High-dimensional Data Analysis Research Articles

Data-driven assessment of dimension reduction quality for single-cell omics data

Dimension reduction (DR) techniques have become synonymous with single-cell omics data due to their ability to generate attractive visualizations and enable analyses of high-dimensional data. In this issue of Patterns, Johnsona et al. develop a statistical approach to assist in selecting high-quality reduced representations to improve analyses and biological interpretations.

Analyzing immune response to engineered hydrogels by hierarchical clustering of inflammatory cell subsets.

Understanding the immune response to hydrogel implantation is critical for the design of immunomodulatory biomaterials. To study the progression of inflammation around poly(ethylene glycol) hydrogels presenting Arg-Gly-Asp (RGD) peptides and vascular endothelial growth factor, we used temporal analysis of high-dimensional flow cytometry data paired with intravital imaging, immunohistochemistry, and multiplexed proteomic profiling. RGD-presenting hydrogels created a reparative microenvironment promoting CD206+ cellular infiltration and revascularization in wounded dorsal skin tissue. Unbiased clustering algorithms (SPADE) revealed significant phenotypic transition shifts as a function of the cell-adhesion hydrogel properties. SPADE identified an intermediate macrophage subset functionally regulating in vivo cytokine secretion that was preferentially recruited for RGD-presenting hydrogels, whereas dendritic cell subsets were preferentially recruited to RDG-presenting hydrogels. Last, RGD-presenting hydrogels controlled macrophage functional cytokine secretion to direct polarization and vascularization. Our studies show that unbiased clustering of single-cell data provides unbiased insights into the underlying immune response to engineered materials.

Combination of Reduction Detection Using TOPSIS for Gene Expression Data Analysis

In high-dimensional data analysis, Feature Selection (FS) is one of the most fundamental issues in machine learning and requires the attention of researchers. These datasets are characterized by huge space due to a high number of features, out of which only a few are significant for analysis. Thus, significant feature extraction is crucial. There are various techniques available for feature selection; among them, the filter techniques are significant in this community, as they can be used with any type of learning algorithm and drastically lower the running time of optimization algorithms and improve the performance of the model. Furthermore, the application of a filter approach depends on the characteristics of the dataset as well as on the machine learning model. Thus, to avoid these issues in this research, a combination of feature reduction (CFR) is considered designing a pipeline of filter approaches for high-dimensional microarray data classification. Considering four filter approaches, sixteen combinations of pipelines are generated. The feature subset is reduced in different levels, and ultimately, the significant feature set is evaluated. The pipelined filter techniques are Correlation-Based Feature Selection (CBFS), Chi-Square Test (CST), Information Gain (InG), and Relief Feature Selection (RFS), and the classification techniques are Decision Tree (DT), Logistic Regression (LR), Random Forest (RF), and k-Nearest Neighbor (k-NN). The performance of CFR depends highly on the datasets as well as on the classifiers. Thereafter, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method is used for ranking all reduction combinations and evaluating the superior filter combination among all.

Multielectrode Arrays for Functional Phenotyping of Neurons from Induced Pluripotent Stem Cell Models of Neurodevelopmental Disorders.

Simple SummaryMultielectrode array technology allows researchers to record the spontaneous firing activity of cultured neurons over a period of multiple weeks or months. These data can be valuable for understanding how the functional relationships between neurons evolve as they begin to form connections and wire into a functional network. This technology has been adopted by researchers using stem cells to produce human neurons in culture to study neurodevelopmental disorders. However, the dizzying complexity and scale of the data generated have posed some challenges with the analysis and interpretation of experimental results. Here, we first provide historical context as to why multielectrode array platforms were originally developed, and use this perspective to explore some of the challenges currently facing the field. We then highlight new analysis methods, provide some guidance for improving the analysis of multielectrode array data, and discuss standardizing how these findings are communicated in scientific publications.In vitro multielectrode array (MEA) systems are increasingly used as higher-throughput platforms for functional phenotyping studies of neurons in induced pluripotent stem cell (iPSC) disease models. While MEA systems generate large amounts of spatiotemporal activity data from networks of iPSC-derived neurons, the downstream analysis and interpretation of such high-dimensional data often pose a significant challenge to researchers. In this review, we examine how MEA technology is currently deployed in iPSC modeling studies of neurodevelopmental disorders. We first highlight the strengths of in vitro MEA technology by reviewing the history of its development and the original scientific questions MEAs were intended to answer. Methods of generating patient iPSC-derived neurons and astrocytes for MEA co-cultures are summarized. We then discuss challenges associated with MEA data analysis in a disease modeling context, and present novel computational methods used to better interpret network phenotyping data. We end by suggesting best practices for presenting MEA data in research publications, and propose that the creation of a public MEA data repository to enable collaborative data sharing would be of great benefit to the iPSC disease modeling community.

Feature Extraction of High-dimensional Data Based on J-HOSVD for Cyber-Physical-Social Systems

With the further integration of Cyber-Physical-Social systems (CPSSs), there is explosive growth of the data in CPSSs. How to discover effective information or knowledge from CPSSs big data and provide support for subsequent learning tasks has become a core issue. Moreover, modern applications in CPSSs increasingly rely on the processing and analysis of high-dimensional data; the correlation and internal structure of these high-dimensional data are gradually becoming more complex, which further makes traditional machine learning algorithms a little inadequate in processing these data. In this article, we propose two general dimension reduction and feature extraction methods for high-dimensional data based on joint tensor decomposition, namely core feature extraction methods and factor feature extraction methods, which can effectively mine out the common components and hidden patterns of high-dimensional data by joint analysis while maintaining the original data structure. We also verified the effectiveness of the methods from both theoretical and practical aspects. Furthermore, we extend the two feature extraction methods to the tensor distance scenario and illustrate that the compressed features extracted by our models can keep the global information of original data well. Finally, we evaluated proposed methods on two benchmark datasets through classification tasks, and experimental results show that the low-dimensional features extracted by the proposed models have higher classification accuracy than the direct classification of the original data, which further verifies the effectiveness and robustness of our methods.

Robust sparse precision matrix estimation for high-dimensional compositional data

Motivated by the rapid development in the high-dimensional compositional data analysis, an ”Approximate-Plug” framework with theoretical justifications is proposed to provide robust precision matrix estimation for this kind of data under the sparsity assumption. To be specific, we first construct a Huber-robustness estimator Γ̃ to approximate the centered log-ratio covariance matrix. Then we plug Γ̃ into a constrained ℓ1-minimization procedure to obtain the final estimator Ω̃. Through imposing some mild conditions, we derive the convergence rate under the entrywise maximum norm and the spectral norm. Given that SpiecEasi in Kurtz et al. (2015) shares same routine with us but lacks of robustness and theoretical guarantees, simulation studies are conducted to show the privileges of our procedure. We also apply the proposed method on a real data.

Advances in and the Applicability of Machine Learning-Based Screening and Early Detection Approaches for Cancer: A Primer.

Simple SummaryNon-communicable diseases in general, and cancer in particular, contribute greatly to the global burden of disease. Although significant advances have been made to address this burden, cancer is still among the top drivers of mortality, second only to cardiovascular diseases. Consensus has been established that a key factor to reduce the burden of disease from cancer is to improve screening for and the early detection of such conditions. To date, however, most approaches in this field relied on established screening methods, such as a clinical examination, radiographic imaging, tissue staining or biochemical markers. Yet, with the advances of information technology, new data-driven screening and diagnostic tools have been developed. This article provides a brief overview of the theoretical foundations of these data-driven approaches, highlights the promising use cases and underscores the challenges and limitations that come with the introduction of these approaches to the clinical field.Despite the efforts of the past decades, cancer is still among the key drivers of global mortality. To increase the detection rates, screening programs and other efforts to improve early detection were initiated to cover the populations at a particular risk for developing a specific malignant condition. These diagnostic approaches have, so far, mostly relied on conventional diagnostic methods and have made little use of the vast amounts of clinical and diagnostic data that are routinely being collected along the diagnostic pathway. Practitioners have lacked the tools to handle this ever-increasing flood of data. Only recently, the clinical field has opened up more for the opportunities that come with the systematic utilisation of high-dimensional computational data analysis. We aim to introduce the reader to the theoretical background of machine learning (ML) and elaborate on the established and potential use cases of ML algorithms in screening and early detection. Furthermore, we assess and comment on the relevant challenges and misconceptions of the applicability of ML-based diagnostic approaches. Lastly, we emphasise the need for a clear regulatory framework to responsibly introduce ML-based diagnostics in clinical practice and routine care.

Using Decision Trees to Identify Salient Predictors of Cannabis-Related Outcomes

ABSTRACT Cannabis use continues to escalate among emerging adults and college attendance may be a risk factor for use. Severe cases of cannabis use can escalate to a cannabis use disorder, which is associated with worse psychosocial functioning. Predictors of cannabis use consequences and cannabis use disorder symptom severity have been identified; however, they typically employ a narrow set of predictors and rely on linear models. Machine learning is well suited for exploratory data analyses of high-dimensional data. This study applied decision tree learning to identify predictors of cannabis user status, negative cannabis-related consequences, and cannabis use disorder symptoms. Undergraduate college students (N = 7000) were recruited from nine universities in nine states across the U.S. Among the 7 trees, 24 splits created by 15 distinct predictors were identified. Consistent with prior research, one’s beliefs about cannabis were strong predictors of user status. Negative reinforcement cannabis use motives were the most consistent predictors of cannabis use disorder symptoms, and past month cannabis use was the most consistent predictor of probable cannabis use disorder. Typical frequency of cannabis use was the only predictor of negative cannabis-related consequences. Our results demonstrate that decision trees are a useful methodological tool for identifying targets for future clinical research.

Aberrant Structure MRI in Parkinson's Disease and Comorbidity with Depression Based on Multinomial Tensor Regression Analysis.

Background: Depression is a prominent and highly prevalent nonmotor feature in patients with Parkinson’s disease (PD). The neural and pathophysiologic mechanisms of PD with depression (DPD) remain unclear. The current diagnosis of DPD largely depends on clinical evaluation. Methods: We proposed a new family of multinomial tensor regressions that leveraged whole-brain structural magnetic resonance imaging (MRI) data to discriminate among 196 non-depressed PD (NDPD) patients, 84 DPD patients, 200 healthy controls (HC), and to assess the special brain microstructures in NDPD and DPD. The method of maximum likelihood estimation coupled with state-of-art gradient descent algorithms was used to predict the individual diagnosis of PD and the development of DPD in PD patients. Results: The results reveal that the proposed efficient approach not only achieved a high prediction accuracy (0.94) with a multi-class AUC (0.98) for distinguishing between NDPD, DPD, and HC on the testing set but also located the most discriminative regions for NDPD and DPD, including cortical regions, the cerebellum, the brainstem, the bilateral basal ganglia, and the thalamus and limbic regions. Conclusions: The proposed imaging technique based on tensor regression performs well without any prior feature information, facilitates a deeper understanding into the abnormalities in DPD and PD, and plays an essential role in the statistical analysis of high-dimensional complex MRI imaging data to support the radiological diagnosis of comorbidity of depression with PD.

Graph Based Feature Selection for Reduction of Dimensionality in Next-Generation RNA Sequencing Datasets

Analysis of high-dimensional data, with more features (p) than observations (N) (p>N), places significant demand in cost and memory computational usage attributes. Feature selection can be used to reduce the dimensionality of the data. We used a graph-based approach, principal component analysis (PCA) and recursive feature elimination to select features for classification from RNAseq datasets from two lung cancer datasets. The selected features were discretized for association rule mining where support and lift were used to generate informative rules. Our results show that the graph-based feature selection improved the performance of sequential minimal optimization (SMO) and multilayer perceptron classifiers (MLP) in both datasets. In association rule mining, features selected using the graph-based approach outperformed the other two feature-selection techniques at a support of 0.5 and lift of 2. The non-redundant rules reflect the inherent relationships between features. Biological features are usually related to functions in living systems, a relationship that cannot be deduced by feature selection and classification alone. Therefore, the graph-based feature-selection approach combined with rule mining is a suitable way of selecting and finding associations between features in high-dimensional RNAseq data.

Improving Visualization Interpretation Using Counterfactuals.

Complex, high-dimensional data is used in a wide range of domains to explore problems and make decisions. Analysis of high-dimensional data, however, is vulnerable to the hidden influence of confounding variables, especially as users apply ad hoc filtering operations to visualize only specific subsets of an entire dataset. Thus, visual data-driven analysis can mislead users and encourage mistaken assumptions about causality or the strength of relationships between features. This work introduces a novel visual approach designed to reveal the presence of confounding variables via counterfactual possibilities during visual data analysis. It is implemented in CoFact, an interactive visualization prototype that determines and visualizes counterfactual subsets to better support user exploration of feature relationships. Using publicly available datasets, we conducted a controlled user study to demonstrate the effectiveness of our approach; the results indicate that users exposed to counterfactual visualizations formed more careful judgments about feature-to-outcome relationships.

Principal wave analysis for high-dimensional structured data with applications to epigenomics and neuroimaging studies

Principal wave analysis for high-dimensional structured data with applications to epigenomics and neuroimaging studies

Collective variable discovery in the age of machine learning: reality, hype and everything in between.

Understanding the kinetics and thermodynamics profile of biomolecules is necessary to understand their functional roles which has a major impact in mechanism driven drug discovery. Molecular dynamics simulation has been routinely used to understand conformational dynamics and molecular recognition in biomolecules. Statistical analysis of high-dimensional spatiotemporal data generated from molecular dynamics simulation requires identification of a few low-dimensional variables which can describe the essential dynamics of a system without significant loss of information. In physical chemistry, these low-dimensional variables are often called collective variables. Collective variables are used to generate reduced representations of free energy surfaces and calculate transition probabilities between different metastable basins. However the choice of collective variables is not trivial for complex systems. Collective variables range from geometric criteria such as distances and dihedral angles to abstract ones such as weighted linear combinations of multiple geometric variables. The advent of machine learning algorithms led to increasing use of abstract collective variables to represent biomolecular dynamics. In this review, I will highlight several nuances of commonly used collective variables ranging from geometric to abstract ones. Further, I will put forward some cases where machine learning based collective variables were used to describe simple systems which in principle could have been described by geometric ones. Finally, I will put forward my thoughts on artificial general intelligence and how it can be used to discover and predict collective variables from spatiotemporal data generated by molecular dynamics simulations.

Low-Rank Characteristic Tensor Density Estimation Part I: Foundations

Effective non-parametric density estimation is a key challenge in high-dimensional multivariate data analysis. In this paper,we propose a novel approach that builds upon tensor factorization tools. Any multivariate density can be represented by its characteristic function, via the Fourier transform. If the sought density is compactly supported, then its characteristic function can be approximated, within controllable error, by a finite tensor of leading Fourier coefficients, whose size de-pends on the smoothness of the underlying density. This tensor can be naturally estimated from observed realizations of the random vector of interest, via sample averaging. In order to circumvent the curse of dimensionality, we introduce a low-rank model of this characteristic tensor, which significantly improves the density estimate especially for high-dimensional data and/or in the sample-starved regime. By virtue of uniqueness of low-rank tensor decomposition, under certain conditions, our method enables learning the true data-generating distribution. We demonstrate the very promising performance of the proposed method using several measured datasets.

A High-dimensional Outlier Detection Approach Based on Local Coulomb Force

Traditional outlier detections are inadequate for high-dimensional data analysis due to the interference of distance tending to be concentrated (curse of dimensionality). Inspired by the Coulombs law, we propose a new high-dimensional data similarity measure vector, which consists of outlier Coulomb force and outlier Coulomb resultant force. Outlier Coulomb force not only effectively gauges similarity measures among data objects, but also fully reflects differences among dimensions of data objects by vector projection in each dimension. More importantly, Coulomb resultant force can effectively measure deviations of data objects from a data center, making detection results interpretable. We introduce a new neighborhood outlier factor, which drives the development of a high-dimensional outlier detection algorithm. In our approach, attribute values with a high deviation degree is treated as interpretable information of outlier data. Finally, we implement and evaluate our algorithm using the UCI and synthetic datasets. Our experimental results show that the algorithm effectively alleviates the interference of Curse of Dimensionality. The findings confirm that high-dimensional outlier data originated by the algorithm are interpretable.

Topology Structure Analysis of High Dimensional Dataset by Flattening Deformation of Data Manifold

A new analysis method for high dimensional sets is proposed by autonomous deforming of data manifolds. The deformation is guided by two kinds of virtual interactions between data points. The flattening of data manifold is achieved under the elastic and repelling interactions, meanwhile the topological structure of the manifold is preserved. The proposed method provides a novel geometric viewpoint on high-dimensional data analysis. Experimental results prove the effectiveness of the proposed method in dataset structure analysis.

Minimax and Multi-Criteria Selection of Representative Model Portfolios for Complex Systems Analysis

The analysis of complex systems typically requires a large and diverse ensemble of models to confront the richness and complexity of the problem. Nevertheless, a common development and validation process of each individual model can be rigorous and time consuming. Because of limited time and resources, it is sometimes unrealistic to model every individual object in the population to capture the complex phenomena of the system. One such challenge arises in aerospace engineering when only a very limited number of aircraft performance models can be built to cover the aircraft fleet of the world for the environmental impact modeling of air transportation system. This paper considers the problem of selecting a small proportion of representative models to sufficiently cover and represent the population for more efficient and accurate systems analysis. At the intersection of unsupervised data mining and high-dimensional data analysis, the proposed methodology uses minimax and multi-criteria considerations to select a representative model portfolio at each budget level. Applying on the case study of representative aircraft models for environmental impact modeling, the benefits of the proposed method are demonstrated through both data visualization and quantitative metrics in multiple experiments. Potential limitations, extensions, and broader impacts of the method are also thoroughly discussed.

PhosPiR: an automated phosphoproteomic pipeline in R.

Large-scale phosphoproteome profiling using mass spectrometry (MS) provides functional insight that is crucial for disease biology and drug discovery. However, extracting biological understanding from these data is an arduous task requiring multiple analysis platforms that are not adapted for automated high-dimensional data analysis. Here, we introduce an integrated pipeline that combines several R packages to extract high-level biological understanding from large-scale phosphoproteomic data by seamless integration with existing databases and knowledge resources. In a single run, PhosPiR provides data clean-up, fast data overview, multiple statistical testing, differential expression analysis, phosphosite annotation and translation across species, multilevel enrichment analyses, proteome-wide kinase activity and substrate mapping and network hub analysis. Data output includes graphical formats such as heatmap, box-, volcano- and circos-plots. This resource is designed to assist proteome-wide data mining of pathophysiological mechanism without a need for programming knowledge.

A Method for Aero-Engine Gas Path Anomaly Detection Based on Markov Transition Field and Multi-LSTM

There are some problems such as uncertain thresholds, high dimension of monitoring parameters and unclear parameter relationships in the anomaly detection of aero-engine gas path. These problems make it difficult for the high accuracy of anomaly detection. In order to improve the accuracy of aero-engine gas path anomaly detection, a method based on Markov Transition Field and LSTM is proposed in this paper. The correlation among high-dimensional QAR data is obtained based on Markov Transition Field and hierarchical clustering. According to the correlation analysis of high-dimensional QAR data, a multi-input and multi-output LSTM network is constructed to realize one-step rolling prediction. A Gaussian mixture model of the residuals between predicted value and true value is constructed. The three-sigma rule is applied to detect outliers based on the Gaussian mixture model of the residuals. The experimental results show that the proposed method has high accuracy for aero-engine gas path anomaly detection.

Quantized Tensor Neural Network

Tensor network as an effective computing framework for efficient processing and analysis of high-dimensional data has been successfully applied in many fields. However, the performance of traditional tensor networks still cannot match the strong fitting ability of neural networks, so some data processing algorithms based on tensor networks cannot achieve the same excellent performance as deep learning models. To further improve the learning ability of tensor network, we propose a quantized tensor neural network in this article (QTNN), which integrates the advantages of neural networks and tensor networks, namely, the powerful learning ability of neural networks and the simplicity of tensor networks. The QTNN model can be further regarded as a generalized multilayer nonlinear tensor network, which can efficiently extract low-dimensional features of the data while maintaining the original structure information. In addition, to more effectively represent the local information of data, we introduce multiple convolution layers in QTNN to extract the local features. We also develop a high-order back-propagation algorithm for training the parameters of QTNN. We conducted classification experiments on multiple representative datasets to further evaluate the performance of proposed models, and the experimental results show that QTNN is simpler and more efficient while compared to the classic deep learning models.