconstruction loss. Then, a bipartite graph ensemble clustering algorithm is designed to exploit the relationships between cells and the learned latent embedded space by means of a graph-based consensus function. Multiple comparison experiments were conducted on 20 scRNA-seq datasets from different sequencing platforms using a variety of clustering metrics. The experimental results indicated that scBGEDA outperforms other state-of-the-art methods on these datasets, and also demonstrated its scalability to large-scale scRNA-seq datasets. Moreover, scBGEDA was able to identify cell-type specific marker genes and provide functional genomic analysis by quantifying the influence of genes on cell clusters, bringing new insights into identifying cell types and characterizing the scRNA-seq data from different perspectives. AVAILABILITY AND IMPLEMENTATION: The source code of scBGEDA is available at https://github.com/wangyh082/scBGEDA. The software and the supporting data can be downloaded from https://figshare.com/articles/software/scBGEDA/19657911. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Recently, low-rank tensor recovery methods based on subspace representation have received increased attention in the field of hyperspectral image (HSI) denoising. Unfortunately, those methods usually analyze the prior structural information within different dimensions indiscriminately, ignoring the differences between modes, leaving substantial room for improvement. In this article, we first consider the low-rank properties in the subspace and prove that the structure correlation across the nonlocal self-similarity mode is much stronger than in the spatial sparsity and spectral correlation modes. On that basis, we introduce a new multidirectional low-rank regularization, in which each mode is assigned a different weight to characterize its contribution to estimating the tensor rank. After that, integrating the proposed regularization with the subspace-based tensor recovery framework, an optimization model for HSI mixed noise removal is developed. The proposed model can be addressed efficiently via the alternating minimization algorithm. Extensive experiments implemented with synthetic and real data demonstrate that the proposed method significantly outperforms other state-of-the-art HSI denoising methods, which clearly indicates the effectiveness of the proposed approach in HSI denoising.

Single-cell RNA sequencing (scRNA-seq) provides high-throughput information about the genome-wide gene expression levels at the single-cell resolution, bringing a precise understanding on the transcriptome of individual cells. Unfortunately, the rapidly growing scRNA-seq data and the prevalence of dropout events pose substantial challenges for cell type annotation. Here, we propose a single-cell model-based deep graph embedding clustering (scTAG) method, which simultaneously learns cell–cell topology representations and identifies cell clusters based on deep graph convolutional network. scTAG integrates the zero-inflated negative binomial (ZINB) model into a topology adaptive graph convolutional autoencoder to learn the low-dimensional latent representation and adopts Kullback–Leibler (KL) divergence for the clustering tasks. By simultaneously optimizing the clustering loss, ZINB loss, and the cell graph reconstruction loss, scTAG jointly optimizes cluster label assignment and feature learning with the topological structures preserved in an end-to-end manner. Extensive experiments on 16 single-cell RNA-seq datasets from diverse yet representative single-cell sequencing platforms demonstrate the superiority of scTAG over various state-of-the-art clustering methods.

MOTIVATION: The rapid growth in literature accumulates diverse and yet comprehensive biomedical knowledge hidden to be mined such as drug interactions. However, it is difficult to extract the heterogeneous knowledge to retrieve or even discover the latest and novel knowledge in an efficient manner. To address such a problem, we propose EGFI for extracting and consolidating drug interactions from large-scale medical literature text data. Specifically, EGFI consists of two parts: classification and generation. In the classification part, EGFI encompasses the language model BioBERT which has been comprehensively pretrained on biomedical corpus. In particular, we propose the multihead self-attention mechanism and packed BiGRU to fuse multiple semantic information for rigorous context modeling. In the generation part, EGFI utilizes another pretrained language model BioGPT-2 where the generation sentences are selected based on filtering rules. RESULTS: We evaluated the classification part on 'DDIs 2013' dataset and 'DTIs' dataset, achieving the F1 scores of 0.842 and 0.720 respectively. Moreover, we applied the classification part to distinguish high-quality generated sentences and verified with the existing growth truth to confirm the filtered sentences. The generated sentences that are not recorded in DrugBank and DDIs 2013 dataset demonstrated the potential of EGFI to identify novel drug relationships. AVAILABILITY: Source code are publicly available at https://github.com/Layne-Huang/EGFI.

MOTIVATION: The identification of drug-target interactions (DTIs) plays a vital role for in silico drug discovery, in which the drug is the chemical molecule, and the target is the protein residues in the binding pocket. Manual DTI annotation approaches remain reliable; however, it is notoriously laborious and time-consuming to test each drug-target pair exhaustively. Recently, the rapid growth of labelled DTI data has catalysed interests in high-throughput DTI prediction. Unfortunately, those methods highly rely on the manual features denoted by human, leading to errors. RESULTS: Here, we developed an end-to-end deep learning framework called CoaDTI to significantly improve the efficiency and interpretability of drug target annotation. CoaDTI incorporates the Co-attention mechanism to model the interaction information from the drug modality and protein modality. In particular, CoaDTI incorporates transformer to learn the protein representations from raw amino acid sequences, and GraphSage to extract the molecule graph features from SMILES. Furthermore, we proposed to employ the transfer learning strategy to encode protein features by pre-trained transformer to address the issue of scarce labelled data. The experimental results demonstrate that CoaDTI achieves competitive performance on three public datasets compared with state-of-the-art models. In addition, the transfer learning strategy further boosts the performance to an unprecedented level. The extended study reveals that CoaDTI can identify novel DTIs such as reactions between candidate drugs and severe acute respiratory syndrome coronavirus 2-associated proteins. The visualization of co-attention scores can illustrate the interpretability of our model for mechanistic insights. AVAILABILITY: Source code are publicly available at https://github.com/Layne-Huang/CoaDTI.

Single-cell RNA sequencing (scRNA-seq) technologies have been heavily developed to probe gene expression profiles at single-cell resolution. Deep imputation methods have been proposed to address the related computational challenges (e.g. the gene sparsity in single-cell data). In particular, the neural architectures of those deep imputation models have been proven to be critical for performance. However, deep imputation architectures are difficult to design and tune for those without rich knowledge of deep neural networks and scRNA-seq. Therefore, Surrogate-assisted Evolutionary Deep Imputation Model (SEDIM) is proposed to automatically design the architectures of deep neural networks for imputing gene expression levels in scRNA-seq data without any manual tuning. Moreover, the proposed SEDIM constructs an offline surrogate model, which can accelerate the computational efficiency of the architectural search. Comprehensive studies show that SEDIM significantly improves the imputation and clustering performance compared with other benchmark methods. In addition, we also extensively explore the performance of SEDIM in other contexts and platforms including mass cytometry and metabolic profiling in a comprehensive manner. Marker gene detection, gene ontology enrichment and pathological analysis are conducted to provide novel insights into cell-type identification and the underlying mechanisms. The source code is available at https://github.com/li-shaochuan/SEDIM.

Healthcare disparities in multiethnic medical data is a major challenge; the main reason lies in the unequal data distribution of ethnic groups among data cohorts. Biomedical data collected from different cancer genome research projects may consist of mainly one ethnic group, such as people with European ancestry. In contrast, the data distribution of other ethnic races such as African, Asian, Hispanic, and Native Americans can be less visible than the counterpart. Data inequality in the biomedical field is an important research problem, resulting in the diverse performance of machine learning models while creating healthcare disparities. Previous researches have reduced the healthcare disparities only using limited data distributions. In our study, we work on fine-tuning of deep learning and transfer learning models with different multiethnic data distributions for the prognosis of 33 cancer types. In previous studies, to reduce the healthcare disparities, only a single ethnic cohort was used as the target domain with one major source domain. In contrast, we focused on multiple ethnic cohorts as the target domain in transfer learning using the TCGA and MMRF CoMMpass study datasets. After performance comparison for experiments with new data distributions, our proposed model shows promising performance for transfer learning schemes compared to the baseline approach for old and new data distributation experiments.

Identifying genome-wide binding events between circular RNAs (circRNAs) and RNA-binding proteins (RBPs) can greatly facilitate our understanding of functional mechanisms within circRNAs. Thanks to the development of cross-linked immunoprecipitation sequencing technology, large amounts of genome-wide circRNA binding event data have accumulated, providing opportunities for designing high-performance computational models to discriminate RBP interaction sites and thus to interpret the biological significance of circRNAs. Unfortunately, there are still no computational models sufficiently flexible to accommodate circRNAs from different data scales and with various degrees of feature representation. Here, we present HCRNet, a novel end-to-end framework for identification of circRNA-RBP binding events. To capture the hierarchical relationships, the multi-source biological information is fused to represent circRNAs, including various natural language sequence features. Furthermore, a deep temporal convolutional network incorporating global expectation pooling was developed to exploit the latent nucleotide dependencies in an exhaustive manner. We benchmarked HCRNet on 37 circRNA datasets and 31 linear RNA datasets to demonstrate the effectiveness of our proposed method. To evaluate further the model's robustness, we performed HCRNet on a full-length dataset containing 740 circRNAs. Results indicate that HCRNet generally outperforms existing methods. In addition, motif analyses were conducted to exhibit the interpretability of HCRNet on circRNAs. All supporting source code and data can be downloaded from https://github.com/yangyn533/HCRNet and https://doi.org/10.6084/m9.figshare.16943722.v1. And the web server of HCRNet is publicly accessible at http://39.104.118.143:5001/.

MOTIVATION: Thanks to the development of high-throughput sequencing technologies, massive amounts of various biomolecular data have been accumulated to revolutionize the study of genomics and molecular biology. One of the main challenges in analyzing this biomolecular data is to cluster their subtypes into subpopulations to facilitate subsequent downstream analysis. Recently, many clustering methods have been developed to address the biomolecular data. However, the computational methods often suffer from many limitations such as high dimensionality, data heterogeneity and noise. RESULTS: In our study, we develop a novel Graph-based Multiple Hierarchical Consensus Clustering (GMHCC) method with an unsupervised graph-based feature ranking (FR) and a graph-based linking method to explore the multiple hierarchical information of the underlying partitions of the consensus clustering for multiple types of biomolecular data. Indeed, we first propose to use a graph-based unsupervised FR model to measure each feature by building a graph over pairwise features and then providing each feature with a rank. Subsequently, to maintain the diversity and robustness of basic partitions (BPs), we propose multiple diverse feature subsets to generate several BPs and then explore the hierarchical structures of the multiple BPs by refining the global consensus function. Finally, we develop a new graph-based linking method, which explicitly considers the relationships between clusters to generate the final partition. Experiments on multiple types of biomolecular data including 35 cancer gene expression datasets and eight single-cell RNA-seq datasets validate the effectiveness of our method over several state-of-the-art consensus clustering approaches. Furthermore, differential gene analysis, gene ontology enrichment analysis and KEGG pathway analysis are conducted, providing novel insights into cell developmental lineages and characterization mechanisms. AVAILABILITY AND IMPLEMENTATION: The source code is available at GitHub: https://github.com/yifuLu/GMHCC. The software and the supporting data can be downloaded from: https://figshare.com/articles/software/GMHCC/17111291. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Single-cell RNA sequencing (scRNA-seq) can provide insight into gene expression patterns at the resolution of individual cells, which offers new opportunities to study the behavior of different cell types. However, it is often plagued by dropout events, a phenomenon where the expression value of a gene tends to be measured as zero in the expression matrix due to various technical defects. RESULTS: In this article, we argue that borrowing gene and cell information across column and row subspaces directly results in suboptimal solutions due to the noise contamination in imputing dropout values. Thus, to impute more precisely the dropout events in scRNA-seq data, we develop a regularization for leveraging that imperfect prior information to estimate the true underlying prior subspace and then embed it in a typical low-rank matrix completion-based framework, named scWMC. To evaluate the performance of the proposed method, we conduct comprehensive experiments on simulated and real scRNA-seq data. Extensive data analysis, including simulated analysis, cell clustering, differential expression analysis, functional genomic analysis, cell trajectory inference and scalability analysis, demonstrate that our method produces improved imputation results compared to competing methods that benefits subsequent downstream analysis. AVAILABILITY AND IMPLEMENTATION: The source code is available at https://github.com/XuYuanchi/scWMC and test data is available at https://doi.org/10.5281/zenodo.6832477. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: RNA-binding proteins (RBPs) are a group of proteins associated with RNA regulation and metabolism, and play an essential role in mediating the maturation, transport, localization and translation of RNA. Recently, Genome-wide RNA-binding event detection methods have been developed to predict RBPs. Unfortunately, the existing computational methods usually suffer some limitations, such as high-dimensionality, data sparsity and low model performance. RESULTS: Deep convolution neural network has a useful advantage for solving high-dimensional and sparse data. To improve further the performance of deep convolution neural network, we propose evolutionary deep convolutional neural network (EDCNN) to identify protein-RNA interactions by synergizing evolutionary optimization with gradient descent to enhance deep conventional neural network. In particular, EDCNN combines evolutionary algorithms and different gradient descent models in a complementary algorithm, where the gradient descent and evolution steps can alternately optimize the RNA-binding event search. To validate the performance of EDCNN, an experiment is conducted on two large-scale CLIP-seq datasets, and results reveal that EDCNN provides superior performance to other state-of-the-art methods. Furthermore, time complexity analysis, parameter analysis and motif analysis are conducted to demonstrate the effectiveness of our proposed algorithm from several perspectives. AVAILABILITY AND IMPLEMENTATION: The EDCNN algorithm is available at GitHub: https://github.com/yaweiwang1232/EDCNN. Both the software and the supporting data can be downloaded from: https://figshare.com/articles/software/EDCNN/16803217. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Enhancers are short non-coding DNA sequences outside of the target promoter regions that can be bound by specific proteins to increase a gene's transcriptional activity, which has a crucial role in the spatiotemporal and quantitative regulation of gene expression. However, enhancers do not have a specific sequence motifs or structures, and their scattered distribution in the genome makes the identification of enhancers from human cell lines particularly challenging. Here we present a novel, stacked multivariate fusion framework called SMFM, which enables a comprehensive identification and analysis of enhancers from regulatory DNA sequences as well as their interpretation. Specifically, to characterize the hierarchical relationships of enhancer sequences, multi-source biological information and dynamic semantic information are fused to represent regulatory DNA enhancer sequences. Then, we implement a deep learning-based sequence network to learn the feature representation of the enhancer sequences comprehensively and to extract the implicit relationships in the dynamic semantic information. Ultimately, an ensemble machine learning classifier is trained based on the refined multi-source features and dynamic implicit relations obtained from the deep learning-based sequence network. Benchmarking experiments demonstrated that SMFM significantly outperforms other existing methods using several evaluation metrics. In addition, an independent test set was used to validate the generalization performance of SMFM by comparing it to other state-of-the-art enhancer identification methods. Moreover, we performed motif analysis based on the contribution scores of different bases of enhancer sequences to the final identification results. Besides, we conducted interpretability analysis of the identified enhancer sequences based on attention weights of EnhancerBERT, a fine-tuned BERT model that provides new insights into exploring the gene semantic information likely to underlie the discovered enhancers in an interpretable manner. Finally, in a human placenta study with 4,562 active distal gene regulatory enhancers, SMFM successfully exposed tissue-related placental development and the differential mechanism, demonstrating the generalizability and stability of our proposed framework.

Patient stratification has been studied widely to tackle subtype diagnosis problems for effective treatment. Due to the dimensionality curse and poor interpretability of data, there is always a long-lasting challenge in constructing a stratification model with high diagnostic ability and good generalization. To address these problems, this article proposes two novel evolutionary multiobjective clustering algorithms with ensemble (NSGA-II-ECFE and MOEA/D-ECFE) with four cluster validity indices used as the objective functions. First, an effective ensemble construction method is developed to enrich the ensemble diversity. After that, an ensemble clustering fitness evaluation (ECFE) method is proposed to evaluate the ensembles by measuring the consensus clustering under those four objective functions. To generate the consensus clustering, ECFE exploits the hybrid co-association matrix from the ensembles and then dynamically selects the suitable clustering algorithm on that matrix. Multiple experiments have been conducted to demonstrate the effectiveness of the proposed algorithm in comparison with seven clustering algorithms, twelve ensemble clustering approaches, and two multiobjective clustering algorithms on 55 synthetic datasets and 35 real patient stratification datasets. The experimental results demonstrate the competitive edges of the proposed algorithms over those compared methods. Furthermore, the proposed algorithm is applied to extend its advantages by identifying cancer subtypes from five cancer-related single-cell RNA-seq datasets.

Prostate cancer is the second leading cancer in men, according to the WHO world cancer report. Its prevention and treatment demand proper attention. Despite numerous attempts for disease prevention, prostate tumours can still become metastatic by blood circulation to other organs. Several treatments have been adopted. However, findings show that the docetaxel treatment induces adverse reactions in patients. Particle Swarm Optimized Gaussian Process Classifier (PSO-GPC) is proposed to determine when to discontinue treatment. Based on three cohorts of prostate cancer patients, we propose and compare several classifiers for the best performance in determining treatment discontinuation. Given the data skewness and class imbalance, the models are evaluated based on both the area under receiver operating characteristics curve (AUC) and area under precision recall curve (AUPRC). With the AUCs ranging between 0.6717-0.8499, and AUPRCs ranging between 0.1392-0.5423, PSO-GPC performs better than the state-of-the-art. We have carried out statistical analysis for ranking methods and analyzed independent cohort data with PSO-GPC, demonstrating its unbiased performance. A proper determination of treatment discontinuation in metastatic castration-resistant prostate cancer patients will reduce the mortality rate in cancer patients.

Exploring the prognostic classification and biomarkers in Head and Neck Squamous Carcinoma (HNSC) is of great clinical significance. We hybridized three prominent strategies to comprehensively characterize the molecular features of HNSC. We constructed a 15-gene signature to predict patients' death risk with an average AUC of 0.744 for 1-, 3-, and 5-year on TCGA-HNSC training set, and average AUCs of 0.636, 0.584, 0.755 in GSE65858, GSE-112026, CPTAC-HNSCC datasets, respectively. By combined with NMF clustering and consensus clustering of fraction of tumor immune cell infiltration (ICI) in the tumor microenvironment (TME), we captured a more refined biological characteristics of HNSC, and observed a prognosis heterogeneity in high tumor immunity patients. By matching tumor subset-specific expression signatures to drug-induced cell line expression profiles from large-scale pharmacogenomic databases in the OCTAD workspace, we identified a group of HNSC patients featured with poor prognosis and demonstrated that the individuals in this group are likely to receive increased drug sensitivity to reverse differentially expressed disease signature genes. This trend is especially highlighted among those with higher death risk and tumour immunity.

Single-cell RNA sequencing is a transformative technology that enables us to study the heterogeneity of the tissue at the cellular level. Clustering is used as the key computational approach to group cells under the transcriptome profiles from single-cell RNA-seq data. However, accurate identification of distinct cell types is facing the challenge of high dimensionality, and it could cause uninformative clusters when clustering is directly applied on the original transcriptome. To address such challenge, an evolutionary multiobjective deep clustering (EMDC) algorithm is proposed to identify single-cell RNA-seq data in this study. First, EMDC removes redundant and irrelevant genes by applying the differential gene expression analysis to identify differentially expressed genes across biological conditions. After that, a deep autoencoder is proposed to project the high-dimensional data into different low-dimensional nonlinear embedding subspaces under different bottleneck layers. Then, the basic clustering algorithm is applied in those nonlinear embedding subspaces to generate some basic clustering results to produce the cluster ensemble. To lessen the unnecessary cost produced by those clusterings in the ensemble, the multiobjective evolutionary optimization is designed to prune the basic clustering results in the ensemble, unleashing its cell type discovery performance under three objective functions. Multiple experiments have been conducted on 30 synthetic single-cell RNA-seq datasets and six real single-cell RNA-seq datasets, which reveal that EMDC outperforms eight other clustering methods and three multiobjective optimization algorithms in cell type identification. In addition, we have conducted extensive comparisons to effectively demonstrate the impact of each component in our proposed EMDC.

Mitochondria are membrane-bound organelles containing over 1000 different proteins involved in mitochondrial function, gene expression and metabolic processes. Accurate localization of those proteins in the mitochondrial compartments is critical to their operation. A few computational methods have been developed for predicting submitochondrial localization from the protein sequences. Unfortunately, most of these computational methods focus on employing biological features or evolutionary information to extract sequence features, which greatly limits the performance of subsequent identification. Moreover, the efficiency of most computational models is still under explored, especially the deep learning feature, which is promising but requires improvement. To address these limitations, we propose a novel computational method called iDeepSubMito to predict the location of mitochondrial proteins to the submitochondrial compartments. First, we adopted a coding scheme using the ProteinELMo to model the probability distribution over the protein sequences and then represent the protein sequences as continuous vectors. Then, we proposed and implemented convolutional neural network architecture based on the bidirectional LSTM with self-attention mechanism, to effectively explore the contextual information and protein sequence semantic features. To demonstrate the effectiveness of our proposed iDeepSubMito, we performed cross-validation on two datasets containing 424 proteins and 570 proteins respectively, and consisting of four different mitochondrial compartments (matrix, inner membrane, outer membrane and intermembrane regions). Experimental results revealed that our method outperformed other computational methods. In addition, we tested iDeepSubMito on the M187, M983 and MitoCarta3.0 to further verify the efficiency of our method. Finally, the motif analysis and the interpretability analysis were conducted to reveal novel insights into subcellular biological functions of mitochondrial proteins. iDeepSubMito source code is available on GitHub at https://github.com/houzl3416/iDeepSubMito.

The identification of hidden responders is often an essential challenge in precision oncology. A recent attempt based on machine learning has been proposed for classifying aberrant pathway activity from multiomic cancer data. However, we note several critical limitations there, such as high-dimensionality, data sparsity and model performance. Given the central importance and broad impact of precision oncology, we propose nature-inspired deep Ras activation pan-cancer (NatDRAP), a deep neural network (DNN) model, to address those restrictions for the identification of hidden responders. In this study, we develop the nature-inspired deep learning model that integrates bulk RNA sequencing, copy number and mutation data from PanCanAltas to detect pan-cancer Ras pathway activation. In NatDRAP, we propose to synergize the nature-inspired artificial bee colony algorithm with different gradient-based optimizers in one framework for optimizing DNNs in a collaborative manner. Multiple experiments were conducted on 33 different cancer types across PanCanAtlas. The experimental results demonstrate that the proposed NatDRAP can provide superior performance over other benchmark methods with strong robustness towards diagnosing RAS aberrant pathway activity across different cancer types. In addition, gene ontology enrichment and pathological analysis are conducted to reveal novel insights into the RAS aberrant pathway activity identification and characterization. NatDRAP is written in Python and available at https://github.com/lixt314/NatDRAP1.

In recent years, single-cell RNA sequencing (scRNA-seq) technologies have been widely adopted to interrogate gene expression of individual cells; it brings opportunities to understand the underlying processes in a high-throughput manner. Deep embedded clustering (DEC) was demonstrated successful in high-dimensional sparse scRNA-seq data by joint feature learning and cluster assignment for identifying cell types simultaneously. However, the deep network architecture for embedding clustering is not trivial to optimize. Therefore, we propose an evolutionary multiobjective DEC by synergizing the multiobjective evolutionary optimization to simultaneously evolve the hyperparameters and architectures of DEC in an automatic manner. Firstly, a denoising autoencoder is integrated into the DEC to project the high-dimensional sparse scRNA-seq data into a low-dimensional space. After that, to guide the evolution, three objective functions are formulated to balance the model's generality and clustering performance for robustness. Meanwhile, migration and mutation operators are proposed to optimize the objective functions to select the suitable hyperparameters and architectures of DEC in the multiobjective framework. Multiple comparison analyses are conducted on twenty synthetic data and eight real data from different representative single-cell sequencing platforms to validate the effectiveness. The experimental results reveal that the proposed algorithm outperforms other state-of-the-art clustering methods under different metrics. Meanwhile, marker genes identification, gene ontology enrichment and pathology analysis are conducted to reveal novel insights into the cell type identification and characterization mechanisms.

Circular RNAs (circRNAs) are widely expressed in eukaryotes. The genome-wide interactions between circRNAs and RNA-binding proteins (RBPs) can be probed from cross-linking immunoprecipitation with sequencing data. Therefore, computational methods have been developed for identifying RBP binding sites on circRNAs. Unfortunately, those computational methods often suffer from the low discriminative power of feature representations, numerical instability and poor scalability. To address those limitations, we propose a novel computational method called iCircRBP-DHN using deep hierarchical network for discriminating circRNA-RBP binding sites. The network architecture can be regarded as a deep multi-scale residual network followed by bidirectional gated recurrent units (BiGRUs) with the self-attention mechanism, which can simultaneously extract local and global contextual information. Meanwhile, we propose novel encoding schemes by integrating CircRNA2Vec and the K-tuple nucleotide frequency pattern to represent different degrees of nucleotide dependencies. To validate the effectiveness of our proposed iCircRBP-DHN, we compared its performance with other computational methods on 37 circRNAs datasets and 31 linear RNAs datasets, respectively. The experimental results reveal that iCircRBP-DHN can achieve superior performance over those state-of-the-art algorithms. Moreover, we perform motif analysis on circRNAs bound by those different RBPs, demonstrating that our proposed CircRNA2Vec encoding scheme can be promising. The iCircRBP-DHN method is made available at https://github.com/houzl3416/iCircRBP-DHN.

Haploinsufficiency, wherein a single allele is not enough to maintain normal functions, can lead to many diseases including cancers and neurodevelopmental disorders. Recently, computational methods for identifying haploinsufficiency have been developed. However, most of those computational methods suffer from study bias, experimental noise and instability, resulting in unsatisfactory identification of haploinsufficient genes. To address those challenges, we propose a deep forest model, called HaForest, to identify haploinsufficient genes. The multiscale scanning is proposed to extract local contextual representations from input features under Linear Discriminant Analysis. After that, the cascade forest structure is applied to obtain the concatenated features directly by integrating decision-tree-based forests. Meanwhile, to exploit the complex dependency structure among haploinsufficient genes, the LightGBM library is embedded into HaForest to reveal the highly expressive features. To validate the effectiveness of our method, we compared it to several computational methods and four deep learning algorithms on five epigenomic data sets. The results reveal that HaForest achieves superior performance over the other algorithms, demonstrating its unique and complementary performance in identifying haploinsufficient genes. The standalone tool is available at https://github.com/yangyn533/HaForest.

Gene-expression profiling can define the cell state and gene-expression pattern of cells at the genetic level in a high-throughput manner. With the development of transcriptome techniques, processing high-dimensional genetic data has become a major challenge in expression profiling. Thanks to the recent widespread use of matrix decomposition methods in bioinformatics, a computational framework based on compressed sensing was adopted to reduce dimensionality. However, compressed sensing requires an optimization strategy to learn the modular dictionaries and activity levels from the low-dimensional random composite measurements to reconstruct the high-dimensional gene-expression data. Considering this, here we introduce and compare four compressed sensing frameworks coming from nature-inspired optimization algorithms (CSCS, ABCCS, BACS and FACS) to improve the quality of the decompression process. Several experiments establish that the three proposed methods outperform benchmark methods on nine different datasets, especially the FACS method. We illustrate therefore, the robustness and convergence of FACS in various aspects; notably, time complexity and parameter analyses highlight properties of our proposed FACS. Furthermore, differential gene-expression analysis, cell-type clustering, gene ontology enrichment and pathology analysis are conducted, which bring novel insights into cell-type identification and characterization mechanisms from different perspectives. All algorithms are written in Python and available at https://github.com/Philyzh8/Nature-inspired-CS.

MOTIVATION: The early detection of cancer through accessible blood tests can foster early patient interventions. Although there are developments in cancer detection from cell-free DNA (cfDNA), its accuracy remains speculative. Given its central importance with broad impacts, we aspire to address the challenge. METHOD: A bagging Ensemble Meta Classifier (CancerEMC) is proposed for early cancer detection based on circulating protein biomarkers and mutations in cfDNA from blood. CancerEMC is generally designed for both binary cancer detection and multi-class cancer type localization. It can address the class imbalance problem in multi-analyte blood test data based on robust oversampling and adaptive synthesis techniques. RESULTS: Based on the clinical blood test data, we observe that the proposed CancerEMC has outperformed other algorithms and state-of-the-arts studies (including CancerSEEK) for cancer detection. The results reveal that our proposed method (i.e. CancerEMC) can achieve the best performance result for both binary cancer classification with 99.17% accuracy (AUC = 0.999) and localized multiple cancer detection with 74.12% accuracy (AUC = 0.938). Addressing the data imbalance issue with oversampling techniques, the accuracy can be increased to 91.50% (AUC = 0.992), where the state-of-the-art method can only be estimated at 69.64% (AUC = 0.921). Similar results can also be observed on independent and isolated testing data. AVAILABILITY: https://github.com/saifurcubd/Cancer-Detection. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Transcriptomic profiling plays an important role in post-genomic analysis. Especially, the single-cell RNA-seq technology has advanced our understanding of gene expression from cell population level into individual cell level. Many computational methods have been proposed to decipher transcriptomic profiles from those RNA-seq data. However, most of the related algorithms suffer from realistic restrictions such as high dimensionality and premature convergence. In this paper, we propose and formulate an evolutionary multiobjective blind compressed sensing (EMOBCS) to address those problems for evolving transcriptomic profiles from single-cell RNA-seq data. In the proposed framework, to characterize various gene expression profile models, two objective functions including chi-squared kernel score and euclidean distance of different gene expression profiles are formulated. After that, multiobjective blind compressed sensing based on artificial bee colony is designed to optimize the two objective functions on single-cell RNA-seq data by proposing a rank probability model and two new search strategies into the cooperative convolution framework in an unbiased manner. To demonstrate its effectiveness, extensive experiments have been conducted, comparing the proposed algorithm with 14 algorithms including eight state-of-the-art algorithms and six different EMOBCS algorithms under different search strategies on 10 single-cell RNA-seq datasets and one case study. The experimental results reveal that the proposed algorithm is better than or comparable with those compared algorithms. Furthermore, we also conduct the time complexity analysis, convergence analysis, and parameter analysis to demonstrate various properties of EMOBCS.

Detection and diagnosis of cancer are especially essential for early prevention and effective treatments. Many studies have been proposed to tackle the subtype diagnosis problems with those data, which often suffer from low diagnostic ability and bad generalization. This article studies a multiobjective PSO-based hybrid algorithm (MOPSOHA) to optimize four objectives including the number of features, the accuracy, and two entropy-based measures: the relevance and the redundancy simultaneously, diagnosing the cancer data with high classification power and robustness. First, we propose a novel binary encoding strategy to choose informative gene subsets to optimize those objective functions. Second, a mutation operator is designed to enhance the exploration capability of the swarm. Finally, a local search method based on the "best/1" mutation operator of differential evolutionary algorithm (DE) is employed to exploit the neighborhood area with sparse high-quality solutions since the base vector always approaches to some good promising areas. In order to demonstrate the effectiveness of MOPSOHA, it is tested on 41 cancer datasets including thirty-five cancer gene expression datasets and six independent disease datasets. Compared MOPSOHA with other state-of-the-art algorithms, the performance of MOPSOHA is superior to other algorithms in most of the benchmark datasets.

RNA-binding proteins (RBPs) are the master regulators of mRNA processing, which are vital players for the post-transcriptional control of gene expression. In recent years, crosslinking immunoprecipitation sequencing (CLIP-seq) technologies have enabled us to sequence massive amounts of genome-wide RNA-binding event data. Its increasing availability provides opportunities to identify protein-RNA interactions on a genome-wide scale. Genome-wide RNA-binding event detection methods have been developed to the understanding of the proteins' functions within cellular processes. Unfortunately, those methods often suffer from realistic restrictions, such as high costs, intensive computation, high dimensionality, numerical instability, and data sparsity. We present a computational method [multiobjective forest algorithm (MFA)] to identify protein-RNA interactions from CLIP-seq data by synergizing multiobjective biogeography-based optimization (BBO) with random forest (RF). Since most of the tree-structured classifiers in RF are unnecessarily bulky with extra time costs and memory consumption, multiobjective BBO is designed to prune the unsuitable tree-structured classifiers dynamically. Moreover, to direct the evolution dynamics of the MFA, two objective functions are formulated to balance model generality and complexity for robust performance. To validate our MFA method, we compare its performance across 31 large-scale CLIP-seq datasets. The experimental results demonstrate that MFA can obtain superior performance over the current state-of-the-art methods. Mechanistic insights are also revealed and discussed to explore the multifaceted aspects of MFA through data source importance analysis, matrix rank estimations, seeding component perturbations, and multiobjective optimization methodology comparisons.

Transcriptomic profiling is a high-throughput approach to measure gene expression levels under different experimental conditions at different timings. With the development of the related technologies such as single-cell RNA-Seq, the dimensions of gene expression data are increased to hundreds of thousands or more for high-resolution insights. There is a long-lasting challenge in exploiting the relations between transcriptomic profiles and random composite measurements. To address it, we proposed a mathematical framework based on differential evolution (global search) with the help of compressed sensing (local search) termed as DECS. Exploiting the inherent sparse nature of gene expression data, the proposed DECS method can learn the sparse module dictionaries and levels from the low-dimensional random composite measurements for reconstructing the high-dimensional gene expression data with significant orders of magnitude (e.g. 200 × ). Several experiments were conducted to compare DECS with three benchmark methods, demonstrating that the proposed DECS outperforms the benchmark methods and can recover most of the gene expression patterns. The underlying reasons are discussed and illustrated by revealing the related mechanistic insights through extensive benchmarks on nine GSE datasets and their sensitivity analysis.

In recent years, single-cell RNA sequencing reveals diverse cell genetics at unprecedented resolutions. Such technological advances enable researchers to uncover the functionally distinct cell subtypes such as hematopoietic stem cell subpopulation identification. However, most of the related algorithms have been hindered by the high-dimensionality and sparse nature of single-cell RNA sequencing (RNA-seq) data. To address those problems, we propose a multiobjective evolutionary clustering based on adaptive non-negative matrix factorization (MCANMF) for multiobjective single-cell RNA-seq data clustering. First, adaptive non-negative matrix factorization is proposed to decompose data for feature extraction. After that, a multiobjective clustering algorithm based on learning vector quantization is proposed to analyze single-cell RNA-seq data. To validate the effectiveness of MCANMF, we benchmark MCANMF against 15 state-of-the-art methods including seven feature extraction methods, seven clustering methods, and the kernel-based similarity learning method on six published single-cell RNA sequencing datasets comprehensively. When compared with those 15 state-of-the-art methods, MCANMF performs better than the others on those single-cell RNA sequencing datasets according to multiple evaluation metrics. Moreover, the MCANMF component analysis, time complexity analysis, and parameter analysis are conducted to demonstrate various properties of our proposed algorithm.

In recent years, the detection of epistatic interactions of multiple genetic variants on the causes of complex diseases brings a significant challenge in genome-wide association studies (GWAS). However, most of the existing methods still suffer from algorithmic limitations such as single-objective optimization, intensive computational requirement, and premature convergence. In this paper, we propose and formulate an epistatic interaction multi-objective artificial bee colony algorithm based on decomposition (EIMOABC/D) to address those problems for genetic interaction detection in genome-wide association studies. First, to direct the genetic interaction detection, two objective functions are formulated to characterize various epistatic models; rank probability model is proposed to sort each population into different nondomination levels based on the fast nondominated sorting approach. After that, the mutual information based local search algorithm is proposed to guide the population search for disease model evaluations in an unbiased manner. To validate the effectiveness of EIMOABC/D, we compare EIMOABC/D against seven state-of-the-art methods on 77 epistatic models including eight small-scale epistatic models with marginal effects, eight large-scale epistatic models with marginal effects, 60 large-scale epistatic models without any marginal effect, and one case study. The experimental results indicate that our proposed algorithm EIMOABC/D outperforms seven state-of-the-art methods on those epistatic models. Furthermore, time complexity analysis and parameter analysis are conducted to demonstrate various properties of our proposed algorithm.

Transcription factors (TFs) are the major components of human gene regulation. In particular, they bind onto specific DNA sequences and regulate neighborhood genes in different tissues at different developmental stages. Non-synonymous single nucleotide polymorphisms on its protein-coding sequences could result in undesired consequences in human. Therefore, it is necessary to develop methods for predicting any abnormality among those non-synonymous single nucleotide polymorphisms. To address it, we have developed and compared different strategies to predict deleterious non-synonymous single nucleotide polymorphisms (also known as missense mutations) on the protein-coding sequences of human TFs. Taking advantage of evolutionary conservation signals, we have developed and compared different classifiers with different feature sets as computed from different evolutionarily related sequence collections. The results indicate that the classic ensemble algorithm, Adaboost with decision stumps, with orthologous sequence collection, has performed the best (namely, TFmedic). We have further compared TFmedic with other state-of-the-arts methods (i.e., PolyPhen-2 and SIFT) on PolyPhen-2's own datasets, demonstrating that TFmedic can outperform the others. As applications, we have further applied TFmedic to all possible missense mutations on all human transcription factors; the proteome-wide results reveal interesting insights, consistent with the existing physiochemical knowledge. A case study with the actual 3D structure is conducted, revealing how TFmedic can be contributed to protein-DNA binding complex studies.

MOTIVATION: In recent years, single-cell RNA sequencing enables us to discover cell types or even subtypes. Its increasing availability provides opportunities to identify cell populations from single-cell RNA-seq data. Computational methods have been employed to reveal the gene expression variations among multiple cell populations. Unfortunately, the existing ones can suffer from realistic restrictions such as experimental noises, numerical instability, high dimensionality and computational scalability. RESULTS: We propose an evolutionary multiobjective ensemble pruning algorithm (EMEP) that addresses those realistic restrictions. Our EMEP algorithm first applies the unsupervised dimensionality reduction to project data from the original high dimensions to low-dimensional subspaces; basic clustering algorithms are applied in those new subspaces to generate different clustering results to form cluster ensembles. However, most of those cluster ensembles are unnecessarily bulky with the expense of extra time costs and memory consumption. To overcome that problem, EMEP is designed to dynamically select the suitable clustering results from the ensembles. Moreover, to guide the multiobjective ensemble evolution, three cluster validity indices including the overall cluster deviation, the within-cluster compactness and the number of basic partition clusters are formulated as the objective functions to unleash its cell type discovery performance using evolutionary multiobjective optimization. We applied EMEP to 55 simulated datasets and seven real single-cell RNA-seq datasets, including six single-cell RNA-seq dataset and one large-scale dataset with 3005 cells and 4412 genes. Two case studies are also conducted to reveal mechanistic insights into the biological relevance of EMEP. We found that EMEP can achieve superior performance over the other clustering algorithms, demonstrating that EMEP can identify cell populations clearly. AVAILABILITY AND IMPLEMENTATION: EMEP is written in Matlab and available at https://github.com/lixt314/EMEP. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: The RNA-guided CRISPR/Cas9 system has been widely applied to genome editing. CRISPR/Cas9 system can effectively edit the on-target genes. Nonetheless, it has recently been demonstrated that many homologous off-target genomic sequences could be mutated, leading to unexpected gene-editing outcomes. Therefore, a plethora of tools were proposed for the prediction of off-target activities of CRISPR/Cas9. Nonetheless, each computational tool has its own advantages and drawbacks under diverse conditions. It is hardly believed that a single tool is optimal for all conditions. Hence, we would like to explore the ensemble learning potential on synergizing multiple tools with genomic annotations together to enhance its predictive abilities. RESULTS: We proposed an ensemble learning framework which synergizes multiple tools together to predict the off-target activities of CRISPR/Cas9 in different combinations. Interestingly, the ensemble learning using AdaBoost outperformed other individual off-target predictive tools. We also investigated the effect of evolutionary conservation (PhyloP and PhastCons) and chromatin annotations (ChromHMM and Segway) and found that only PhyloP can enhance the predictive capabilities further. Case studies are conducted to reveal ensemble insights into the off-target predictions, demonstrating how the current study can be applied in different genomic contexts. The best prediction predicted by AdaBoost is up to 0.9383 (AUC) and 0.2998 (PRC) that outperforms other classifiers. This is ascribable to the fact that AdaBoost introduces a new weak classifier (i.e. decision stump) in each iteration to learn the DNA sequences that were misclassified as off-targets until a small error rate is reached iteratively. AVAILABILITY AND IMPLEMENTATION: The source codes are freely available on GitHub at https://github.com/Alexzsx/CRISPR. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

RNA-binding proteins (RBPs) play an important role in the post-transcriptional control of RNAs, such as splicing, polyadenylation, mRNA stabilization, mRNA localization, and translation. Thanks to the recent breakthrough, non-negative matrix factorization (NMF) has been developed to combine multiple data sources to discover non-overlapping and class-specific RNA binding patterns. However, several challenges still exist in determining the number of latent dimensions in the factorization steps. In most circumstances, it is often assumed that the number of latent dimensions (or components) is given. Such trial-and-error procedures can be tedious in practice. In order to address this problem, differential evolution algorithm is proposed as the model selection method to choose the suitable number of ranks, which can adaptively decompose the input protein-RNA data matrix into different nonnegative components. Experimental results demonstrate that the proposed algorithms can improve the factorization quality over the recent state-of-the-arts. The effectiveness of the proposed algorithms are supported by comprehensive performance benchmarking on 31 genome-wide cross-linking immunoprecipitation (CLIP) coupled with high-throughput sequencing (CLIP-seq) datasets. In addition, time complexity analysis and parameter analysis are conducted to demonstrate the robustness of the proposed methods.

Patient stratification has a major role in enabling efficient and personalized medicine. An important task in patient stratification is to discover disease subtypes for effective treatment. To achieve this goal, the research on clustering algorithms for patient stratification has brought attention from both academia and medical community over the past decades. However, existing clustering algorithms suffer from realistic restrictions such as experimental noises, high dimensionality, and poor interpretability. In particular, the existing clustering algorithms usually determine clustering quality using only one internal evaluation function. Unfortunately, it is obvious that one internal evaluation function is hard to be fitted and robust for all datasets. Therefore, in this paper, a novel multiobjective framework called multiobjective clustering algorithm by fast search and find of density peaks is proposed to address those limitations altogether. In the proposed framework, a parameter candidate population is evolved under multiple objectives to select features and evaluate clustering densities automatically. To guide the multiobjective evolution, five cluster validity indices including compactness, separation, Calinski-Harabasz index, Davies-Bouldin index, and Dunn index, are chosen as the objective functions, capturing multiple characteristics of the evolving clusters. Multiobjective differential evolution algorithm based on decomposition is adopted to optimize those five objective functions simultaneously. To demonstrate its effectiveness, extensive experiments have been conducted, comparing the proposed algorithm with 45 algorithms including nine state-of-the-art clustering algorithms, five multiobjective evolutionary algorithms, and 31 baseline algorithms under different objective subsets on 94 datasets featuring 35 real patient stratification datasets, 55 synthetic datasets based on a real human transcription regulation network model, and four other medical datasets. The numerical results reveal that the proposed algorithm can achieve better or competitive solutions than the others. Besides, time complexity analysis, convergence analysis, and parameter analysis are conducted to demonstrate the robustness of the proposed algorithm from different perspectives.

In the past years, the high-throughput sequencing technologies have enabled massive insights into genomic annotations. In contrast, the full-scale three-dimensional arrangements of genomic regions are relatively unknown. Thanks to the recent breakthroughs in High-throughput Chromosome Conformation Capture (Hi-C) techniques, non-negative matrix factorization (NMF) has been adopted to identify local spatial clusters of genomic regions from Hi-C data. However, such non-negative matrix factorization entails a high-dimensional non-convex objective function to be optimized with non-negative constraints. We propose and compare more than ten optimization algorithms to improve the identification of local spatial clusters via NMF. To circumvent and optimize the high-dimensional, non-convex, and constrained objective function, we draw inspiration from the nature to perform in silico evolution. The proposed algorithms consist of a population of candidates to be evolved while the NMF acts as local search during the evolutions. The population based optimization algorithm coordinates and guides the non-negative matrix factorization toward global optima. Experimental results show that the proposed algorithms can improve the quality of non-negative matrix factorization over the recent state-of-the-arts. The effectiveness and robustness of the proposed algorithms are supported by comprehensive performance benchmarking on chromosome-wide Hi-C contact maps of yeast and human. In addition, time complexity analysis, convergence analysis, parameter analysis, biological case studies, and gene ontology similarity analysis are conducted to demonstrate the robustness of the proposed methods from different perspectives.

One of the main challenges in modern medic-ine is to stratify patients for personalized care. Many different clustering methods have been proposed to solve the problem in both quantitative and biologically meaningful manners. However, existing clustering algorithms suffer from numerous restrictions such as experimental noises, high dimensionality, and poor interpretability. To overcome those limitations altogether, we propose and formulate a multiobjective framework based on evolutionary multiobjective optimization to balance the feature relevance and redundancy for patient stratification. To demonstrate the effectiveness of our proposed algorithms, we benchmark our algorithms across 55 synthetic datasets based on a real human transcription regulation network model, 35 real cancer gene expression datasets, and two case studies. Experimental results suggest that the proposed algorithms perform better than the recent state-of-the-arts. In addition, time complexity analysis, convergence analysis, and parameter analysis are conducted to demonstrate the robustness of the proposed methods from different perspectives. Finally, the t-Distributed Stochastic Neighbor Embedding (t-SNE) is applied to project the selected feature subsets onto two or three dimensions to visualize the high-dimensional patient stratification data.

In this paper, we propose a novel hybrid binary animal migration optimization (BAMO) with k-nearest neighbor approach (KNN) to predict apoptosis protein sequences using statistical factors and dipeptide composition. Binary animal migration optimization is used for selecting a near-optimal subset of informative features that is most relevant for the classification. K-nearest neighbor approach is used as the classifier with the jackknife cross-validation. Finally, BAMOKNN is tested on a dataset including 317 proteins. Our method achieves the accuracy of 92.43%. Then, our model also tests on a testing dataset including 98 apoptosis proteins and obtains the accuracy of 94.90%. High prediction accuracy and successful prediction of apoptosis proteins suggest that BAMOKNN can be a useful approach to identify apoptosis protein locations.

This paper investigates the problem of minimizing makespan for the distributed assembly permutation flowshop scheduling problem (DAPFSP)-a new generalization of the distributed permutation flowshop scheduling problem (DPFSP). DAPFSP consists of two stages: production and assembly. The first stage is production at several identical factories. Each factory is a permutation flowshop scheduling problem with multi-machine. And the second stage is to assemble jobs produced at the first stage into final products. We proposed a genetic algorithm for this problem. An enhanced crossover strategy and three different local searches are adopted. After the exhaustive computational and statistical analysis, we can conclude that the proposed methods are robust and outperformed the existing algorithm.

The permutation flow shop problem (PFSSP) is a well-known difficult combinatorial optimization problem. In this paper, we present a new hybrid optimization algorithm named SIGSA to solve the PFSSP. This algorithm is composed by the LRV rule, SA-based local search and IIS-based local search. First, to make GSA suitable for PFSSP, a new LRV rule based on random key is introduced to convert the continuous position in GSA to the discrete job permutation. Second, to enhance the searching capability, the SA-based local search is designed to help the algorithm to escape from local minimum. Then, the IIS-based local search is used for enhancing the individuals in GSA with a certain probability. Additionally, Comparison with other results in the literature shows that the SIGSA is an efficient and effective approach for the PFSSP.