Single-cell transcriptomics characterizes gene expression profiles at the single-cell level, offering an unprecedented opportunity to understand cellular systems. As a fundamental task in single-cell data analysis, cell clustering significantly contributes to identifying cellular heterogeneity, thereby affecting downstream analyses. A number of deep learning methods have been proposed for clustering single-cell RNA sequencing (scRNA-seq) data. However, the large parameter space makes these methods sensitive to parameter settings. To leverage the strong capabilities of deep learning in capturing complex structures in single-cell data while ensuring algorithmic robustness, we propose a contrastive ensemble learning method named scRECL for scRNA-seq data clustering. In our approach, Siamese neural networks are trained under various $k$-nearest neighbors partitions to obtain low-dimensional embeddings of the scRNA-seq data. Multiplex graphs in representative element selection help filter out noisy and redundant cells. Consequently, contrastive ensemble learning is performed for efficient and effective latent embedding, as well as robust analysis of cellular heterogeneity in scRNA-seq data.

This article proposes a strategy to accelerate the convergence of iterative learning control (ILC) while maintaining robustness against stochastic noise. The strategy adaptively reweights the error signals used in conventional ILC schemes, casting greater influence to larger errors during input updates, thereby accelerating the correction of noisy inputs and improving overall convergence behavior. Furthermore, to mitigate the impact of noise-dominated small errors on weight computation, a saturation mechanism is introduced. A convergence theorem is established to characterize how the saturation parameters affect the asymptotic convergence of the input deviation-induced errors. Simulation and experimental results demonstrate that incorporating this strategy consistently improves convergence speed while maintaining tracking accuracy across different ILC implementations.

With the emergence of large amount of single-cell RNA sequencing (scRNA-seq) data, the exploration of computational methods has become critical in revealing biological mechanisms. Clustering is a representative for deciphering cellular heterogeneity embedded in scRNA-seq data. However, due to the diversity of datasets, none of the existing single-cell clustering methods shows overwhelming performance on all datasets. Weighted ensemble methods are proposed to integrate multiple results to improve heterogeneity analysis performance. These methods are usually weighted by considering the reliability of the base clustering results, ignoring the performance difference of the same base clustering on different cells. In this paper, we propose a high-order element-wise weighting strategy based self-representative ensemble learning framework: scEWE. By assigning different base clustering weights to individual cells, we construct and optimize the consensus matrix in a careful and exquisite way. In addition, we extracted the high-order information between cells, which enhanced the ability to represent the similarity relationship between cells. scEWE is experimentally shown to significantly outperform the state-of-the-art methods, which strongly demonstrates the effectiveness of the method and supports the potential applications in complex single-cell data analytical problems.

MOTIVATION: Continuous advancements in single-cell RNA sequencing (scRNA-seq) technology have enabled researchers to further explore the study of cell heterogeneity, trajectory inference, identification of rare cell types, and neurology. Accurate scRNA-seq data clustering is crucial in single-cell sequencing data analysis. However, the high dimensionality, sparsity, and presence of "false" zero values in the data can pose challenges to clustering. Furthermore, current unsupervised clustering algorithms have not effectively leveraged prior biological knowledge, making cell clustering even more challenging. RESULTS: This study investigates a semisupervised clustering model called scTPC, which integrates the triplet constraint, pairwise constraint, and cross-entropy constraint based on deep learning. Specifically, the model begins by pretraining a denoising autoencoder based on a zero-inflated negative binomial distribution. Deep clustering is then performed in the learned latent feature space using triplet constraints and pairwise constraints generated from partial labeled cells. Finally, to address imbalanced cell-type datasets, a weighted cross-entropy loss is introduced to optimize the model. A series of experimental results on 10 real scRNA-seq datasets and five simulated datasets demonstrate that scTPC achieves accurate clustering with a well-designed framework. AVAILABILITY AND IMPLEMENTATION: scTPC is a Python-based algorithm, and the code is available from https://github.com/LF-Yang/Code or https://zenodo.org/records/10951780.

Increasing evidence has indicated that RNA-binding proteins (RBPs) play an essential role in mediating alternative splicing (AS) events during epithelial-mesenchymal transition (EMT). However, due to the substantial cost and complexity of biological experiments, how AS events are regulated and influenced remains largely unknown. Thus, it is important to construct effective models for inferring hidden RBP-AS event associations during EMT process. In this paper, a novel and efficient model was developed to identify AS event-related candidate RBPs based on Adaptive Graph-based Multi-Label learning (AGML). In particular, we propose to adaptively learn a new affinity graph to capture the intrinsic structure of data for both RBPs and AS events. Multi-view similarity matrices are employed for maintaining the intrinsic structure and guiding the adaptive graph learning. We then simultaneously update the RBP and AS event associations that are predicted from both spaces by applying multi-label learning. The experimental results have shown that our AGML achieved AUC values of 0.9521 and 0.9873 by 5-fold and leave-one-out cross-validations, respectively, indicating the superiority and effectiveness of our proposed model. Furthermore, AGML can serve as an efficient and reliable tool for uncovering novel AS events-associated RBPs and is applicable for predicting the associations between other biological entities.

This study investigates the trajectory tracking problem for stochastic systems and proposes a novel adaptive gain design to enhance the transient convergence performance of the learning control scheme. Differing from the existing results that mainly focused on gain's transition from constant to decreasing ones to suppress noise influence, this study leverages the adaptive mechanisms based on noisy signals to achieve an acceleration capability by addressing diverse performance at different time instants throughout the operation interval. Specifically, an additional gain matrix is introduced into the adaptive gain design to further enhance transient convergence performance. An iterative learning control approach with such a gain design is proposed to realize high precision tracking and it is proven that the input error generated by the newly proposed learning control scheme converges almost surely to zero. The effectiveness of the proposed scheme and its improvement on the transient performance of the learning process are numerically validated.

This study uses a multistage learning mechanism concept to investigate the accelerated learning control for stochastic systems. In this mechanism, the learning iterations are divided into successive stages, with each stage comprising several iterations. The learning gain is constant in each stage to accelerate the learning process and decreases it from one stage to another to eliminate the noise effect asymptotically. The critical issue is determining the switching iteration when a new stage starts. This study resolves this issue by calculating a virtual performance index of the mean-squared input error and its estimated upper bound. Specifically, the ideal, practical, and improved multistage learning control schemes are proposed to determine the switching iteration and generate the learning gain sequence. The ideal scheme achieves the best performance at the cost of a large computation burden, and the practical scheme saves computation cost, but the performance is not excellent. The improved scheme significantly approximates the best performance by introducing additional stretching parameters to the performance index. Illustrative simulations are provided to verify the theoretical results.

In this study, we investigate the accelerated learning control schemes for point-to-point tracking systems (PTSs) with measurement noise. The asymptotic convergence of the generated input sequence has been a long-standing open issue for point-to-point tracking problems because there are infinite possible input candidates that can drive the system dynamics to track the desired reference at specified time instants. An accelerated gradient algorithm and its generalized version with a novel direction regulation matrix are proposed, with the learning gain is adaptively triggered by the practical tracking errors. The learning gain remains constant at the early stage and begins to decrease after a certain number of iterations. The input sequence generated by the proposed scheme converges to a specified limit for any fixed initial input, with the limit being closest to the initial input, in a certain sense. Numerical simulations are provided to verify the theoretical results.

MOTIVATION: Simultaneous profiling of multi-omics single-cell data represents exciting technological advancements for understanding cellular states and heterogeneity. Cellular indexing of transcriptomes and epitopes by sequencing allowed for parallel quantification of cell-surface protein expression and transcriptome profiling in the same cells; methylome and transcriptome sequencing from single cells allows for analysis of transcriptomic and epigenomic profiling in the same individual cells. However, effective integration method for mining the heterogeneity of cells over the noisy, sparse, and complex multi-modal data is in growing need. RESULTS: In this article, we propose a multi-modal high-order neighborhood Laplacian matrix optimization framework for integrating the multi-omics single-cell data: scHoML. Hierarchical clustering method was presented for analyzing the optimal embedding representation and identifying cell clusters in a robust manner. This novel method by integrating high-order and multi-modal Laplacian matrices would robustly represent the complex data structures and allow for systematic analysis at the multi-omics single-cell level, thus promoting further biological discoveries. AVAILABILITY AND IMPLEMENTATION: Matlab code is available at https://github.com/jianghruc/scHoML.

Advances in single-cell RNA sequencing (scRNA-seq) technology provide an unbiased and high-throughput analysis of each cell at single-cell resolution, and further facilitate the development of cellular heterogeneity analysis. Despite the promise of scRNA-seq, the data generated by this method are sparse and noisy because of the presence of dropout events, which can greatly impact downstream analyses such as differential gene expression, cell type annotation, and linage trajectory reconstruction. The development of effective and robust computational methods to address both dropout and clustering are thus urgently needed. In this study, we propose a flexible, accurate two-stage algorithm for single cell heterogeneity analysis via hierarchical clustering based on an optimal imputation strategy, called scHOIS. At the first stage, masked non-negative matrix factorization is applied to approximate the original observed scRNA-seq data, with optimal rank determined by variance analysis. At the second stage, hierarchical clustering is applied to group the imputed cells using Pearson correlation to measure similarity, with the optimal number of clusters determined by integrating three classical indexes. We performed extensive experiments on real-world datasets, which showed that scHOIS effectively and robustly distinguished cellular differences and that the clustering performance of this algorithm was superior to that of other state-of-the-art methods.

This article studies the conflicting goals of high-precision tracking and quick convergence speed, which is a longstanding problem in the learning control of stochastic systems. In such systems, a decreasing gain sequence is necessary to ensure the asymptotic convergence of the generated input sequence to a fixed limit. However, the convergence speed is adversely affected by gain sequences of this nature. In this article, we propose a novel multistage learning control strategy to resolve this conflict, where each stage consists of several iterations. The learning gain remains constant in each stage but is reduced at the transition from a given stage to the subsequent stage. The switching iteration between two stages is determined by the tracking performance index of the contracted input error and the accumulated noise drift. Furthermore, an improved mechanism is proposed to optimize the lengths of the different stages. The asymptotic convergence of the input sequence generated by the newly proposed strategy is strictly established by thoroughly analyzing the properties of the proposed gain sequence. Numerical simulations are presented to verify the theoretical results.

In reality such as a rehabilitation training, a repetitive control is necessary but the operational lengths may be iteration varying due to health condition. For the issue, this article investigates an intermittent optimal learning control scheme that considers the partially available information for the learning processing. The performance index is to minimize the summation of the quadratic timewise tracking error and the amplified adjacent-iteration timewise inputs drift while the argument is assigned as the iteration-time-varying learning gain. By adopting the latest captured historical timewise input and the tracking error, the optimal learning gain is achieved. Theoretical analysis conveys that the timewise tracking error is asymptotically convergent along the iteration direction. In particular, the tracking error may vanish at some finite iteration if the amplifier is null. Numerical simulations for a permanent magnet linear motor model testify the validity and effectiveness of the proposed scheme.

The core of face recognition task is to learn the discriminative feature representation, which has intra-class compactness and inter-class separability. In recent years, some margin-based softmax loss functions were designed to encourage the intra-class compactness, but they neglect the inter-class separability. RegularFace were proposed to increase the inter-class separability. However, RegularFace is inefficient and memory-consumptive on large datasets with large numbers of identities. In this paper, we propose a novel method, named EogFace. It can encourage both the intra-compactness and the inter-class separability. EogFace has intuitive geometric interpretation and theoretical proof, which is easy to implement and only adds negligible computational overhead. Extensive experiments on popular benchmarks of face recognition showed the effectiveness of method over existing state-of-the-art(SOTA) algorithms. Our codes will be released soon.

Clustering tumor metastasis samples from gene expression data at the whole genome level remains an arduous challenge, in particular, when the number of experimental samples is small and the number of genes is huge. We focus on the prediction of the epithelial-mesenchymal transition (EMT), which is an underlying mechanism of tumor metastasis, here, rather than tumor metastasis itself, to avoid confounding effects of uncertainties derived from various factors. In this paper, we propose a novel model in predicting EMT based on multidimensional scaling (MDS) strategies and integrating entropy and random matrix detection strategies to determine the optimal reduced number of dimension in low dimensional space. We verified our proposed model with the gene expression data for EMT samples of breast cancer and the experimental results demonstrated the superiority over state-of-the-art clustering methods. Furthermore, we developed a novel feature extraction method for selecting the significant genes and predicting the tumor metastasis. The source code is available at "https://github.com/yushanqiu/yushan.qiu-szu.edu.cn".

The identification of drug side-effects is considered to be an important step in drug design, which could not only shorten the time but also reduce the cost of drug development. In this paper, we investigate the relationship between the potential side-effects of drug candidates and their chemical structures. The preliminary Regularized Regression (RR) model for drug side-effects prediction has promising features in the efficiency of model training and the existence of a closed form solution. It performs better than other state-of-the-art methods, in terms of minimum accuracy and average accuracy. In order to dig inside how drug structure will associate with side effect, we further propose weighted GTS (Generalized T-Student Kernel: WGTS) SVM model from a structural risk minimization perspective. The SVM model proposed in this paper provides a better understanding of drug side-effects in the process of drug development. The usefulness of the WGTS model lies in the superior performance in a cross validation setting on 888 approved drugs with 1385 side-effects profiling from SIDER database. This work is expected to shed light on intriguing studies that predict potential un-identifying side-effects and suggest how we can avoid drug side-effects by the removal of some distinguished chemical structures.

Positive semi-definiteness is a critical property in Support Vector Machine (SVM) methods to ensure efficient solutions through convex quadratic programming. In this paper, we introduce a projection matrix on indefinite kernels to formulate a positive semi-definite one. The proposed model can be regarded as a generalized version of the spectrum method (denoising method and flipping method) by varying parameter λ. In particular, our suggested optimal λ under the Bregman matrix divergence theory can be obtained using unconstrained optimization. Experimental results on 4 real world data sets ranging from glycan classification to cancer prediction show that the proposed model can achieve better or competitive performance when compared to the related indefinite kernel methods. This may suggest a new way in motif extractions or cancer predictions.

Boolean network (BN) is a popular mathematical model for revealing the behavior of a genetic regulatory network, and observability plays a vital role in understanding the underlying network feature. However, the observability of attractor cycles, which is an interesting and important problem, has not been addressed in the literature. In this paper, we first proposed a novel problem on attractor observability in BNs. Identification of the minimum set of consecutive nodes can be used to determine uniquely the attractor cycle from the others in the network. We then develop a linear-time algorithm to identify the desired set of nodes. The proposed approaches are demonstrated and verified by numerical examples. The computational results are given to illustrate both the efficiency and effectiveness of our proposed methods.

Driven by the challenge of integrating large amount of experimental data obtained from biological research, computational biology and bioinformatics are growing rapidly. Machine learning methods, especially kernel methods with Support Vector Machines (SVMs) are very popular tools. In the perspective of kernel matrix, a technique namely Eigen-matrix translation has been introduced for protein data classification. The Eigen-matrix translation strategy owns a lot of nice properties while the nature of which needs further exploration. We propose that its importance lies in the dimension reduction of predictor attributes within the data set. This can therefore serve as a novel perspective for future research in dimension reduction problems.