Joint Dimensionality Reduction Research Articles

ScMNMF: a novel method for single-cell multi-omics clustering based on matrix factorization.

The technology for analyzing single-cell multi-omics data has advanced rapidly and has provided comprehensive and accurate cellular information by exploring cell heterogeneity in genomics, transcriptomics, epigenomics, metabolomics and proteomics data. However, because of the high-dimensional and sparse characteristics of single-cell multi-omics data, as well as the limitations of various analysis algorithms, the clustering performance is generally poor. Matrix factorization is an unsupervised, dimensionality reduction-based method that can cluster individuals and discover related omics variables from different blocks. Here, we present a novel algorithm that performs joint dimensionality reduction learning and cell clustering analysis on single-cell multi-omics data using non-negative matrix factorization that we named scMNMF. We formulate the objective function of joint learning as a constrained optimization problem and derive the corresponding iterative formulas through alternating iterative algorithms. The major advantage of the scMNMF algorithm remains its capability to explore hidden related features among omics data. Additionally, the feature selection for dimensionality reduction and cell clustering mutually influence each other iteratively, leading to a more effective discovery of cell types. We validated the performance of the scMNMF algorithm using two simulated and five real datasets. The results show that scMNMF outperformed seven other state-of-the-art algorithms in various measurements. scMNMF code can be found at https://github.com/yushanqiu/scMNMF.

Web-based multi-omics integration using the Analyst software suite.

The growing number of multi-omics studies demands clear conceptual workflows coupled with easy-to-use software tools to facilitate data analysis and interpretation. This protocol covers three key components involved in multi-omics analysis, including single-omics data analysis, knowledge-driven integration using biological networks and data-driven integration through joint dimensionality reduction. Using the dataset from a recent multi-omics study of human pancreatic islet tissue and plasma samples, the first section introduces how to perform transcriptomics/proteomics data analysis using ExpressAnalyst and lipidomics data analysis using MetaboAnalyst. On the basis of significant features detected in these workflows, the second section demonstrates how to perform knowledge-driven integration using OmicsNet. The last section illustrates how to perform data-driven integration from the normalized omics data and metadata using OmicsAnalyst. The complete protocol can be executed in ~2 h. Compared with other available options for multi-omics integration, the Analyst software suite described in this protocol enables researchers to perform a wide range of omics data analysis tasks via a user-friendly web interface.

Geno-Multiomics Strategy Informs Drug Response Profiles in High-Risk Myeloid Neoplasia

Theclonal diversity of myeloid neoplasia (MN) results from the interplay of genomic entities. While diverse molecular lesions suggest distinct leukemogenic mechanisms, various combinations may lead to similar molecular convergence. Such convergence in the context of clinical heterogeneity may be difficult to discern by classic analytic tools leading to selection based on outcome rather than functional overlaps. We leveraged the state-of-the-art machine learning (ML) as a new approach to define likelihood of pharmacologic sensitivity/resistance in high-risk MDS/secondary AML (HR-MDS/sAML). We applied an integrative dimension reduction and subsequent clustering via neural networks generating an Encoder-Decoder architecture. Multiple omics were included as input/output to increase the resolution of drug response characterization. Further, drug response data were used to supervise the embedding. Specifically, we generated a deep feed-forward Encoder with 3 layers to embed distinct data modalities and 2 layers for combined embedding generating 100-d latent representation. Drug response measures (IC 50 values) extracted from The BEAT AML Master Trial 1 was used to supervise the landscape and effectively to generate a non-linear supervised dimension reduction framework. We previously reported the identification of distinct molecular subclasses in MDS. 2 Unsupervised ML via consensus-clustering approach of an autoencoder architecture coupled with GMM resolved clusters according to molecular features, diagnosis, and disease risk. Here, we focus on HR-MDS/sAML (n=1509) clusters. HR-MDS/sAML were grouped in six clusters with mean frequency of 37%. Such clusters, while sharing molecular features were characterized by diverse combinations of genomic features. Therefore, synergistic combination of computational and experimental therapeutics might inform on treatment indications in this group of patients. We noted that treatment response was heterogeneous across the clusters and, in some cases, there was a limited resolution due to molecular heterogeneity. Considering the invariant combinations of dominant and subclonal mutations, we incorporated clonal hierarchy to refine drug response. By adding a loss function for drug-sensitivity mapping, we generated a multi-omic-phenotype map. Similar joint-dimension reduction (jDR) approaches have been successfully utilized previously as well, specifically in the context of multi-omic single-cell sequencing where majority of the tools are either highly regularized/linear or fully unsupervised. 3 We simulated drug response prediction and show two examples of clusters associated with response profiles using two known drugs ( Fig1A, HMA, upper 3D surface plot; low plot 3D surface plot: lenalidomide). We identified clusters of patients likely refractory to HMA and responding to lenalidomide (red circles), clusters of patients predicted to respond to HMA and less likely to lenalidomide (black circles) or poorly to both drugs (yellow dots). Since multiple drugs could be assessed simultaneously, clusters of patients sensitive or resistant to drug combination could be also identified (overlapping hills/valleys). We then applied cluster assignments based on our previous model 2 augmented with VAF and copy number using The Beat AML cohort and characterized drugs with significant difference (ANOVA test). We found significant differences in sensitivity/resistance across the clusters with lower IC 50 values representing high sensitivity scale against a panel of 120 FDA-approved agents ( Fig1B). As an example, we generated a 2D embedding. Individual axes show the multi-modal latent-features associated linearly with drug response. Color-coding shows sensitive/resistant IC 50 profiles for individual samples from The Beat AML cohort. Four drugs with largest F-statistics are depicted. Interestingly, our prediction show feasibility to simultaneously identify clusters of patients characterized by increased resistance for one drug ( e.g., trametinib) and high sensitivity to others ( e.g., rapamycin, dasatinib, doramapimod). In sum, our study suggests that multi-modal genomic configuration increases the power of resolution in HR-MDS/sAML by reducing molecular heterogeneity, which in turn might help resolving therapeutic vulnerabilities.

B-079 Identifying Heterogeneity of Systemic Connective Tissue Diseases by Applying Joint Dimension Reduction and Cluster Analysis to Immunomarkers

Abstract Background Accurate identification of systemic connective tissue diseases (SCTDs) can be challenging due to the heterogeneity of each disease. This study aims to explore the heterogeneity of different SCTDs by applying non-supervised learning to immunomarker data and proposes an alternative classification. Additionally, the study investigates the clinical implications of these different groups. Methods We utilized multiple correspondence analysis and k-means clustering to analyze the immunomarker data of patients with systemic lupus erythematosus (SLE), rheumatoid arthritis (RA), and Sjögren’s syndrome (SS) in Taiwan between 2001 and 2016. To investigate the clinical correlations of the classification results, we conducted a comprehensive review of the clinical findings and compared the results across different groups. Results A total of 11 923 patients with the three SCTDs were classified into six distinct clusters based on their immunomarker patterns. In this clustering system, RA patients were predominantly grouped in cluster 1, whereas SLE and SS patients had a more dispersed distribution. Among patients with SLE, renal involvement was more frequent in clusters 3 and 6 (52% and 51%, respectively) than in other clusters, and discoid lupus was more frequent in cluster 3. Among SS patients, typical SS findings such as inflammation or infection of eyes and allergic reactions were more common in cluster 2 (54% and 51%, respectively). In contrast, patients in cluster 3 had more unspecified benign neoplasms (58%) and were more likely to experience immune disorders (63%). Conclusion The immunomarker-driven clustering yields an alternative classification result with new clinical insights. The data-driven approach would provide a more evidence-based classification and aid in a more accurate diagnosis and management for SCTDs.

Multi-View Learning to Unravel the Different Levels Underlying Hepatitis B Vaccine Response.

The immune system acts as an intricate apparatus that is dedicated to mounting a defense and ensures host survival from microbial threats. To engage this faceted immune response and provide protection against infectious diseases, vaccinations are a critical tool to be developed. However, vaccine responses are governed by levels that, when interrogated, separately only explain a fraction of the immune reaction. To address this knowledge gap, we conducted a feasibility study to determine if multi-view modeling could aid in gaining actionable insights on response markers shared across populations, capture the immune system's diversity, and disentangle confounders. We thus sought to assess this multi-view modeling capacity on the responsiveness to the Hepatitis B virus (HBV) vaccination. Seroconversion to vaccine-induced antibodies against the HBV surface antigen (anti-HBs) in early converters (n = 21; <2 months) and late converters (n = 9; <6 months) and was defined based on the anti-HBs titers (>10IU/L). The multi-view data encompassed bulk RNA-seq, CD4+ T-cell parameters (including T-cell receptor data), flow cytometry data, and clinical metadata (including age and gender). The modeling included testing single-view and multi-view joint dimensionality reductions. Multi-view joint dimensionality reduction outperformed single-view methods in terms of the area under the curve and balanced accuracy, confirming the increase in predictive power to be gained. The interpretation of these findings showed that age, gender, inflammation-related gene sets, and pre-existing vaccine-specific T-cells could be associated with vaccination responsiveness. This multi-view dimensionality reduction approach complements clinical seroconversion and all single modalities. Importantly, this modeling could identify what features could predict HBV vaccine response. This methodology could be extended to other vaccination trials to identify the key features regulating responsiveness.

Hippocampus Parcellation via Discriminative Embedded Clustering of fMRI Functional Connectivity.

Dividing a pre-defined brain region into several heterogenous subregions is crucial for understanding its functional segregation and integration. Due to the high dimensionality of brain functional features, clustering is often postponed until dimensionality reduction in traditional parcellation frameworks occurs. However, under such stepwise parcellation, it is very easy to fall into the dilemma of local optimum since dimensionality reduction could not take into account the requirement of clustering. In this study, we developed a new parcellation framework based on the discriminative embedded clustering (DEC), combining subspace learning and clustering in a common procedure with alternative minimization adopted to approach global optimum. We tested the proposed framework in functional connectivity-based parcellation of the hippocampus. The hippocampus was parcellated into three spatial coherent subregions along the anteroventral-posterodorsal axis; the three subregions exhibited distinct functional connectivity changes in taxi drivers relative to non-driver controls. Moreover, compared with traditional stepwise methods, the proposed DEC-based framework demonstrated higher parcellation consistency across different scans within individuals. The study proposed a new brain parcellation framework with joint dimensionality reduction and clustering; the findings might shed new light on the functional plasticity of hippocampal subregions related to long-term navigation experience.

Translating transcriptomic findings from cancer model systems to humans through joint dimension reduction

Model systems are an essential resource in cancer research. They simulate effects that we can infer into humans, but come at a risk of inaccurately representing human biology. This inaccuracy can lead to inconclusive experiments or misleading results, urging the need for an improved process for translating model system findings into human-relevant data. We present a process for applying joint dimension reduction (jDR) to horizontally integrate gene expression data across model systems and human tumor cohorts. We then use this approach to combine human TCGA gene expression data with data from human cancer cell lines and mouse model tumors. By identifying the aspects of genomic variation joint-acting across cohorts, we demonstrate how predictive modeling and clinical biomarkers from model systems can be improved.

Research on Multi-Domain Dimensionality Reduction Joint Adaptive Processing Method for Range Ambiguous Clutter of FDA-Phase-MIMO Space-Based Early Warning Radar

The ground and sea clutter received by space-based early warning radar (SBEWR) has severely range ambiguous characteristics due to its platform location, and the non-stationary factor caused by Earth’s rotation makes the received clutter at different range ambiguous positions seriously broaden in the Doppler dimension. The complex clutter suppression performance of SBEWR obtained by traditional method is degraded significantly. To solve this problem and achieve better clutter suppression performance, a novel multi-domain adaptive processing method for clutter suppression is proposed in this paper. The proposed method introduced a range related signal processing domain based on conventional space–time domain by using frequency diverse array phase multiple-input multiple-output (FDA-Phase-MIMO) radar. In addition, a novel multi-domain joint dimensionality reduction structure was designed. The novel multi-domain joint adaptive processing using the proposed dimensionality reduction structure could not only obtain great clutter suppression performance of SBEWR, but also minimize the requirement of the number of selected auxiliary channels. Simulation examples show the effectiveness of the proposed method.

DAE-TPGM: A deep autoencoder network based on a two-part-gamma model for analyzing single-cell RNA-seq data

Single-cell RNA sequencing (scRNA-seq) can reveal differences in genetic material at the single-cell level and is widely used in biomedical studies. However, the minute RNA content within individual cells often results in a high number of dropouts and introduces random noise of scRNA-seq data, concealing the original gene expression pattern. Therefore, data normalization is critical in the analysis pipeline to adjust for unexpected biological and technical effects, leading to a particular bimodal expression pattern exhibited in the semi-continuous normalized data. We further find the positive continuous expression presents a right-skewed distribution, which is still under-explored by mainstream dimensionality reduction and imputation methods. We introduced a deep autoencoder network based on a two-part-gamma model (DAE-TPGM) for joint dimensionality reduction and imputation of scRNA-seq data. DAE-TPGM uses a two-part-gamma model to capture the statistical characteristics of semi-continuous normalized data and adaptively explores the potential relationships between genes for promoting data imputation by deep autoencoder. Just as the classic application scenarios that use an autoencoder in dimensionality reduction, our personalized autoendoer can capture phenotypic information on the peripheral blood mononuclear cells (PBMC) better and clearly infer continuous phenotype information for hematopoiesis in mice. Compared with that of mainstream imputation methods such as MAGIC, SAVER, scImpute and DCA, the new model achieved substantial improvement on the recognition of cellular phenotypes in two real datasets, and the comprehensive analyses on synthetic “ground truth” data demonstrated that our method obtains competitive advantages over other imputation methods in discovering underlying gene expression patterns in time-course data.

Joint dimension reduction and clustering analysis of single-cell RNA-seq and spatial transcriptomics data.

Dimension reduction and (spatial) clustering is usually performed sequentially; however, the low-dimensional embeddings estimated in the dimension-reduction step may not be relevant to the class labels inferred in the clustering step. We therefore developed a computation method, Dimension-Reduction Spatial-Clustering (DR-SC), that can simultaneously perform dimension reduction and (spatial) clustering within a unified framework. Joint analysis by DR-SC produces accurate (spatial) clustering results and ensures the effective extraction of biologically informative low-dimensional features. DR-SC is applicable to spatial clustering in spatial transcriptomics that characterizes the spatial organization of the tissue by segregating it into multiple tissue structures. Here, DR-SC relies on a latent hidden Markov random field model to encourage the spatial smoothness of the detected spatial cluster boundaries. Underlying DR-SC is an efficient expectation-maximization algorithm based on an iterative conditional mode. As such, DR-SC is scalable to large sample sizes and can optimize the spatial smoothness parameter in a data-driven manner. With comprehensive simulations and real data applications, we show that DR-SC outperforms existing clustering and spatial clustering methods: it extracts more biologically relevant features than conventional dimension reduction methods, improves clustering performance, and offers improved trajectory inference and visualization for downstream trajectory inference analyses.

Divergence Regulated Encoder Network for Joint Dimensionality Reduction and Classification

Feature representation is an important aspect of remote-sensing based image classification. While deep convolutional neural networks are able to effectively amalgamate information, large numbers of parameters often make learned features inscrutable and difficult to transfer to alternative models. In order to better represent statistical texture information for remote-sensing image classification, in this paper, we investigate performing joint dimensionality reduction and classification using a novel histogram neural network. Motivated by a popular dimensionality reduction approach, t-Distributed Stochastic Neighbor Embedding (t-SNE), our proposed method incorporates a classification loss computed on samples in a low-dimensional embedding space. We compare the learned sample embeddings against coordinates found by t-SNE in terms of classification accuracy and qualitative assessment. We also explore use of various divergence measures in the t-SNE objective. The proposed method has several advantages such as readily embedding out-of-sample points and reducing feature dimensionality while retaining class discriminability. Our results show that the proposed approach maintains and/or improves classification performance and reveals characteristics of features produced by neural networks that may be helpful for other applications.

Low-Rank Characteristic Tensor Density Estimation Part II: Compression and Latent Density Estimation

Learning generative probabilistic models is a core problem in machine learning, which presents significant challenges due to the curse of dimensionality. This paper proposes a joint dimensionality reduction and non-parametric density estimation framework, using a novel estimator that can explicitly capture the underlying distribution of appropriate reduced-dimension representations of the input data. The idea is to jointly design a nonlinear dimensionality reducing auto-encoder to model the training data in terms of a parsimonious set of latent random variables, and learn a canonical low-rank tensor model of the joint distribution of the latent variables in the Fourier domain. The proposed latent density model is non-parametric and universal, as opposed to the predefined prior that is assumed in variational auto-encoders. Joint optimization of the auto-encoder and the latent density estimator is pursued via a formulation which learns both by minimizing a combination of the negative log-likelihood in the latent domain and the auto-encoder reconstruction loss. We demonstrate that the proposed model achieves very promising results on toy, tabular, and image datasets on regression tasks, sampling, and anomaly detection.

Benchmarking joint multi-omics dimensionality reduction approaches for the study of cancer

High-dimensional multi-omics data are now standard in biology. They can greatly enhance our understanding of biological systems when effectively integrated. To achieve proper integration, joint Dimensionality Reduction (jDR) methods are among the most efficient approaches. However, several jDR methods are available, urging the need for a comprehensive benchmark with practical guidelines. We perform a systematic evaluation of nine representative jDR methods using three complementary benchmarks. First, we evaluate their performances in retrieving ground-truth sample clustering from simulated multi-omics datasets. Second, we use TCGA cancer data to assess their strengths in predicting survival, clinical annotations and known pathways/biological processes. Finally, we assess their classification of multi-omics single-cell data. From these in-depth comparisons, we observe that intNMF performs best in clustering, while MCIA offers an effective behavior across many contexts. The code developed for this benchmark study is implemented in a Jupyter notebook—multi-omics mix (momix)—to foster reproducibility, and support users and future developers.

空时联合抗干扰降维处理的设计与实现

空时联合抗干扰降维处理的设计与实现

A novel dimension reduction and dictionary learning framework for high-dimensional data classification

High-dimensional problem poses significant challenges for dictionary learning based classification architecture. Joint Dimension Reduction and Dictionary Learning (JDRDL) framework shows great potential for overcoming the challenges caused by high dimensionality. However, most of the existing JDRDL approaches do not consider the complex nonlinear relationships within high-dimensional data, which limits their classification performance. To overcome this problem, a novel joint dimension reduction and dictionary learning framework is proposed in this paper for high-dimensional data classification. Firstly, at dimension reduction stage, an autoencoder is employed to learn a nonlinear mapping that reduces dimensionality and preserves nonlinear structure of the high-dimensional data. Then, at dictionary learning stage, the locality constraint with label embedding, which takes the locality and label information into account together, is incorporated into the learning process to preserve desirable nonlinear local structure and enhance class discrimination. Moreover, the mapping function and dictionary are optimized simultaneously to enhance the performance. Encouraging experimental results on multiple benchmark datasets confirm that the proposed framework is effective and efficient for high-dimensional data classification.

Low-Rank Preserving t-Linear Projection for Robust Image Feature Extraction.

As the cornerstone for joint dimension reduction and feature extraction, extensive linear projection algorithms were proposed to fit various requirements. When being applied to image data, however, existing methods suffer from representation deficiency since the multi-way structure of the data is (partially) neglected. To solve this problem, we propose a novel Low-Rank Preserving t-Linear Projection (LRP-tP) model that preserves the intrinsic structure of the image data using t-product-based operations. The proposed model advances in four aspects: 1) LRP-tP learns the t-linear projection directly from the tensorial dataset so as to exploit the correlation among the multi-way data structure simultaneously; 2) to cope with the widely spread data errors, e.g., noise and corruptions, the robustness of LRP-tP is enhanced via self-representation learning; 3) LRP-tP is endowed with good discriminative ability by integrating the empirical classification error into the learning procedure; 4) an adaptive graph considering the similarity and locality of the data is jointly learned to precisely portray the data affinity. We devise an efficient algorithm to solve the proposed LRP-tP model using the alternating direction method of multipliers. Extensive experiments on image feature extraction have demonstrated the superiority of LRP-tP compared to the state-of-the-arts.

Testing for stationarity of functional time series in the frequency domain

Interest in functional time series has spiked in the recent past with papers covering both methodology and applications being published at a much increased pace. This article contributes to the research in this area by proposing a new stationarity test for functional time series based on frequency domain methods. The proposed test statistics is based on joint dimension reduction via functional principal components analysis across the spectral density operators at all Fourier frequencies, explicitly allowing for frequency-dependent levels of truncation to adapt to the dynamics of the underlying functional time series. The properties of the test are derived both under the null hypothesis of stationary functional time series and under the smooth alternative of locally stationary functional time series. The methodology is theoretically justified through asymptotic results. Evidence from simulation studies and an application to annual temperature curves suggests that the test works well in finite samples.

Clustering adaptive canonical correlations for high-dimensional multi-modal data

Multi-modal canonical correlation analysis (MCCA) is an important joint dimension reduction method and has been widely applied to clustering tasks of multi-modal data. MCCA-based clustering is usually dimension reduction of high-dimensional data followed by clustering of low-dimensional data. However, the two-stage clustering is difficult to ensure the adaptability of dimension reduction and clustering, which will affect the final clustering performance. To solve the issue, we propose a novel clustering adaptive multi-modal canonical correlations (CAMCCs) method, which constructs a unified optimization model of multi-modal correlation learning and clustering. The method not only realizes discriminant learning of correlation projection directions under unsupervised cases, but also is able to directly obtain class labels of multi-modal data. Additionally, the method also realizes out-of-sample extension in class labels. Solutions of CAMCCs are optimized by an iterative way, and we analyze its convergence. Extensive experimental results on various datasets have demonstrated the effectiveness of the method.

Tensor train representation of MIMO channels using the JIRAFE method

MIMO technology has been subject of increasing interest in both academia and industry for future wireless standards. However, its performance benefits strongly depend on the accuracy of the channel at the base station. In a recent work, a fourth-order channel tensor model was proposed for MIMO systems. In this paper, we extend this model by exploiting additional spatial diversity at the receiver, which induces a fifth order tensor model for the channel. For such high orders, there is a crucial need to break the initial high-dimensional optimization problem into a collection of smaller coupled optimization sub-problems. This paper exploits new results on the equivalence between the canonical polyadic decomposition (CPD) and the tensor train (TT) decomposition for the multi-path scenario. Specifically, we propose a Joint dImensionality Reduction And Factor rEtrieval (JIRAFE) method to find the transmit and receive spatial signatures as well as the complex path gains (which also capture the polarization effects). Monte Carlo simulations show that our proposed TT-based representation of the channel is more robust to noise and computationally more attractive than available competing tensor-based methods, for physical parameters estimation.

An Impartial Trimming Approach for Joint Dimension and Sample Reduction

A robust version of reduced and factorial k-means is proposed that is based on the idea of trimming. Reduced and factorial k-means are data reduction techniques well suited for simultaneous dimension and sample reduction through PCA and clustering. The occurrence of data inadequacies can invalidate standard analyses. Actually, contamination in the data at hand can hide the underlying clustered structure of the data. An appealing approach to develop robust counterparts of factorial and reduced k-means is given by impartial trimming. The idea is to discard a fraction of observations that are selected as the most distant from the centroids. The finite sample behavior of the proposed methods has been investigated by some numerical studies and real data examples.