Spatially resolved transcriptomics (SRT) enables the simultaneous capture of gene expression profiles and spatial localization, providing valuable insights into tissue architecture. However, the preservation of spatial information requires additional experimental procedures, which often introduce substantial technical noise. Existing methods typically perform denoising and spatial domain identification in separate steps, leading to suboptimal performance and limiting their applicability. To address this limitation, we propose an integrative network model, stACN ( spatial transcriptomics Attribute Cell Network), that jointly denoises gene expression data and identifies spatial domains in SRT. Specifically, stACN first learns clean dual cell networks using a graph noise model, and then derives compatible cell features through joint tensor decomposition of the denoised networks. Experimental results demonstrate that stACN effectively enhances data quality, as measured by clustering agreement with reference annotations (Adjusted Rand Index, ARI), and facilitates spatial domain analysis in SRT datasets.

Spatially resolved transcriptomics (SRT) simultaneously captures spatial coordinates, pathological features, and transcriptional profiles of cells within intact tissues, offering unprecedented opportunities to explore tissue architecture. However, SRT data often suffer from substantial technical noise introduced by experimental procedures, posing challenges for downstream analyses. To overcome these challenges, we introduce a Multiview Denoising framework for Spatial Transcriptomics (MvDST), which integrates a deep autoencoder and self-supervised learning to jointly reconstruct expression profiles, denoise features, and enforce cross-view consistency, effectively reducing technical noise, and heterogeneity. As a result, MvDST reliably and accurately delineates tissue subgroups across simulated datasets under various perturbations. In real cancer datasets, it distinguishes tumor-associated domains, identifies region-specific marker genes, and reveals intra-tumoral heterogeneity. Furthermore, we validate the robustness of MvDST across multiple spatial transcriptomics platforms, including 10 $\times $ Visium, STARmap, and osmFISH. Overall, these results demonstrate that MvDST can serve as a crucial initial step for the analysis of spatially resolved transcriptomics data.

Advancements in single-cell technologies concomitantly develop the epigenomic and transcriptomic profiles at the cell levels, providing opportunities to explore the potential biological mechanisms. Even though significant efforts have been dedicated to them, it remains challenging for the integration analysis of multi-omic data of single-cell because of the heterogeneity, complicated coupling and interpretability of data. To handle these issues, we propose a novel self-representation Learning-based Multi-omics data Integrative Clustering algorithm (sLMIC) for the integration of single-cell epigenomic profiles (DNA methylation or scATAC-seq) and transcriptomic (scRNA-seq), which the consistent and specific features of cells are explicitly extracted facilitating the cell clustering. Specifically, sLMIC constructs a graph for each type of single-cell data, thereby transforming omics data into multi-layer networks, which effectively removes heterogeneity of omic data. Then, sLMIC employs the low-rank and exclusivity constraints to separate the self-representation of cells into two parts, i.e., the shared and specific features, which explicitly characterize the consistency and diversity of omic data, providing an effective strategy to model the structure of cell types. Feature extraction and cell clustering are jointly formulated as an overall objective function, where latent features of data are obtained under the guidance of cell clustering. The extensive experimental results on 13 multi-omics datasets of single-cell from diverse organisms and tissues indicate that sLMIC observably exceeds the advanced algorithms regarding various measurements.

Single-cell RNA sequencing (scRNA-seq) measures gene transcriptome at the cell level, paving the way for the identification of cell subpopulations. Although deep learning has been successfully applied to scRNA-seq data, these algorithms are criticized for the undesirable performance and interpretability of patterns because of the noises, high-dimensionality and extraordinary sparsity of scRNA-seq data. To address these issues, a novel deep learning subspace clustering algorithm (aka scGDC) for cell types in scRNA-seq data is proposed, which simultaneously learns the deep features and topological structure of cells. Specifically, scGDC extends auto-encoder by introducing a self-representation layer to extract deep features of cells, and learns affinity graph of cells, which provide a better and more comprehensive strategy to characterize structure of cell types. To address heterogeneity of scRNA-seq data, scGDC projects cells of various types onto different subspaces, where types, particularly rare cell types, are well discriminated by utilizing generative adversarial learning. Furthermore, scGDC joins deep feature extraction, structural learning and cell type discovery, where features of cells are extracted under the guidance of cell types, thereby improving performance of algorithms. A total of 15 scRNA-seq datasets from various tissues and organisms with the number of cells ranging from 56 to 63 103 are adopted to validate performance of algorithms, and experimental results demonstrate that scGDC significantly outperforms 14 state-of-the-art methods in terms of various measurements (on average 25.51% by improvement), where (rare) cell types are significantly associated with topology of affinity graph of cells. The proposed model and algorithm provide an effective strategy for the analysis of scRNA-seq data (The software is coded using python, and is freely available for academic https://github.com/xkmaxidian/scGDC).

Cell types (subpopulations) serve as bio-markers for the diagnosis and therapy of complex diseases, and single-cell RNA-sequencing (scRNA-seq) measures expression of genes at cell level, paving the way for the identification of cell types. Although great efforts have been devoted to this issue, it remains challenging to identify rare cell types in scRNA-seq data because of the few-shot problem, lack of interpretability and separation of generating samples and clustering of cells. To attack these issues, a novel deep generative model for leveraging the small samples of cells (aka scLDS2) is proposed by precisely estimating the distribution of different cells, which discriminate the rare and non-rare cell types with adversarial learning. Specifically, to enhance interpretability of samples, scLDS2 generates the sparse faked samples of cells with $\ell _1$-norm, where the relations among cells are learned, facilitating the identification of cell types. Furthermore, scLDS2 directly obtains cell types from the generated samples by learning the block structure such that cells belonging to the same types are similar to each other with the nuclear-norm. scLDS2 joins the generation of samples, classification of the generated and truth samples for cells and feature extraction into a unified generative framework, which transforms the rare cell types detection problem into a classification problem, paving the way for the identification of cell types with joint learning. The experimental results on 20 datasets demonstrate that scLDS2 significantly outperforms 17 state-of-the-art methods in terms of various measurements with 25.12% improvement in adjusted rand index on average, providing an effective strategy for scRNA-seq data with rare cell types. (The software is coded using python, and is freely available for academic https://github.com/xkmaxidian/scLDS2).

Fuzzy cognitive maps (FCMs) as a kind of knowledge-based tools are widely applied to model complex dynamical systems using causal relations. Besides the representation and reasoning of systems behaviors, how to control the given systems into a desirable target by causal objects established by FCMs is also an open problem. Although, so far, there are some existing works about the applications of FCMs on the control-related problems, it is still a lack of the theoretical analysis in this domain. In this paper, the controllability of k-valued FCMs is studied. To improve the universality of models, a temporal extension of generalized FCMs is implemented. By means of semitensor product, the algebraic representation of k-valued FCMs with controls is established and a generalized formula of control-depending network transition matrices is achieved. A necessary and sufficient condition is proved to determine the control-depending fixed points of k-valued FCMs with temporalization. By utilizing three kinds of controls, the controllability of the discrete FCMs is discussed, respectively. The reachability condition of a specific target state from a given initial state at time s is studied, and the reachable set along with the corresponding reachable probability are also provided by analytic formula. Results provide a way to make FCMs evolving into the designed states by controls, which can further conduct the behaviors of the modeled systems in reality. Examples are shown to demonstrate the effectiveness and feasibility of the proposed scheme.