Nonlinear Dimensionality Reduction Method Research Articles

Wide Area VISTA Extra-galactic Survey (WAVES): Unsupervised star-galaxy separation on the WAVES-Wide photometric input catalogue using UMAP and hdbscan

Abstract Star-galaxy separation is a crucial step in creating target catalogues for extragalactic spectroscopic surveys. A classifier biased towards inclusivity risks including high numbers of stars, wasting fibre hours, while a more conservative classifier might overlook galaxies, compromising completeness and hence survey objectives. To avoid bias introduced by a training set in supervised methods, we employ an unsupervised machine learning approach. Using photometry from the Wide Area VISTA Extragalactic Survey (WAVES)-Wide catalogue comprising 9-band u - Ks data, we create a feature space with colours, fluxes, and apparent size information extracted by ProFound. We apply the non-linear dimensionality reduction method UMAP (Uniform Manifold Approximation and Projection) combined with the classifier hdbscan to classify stars and galaxies. Our method is verified against a baseline colour and morphological method using a truth catalogue from Gaia, SDSS, GAMA, and DESI. We correctly identify 99.75% of galaxies within the AB magnitude limit of Z = 21.2, with an F1 score of 0.9971 ± 0.0018 across the entire ground truth sample, compared to 0.9879 ± 0.0088 from the baseline method. Our method’s higher purity (0.9967 ± 0.0021) compared to the baseline (0.9795 ± 0.0172) increases efficiency, identifying 11% fewer galaxy or ambiguous sources, saving approximately 70,000 fibre hours on the 4MOST instrument. We achieve reliable classification statistics for challenging sources including quasars, compact galaxies, and low surface brightness galaxies, retrieving 92.7%, 84.6%, and 99.5% of them respectively. Angular clustering analysis validates our classifications, showing consistency with expected galaxy clustering, regardless of the baseline classification.

Calibrating dimension reduction hyperparameters in the presence of noise.

The goal of dimension reduction tools is to construct a low-dimensional representation of high-dimensional data. These tools are employed for a variety of reasons such as noise reduction, visualization, and to lower computational costs. However, there is a fundamental issue that is discussed in other modeling problems that is often overlooked in dimension reduction-overfitting. In the context of other modeling problems, techniques such as feature-selection, cross-validation, and regularization are employed to combat overfitting, but rarely are such precautions taken when applying dimension reduction. Prior applications of the two most popular non-linear dimension reduction methods, t-SNE and UMAP, fail to acknowledge data as a combination of signal and noise when assessing performance. These methods are typically calibrated to capture the entirety of the data, not just the signal. In this paper, we demonstrate the importance of acknowledging noise when calibrating hyperparameters and present a framework that enables users to do so. We use this framework to explore the role hyperparameter calibration plays in overfitting the data when applying t-SNE and UMAP. More specifically, we show previously recommended values for perplexity and n_neighbors are too small and overfit the noise. We also provide a workflow others may use to calibrate hyperparameters in the presence of noise.

Mesoscopic structure graphs for interpreting uncertainty in non-linear embeddings

Probabilistic-based non-linear dimensionality reduction (PB-NL-DR) methods, such as t-SNE and UMAP, are effective in unfolding complex high-dimensional manifolds, allowing users to explore and understand the structural patterns of data. However, due to the trade-off between global and local structure preservation and the randomness during computation, these methods may introduce false neighborhood relationships, known as distortion errors and misleading visualizations. To address this issue, we first conduct a detailed survey to illustrate the design space of prior layout enrichment visualizations for interpreting DR results, and then propose a node-link visualization technique, ManiGraph. This technique rethinks the neighborhood fidelity between the high- and low-dimensional spaces by constructing dynamic mesoscopic structure graphs and measuring region-adapted trustworthiness. ManiGraph also addresses the overplotting issue in scatterplot visualization for large-scale datasets and supports examining in unsupervised scenarios. We demonstrate the effectiveness of ManiGraph in different analytical cases, including generic machine learning using 3D toy data illustrations and fashion-MNIST, a computational biology study using a single-cell RNA sequencing dataset, and a deep learning-enabled colorectal cancer study with histopathology-MNIST.

Manifold learning-based UMAP method for geochemical anomaly identification

Geochemical data are usually high-dimensional data that could contain dozens of elements. Geochemical distribution patterns and anomalies related to mineralization and lithological features are always hidden in these high-dimensional data, which cannot be directly observed from the data. To solve this problem, a manifold learning-based uniform manifold approximation and projection (UMAP) method, was introduced to recognize mineralization-related geochemical anomalies from high-dimensional geochemical data in this study. The UMAP method is a nonlinear dimensionality reduction method, which is suitable for dimensionality reduction and visualization of high-dimensional data. A case study was conducted to demonstrate the advantages of the UMAP method for identifying ion-adsorbed rare-earth-element (REE) mineralization-related anomalies from high-dimensional data in the Nanling region, China. Factor analysis was used to determine ion-adsorbed REE mineralization-related element combination that consists of 10 elements. High-dimensional geochemical data were reduced to two dimensions based on the UMAP method. The results indicated that the UMAP method can effectively characterize the spatial distributions of ion-adsorbed REE mineralization-related anomalies by dimensionality reduction analysis and visualization analysis of high-dimensional geochemical data in the study area. To illustrate the superiority of the UMAP method, a comparative study was conducted between the UMAP and other three manifold learning methods, namely locally linear embedding (LLE), isometric feature mapping (Isomap) and t-distributed stochastic neighbor embedding (t-SNE). The performance of the four manifold learning methods was evaluated by receiver operating characteristic (ROC) curve and prediction-area (P-A) plot, showing that the performance of the UMAP method is superior to that of the LLE, Isomap and t-SNE methods in terms of recognizing ion-adsorbed REE mineralization-related anomalies and the spatial distributions of the REE-bearing geological bodies in the Nanling belt.

Exploring visual quality of multidimensional time series projections

Dimensionality reduction is often used to project time series data from multidimensional to two-dimensional space to generate visual representations of the temporal evolution. In this context, we address the problem of multidimensional time series visualization by presenting a new method to show and handle projection errors introduced by dimensionality reduction techniques on multidimensional temporal data. For visualization, subsequent time instances are rendered as dots that are connected by lines or curves to indicate the temporal dependencies. However, inevitable projection artifacts may lead to poor visualization quality and misinterpretation of the temporal information. Wrongly projected data points, inaccurate variations in the distances between projected time instances, and intersections of connecting lines could lead to wrong assumptions about the original data. We adapt local and global quality metrics to measure the visual quality along the projected time series, and we introduce a model to assess the projection error at intersecting lines. These serve as a basis for our new uncertainty visualization techniques that use different visual encodings and interactions to indicate, communicate, and work with the visualization uncertainty from projection errors and artifacts along the timeline of data points, their connections, and intersections. Our approach is agnostic to the projection method and works for linear and non-linear dimensionality reduction methods alike.

Learnable faster kernel-PCA for nonlinear fault detection: Deep autoencoder-based realization

Kernel principal component analysis (KPCA) is a well-recognized nonlinear dimensionality reduction method that has been widely used in nonlinear fault detection tasks. As a kernel trick-based method, KPCA inherits two major problems. First, the form and the parameters of the kernel function are usually selected blindly, depending seriously on trial-and-error. As a result, there may be serious performance degradation in case of inappropriate selections. Second, at the online monitoring stage, KPCA has much computational burden and poor real-time performance, because the kernel method requires to leverage all the offline training data. In this work, to deal with the two drawbacks, a learnable faster realization of the conventional KPCA is proposed. The core idea is to parameterize all feasible kernel functions using the novel nonlinear DAE-FE (deep autoencoder based feature extraction) framework and propose DAE-PCA (deep autoencoder based principal component analysis) approach in detail. The proposed DAE-PCA method is proved to be equivalent to KPCA but has more advantage in terms of automatic searching of the most suitable nonlinear high-dimensional space according to the inputs, which helps to improve the accuracy of fault detection. Furthermore, the online computational efficiency improves by many times compared with the conventional KPCA. Finally, the Tennessee Eastman (TE) process benchmark and wastewater treatment plant (WWTP) benchmark are employed to illustrate the effectiveness of the proposed method, where the average fault detection rates of DAE-PCA are at least 0.27% and 4.69% higher than those of other methods, and its online computational efficiency is faster 90.48% and 24.57% times than that of KPCA respectively.

Interpretation of autoencoder-learned collective variables using Morse-Smale complex and sublevelset persistent homology: An application on molecular trajectories.

Dimensionality reduction often serves as the first step toward a minimalist understanding of physical systems as well as the accelerated simulations of them. In particular, neural network-based nonlinear dimensionality reduction methods, such as autoencoders, have shown promising outcomes in uncovering collective variables (CVs). However, the physical meaning of these CVs remains largely elusive. In this work, we constructed a framework that (1) determines the optimal number of CVs needed to capture the essential molecular motions using an ensemble of hierarchical autoencoders and (2) provides topology-based interpretations to the autoencoder-learned CVs with Morse-Smale complex and sublevelset persistent homology. This approach was exemplified using a series of n-alkanes and can be regarded as a general, explainable nonlinear dimensionality reduction method.

Identification of control equations using low-dimensional flow representations of pitching airfoil

This study investigates the application of data-driven modeling techniques for understanding the complex dynamics of pitching airfoils at low Reynolds numbers and high angles of attack. Linear and nonlinear dimensionality reduction methods, namely principal component analysis (PCA) and isometric mapping (ISOMAP), are employed to obtain low-dimensional representations of the flow field. Subsequently, sparse identification of nonlinear dynamics (SINDy) is utilized to model the governing equations. The key findings are as follows: PCA primarily captures linear information, with the first two to three dimensions maintaining relatively low reconstruction errors. In contrast, ISOMAP excels in capturing nonlinear features, exhibiting noticeably smaller reconstruction errors. The main information is concentrated in the two-dimensional plane constructed by PCA1 and PCA2 (or ISOMAP1 and ISOMAP2). Differences in trajectory planes formed by combinations of other axes reflect flow field disparities. ISOMAP provides a nonlinear low-dimensional representation, advantageous for capturing nonlinear relationships between flow field characteristics and governing equations. The combination of ISOMAP and SINDy yields virtually no errors in identifying governing equations. Conversely, PCA and SINDy result in significantly different linear trajectories, leading to higher reconstruction errors. The identified governing equations using ISOMAP and SINDy remain consistent across different datasets, demonstrating the method's stability and robustness in accurately characterizing flow field properties under similar conditions.

Automatic Active Lesion Tracking in Multiple Sclerosis Using Unsupervised Machine Learning.

Identifying active lesions in magnetic resonance imaging (MRI) is crucial for the diagnosis and treatment planning of multiple sclerosis (MS). Active lesions on MRI are identified following the administration of Gadolinium-based contrast agents (GBCAs). However, recent studies have reported that repeated administration of GBCA results in the accumulation of Gd in tissues. In addition, GBCA administration increases health care costs. Thus, reducing or eliminating GBCA administration for active lesion detection is important for improved patient safety and reduced healthcare costs. Current state-of-the-art methods for identifying active lesions in brain MRI without GBCA administration utilize data-intensive deep learning methods. To implement nonlinear dimensionality reduction (NLDR) methods, locally linear embedding (LLE) and isometric feature mapping (Isomap), which are less data-intensive, for automatically identifying active lesions on brain MRI in MS patients, without the administration of contrast agents. Fluid-attenuated inversion recovery (FLAIR), T2-weighted, proton density-weighted, and pre- and post-contrast T1-weighted images were included in the multiparametric MRI dataset used in this study. Subtracted pre- and post-contrast T1-weighted images were labeled by experts as active lesions (ground truth). Unsupervised methods, LLE and Isomap, were used to reconstruct multiparametric brain MR images into a single embedded image. Active lesions were identified on the embedded images and compared with ground truth lesions. The performance of NLDR methods was evaluated by calculating the Dice similarity (DS) index between the observed and identified active lesions in embedded images. LLE and Isomap, were applied to 40 MS patients, achieving median DS scores of 0.74 ± 0.1 and 0.78 ± 0.09, respectively, outperforming current state-of-the-art methods. NLDR methods, Isomap and LLE, are viable options for the identification of active MS lesions on non-contrast images, and potentially could be used as a clinical decision tool.

Nonlinear dimensionality reduction with q-Gaussian distribution

In recent years, the dimensionality reduction has become more important as the number of dimensions of data used in various tasks such as regression and classification has increased. As popular nonlinear dimensionality reduction methods, t-distributed stochastic neighbor embedding (t-SNE) and uniform manifold approximation and projection (UMAP) have been proposed. However, the former outputs only one low-dimensional space determined by the t-distribution and the latter is difficult to control the distribution of distance between each pair of samples in low-dimensional space. To tackle these issues, we propose novel t-SNE and UMAP extended by q-Gaussian distribution, called q-Gaussian-distributed stochastic neighbor embedding (q-SNE) and q-Gaussian-distributed uniform manifold approximation and projection (q-UMAP). The q-Gaussian distribution is a probability distribution derived by maximizing the tsallis entropy by escort distribution with mean and variance, and a generalized version of Gaussian distribution with a hyperparameter q. Since the shape of the q-Gaussian distribution can be tuned smoothly by the hyperparameter q, q-SNE and q-UMAP can in- tuitively derive different embedding spaces. To show the quality of the proposed method, we compared the visualization of the low-dimensional embedding space and the classification accuracy by k-NN in the low-dimensional space. Empirical results on MNIST, COIL-20, OliverttiFaces and FashionMNIST demonstrate that the q-SNE and q-UMAP can derive better embedding spaces than t-SNE and UMAP.

Predicting S. aureus antimicrobial resistance with interpretable genomic space maps.

Increasing antimicrobial resistance (AMR) represents a global healthcare threat. To decrease the spread of AMR and associated mortality, methods for rapid selection of optimal antibiotic treatment are urgently needed. Machine learning (ML) models based on genomic data to predict resistant phenotypes can serve as a fast screening tool prior to phenotypic testing. Nonetheless, many existing ML methods lack interpretability. Therefore, we present a methodology for visualization of sequence space and AMR prediction based on the non-linear dimensionality reduction method - generative topographic mapping (GTM). This approach, applied to AMR data of >5000 S. aureus isolates retrieved from the PATRIC database, yielded GTM models with reasonable accuracy for all drugs (balanced accuracy values ≥0.75). The Generative Topographic Maps (GTMs) represent data in the form of illustrative maps of the genomic space and allow for antibiotic-wise comparison of resistant phenotypes. The maps were also found to be useful for the analysis of genetic determinants responsible for drug resistance. Overall, the GTM-based methodology is a useful tool for both the illustrative exploration of the genomic sequence space and AMR prediction.

Abstract B063: Investigation of tumor heterogeneity using integrated single-cell RNA sequence data based on HER2 status in patients with breast cancer

Abstract [Introduction] Human epidermal growth factor receptor 2 (HER2), which is characterized by ERBB2 amplification, is one of the important markers for treatment decision related to breast cancer. Many targeted therapies for HER2-positive (immunohistochemistry [IHC] scores of 3+ or 2+ with an in situ hybridization [ISH] gene amplification) or HER2-low (IHC score 1+ or 2+ with no ISH gene amplification) breast cancers have been extensively developed thus far. Meanwhile, tumoral heterogeneity is considered one of the mechanisms for drug resistance; however, it has not been fully elucidated on each HER2 status at single-cell level. Therefore, an integrated analysis of the breast cancer single-cell gene expression data of both public datasets and our cohort was used to investigate tumor heterogeneity based on HER2 status. [Methods] We collected 21 and 6 scRNA-seq samples of primary breast cancer from the public Gene Expression Omnibus (GEO) and our institution, respectively. A total of 27 samples included HER2-positive cases (pure HER2 cases: estrogen receptor [ER]-negative/HER2-positive and Luminal-HER2 cases: ER-positive/HER2-positive) and Luminal cases (ER-positive/HER2-negative). These datasets were imported into R software version 4.2.0. and transformed into Seurat objects with the package Seurat version 4.3.0. UMAP plots, which is a non-linear dimension reduction method, were used for clustering analyses. Seurat in R was used to generate UMAP, feature, and violin plots. Additionally, we performed pathway enrichment analysis with the significant gene list from each cluster between the ERBB2-high and ERBB2-low groups. [Results] Clustering analysis revealed heterogeneous distribution in each gene related to breast cancer (ESR1, PGR, ERBB2, and MKI67). One of the clusters revealed high MKI67 expression. ERBB2 expressions were diffusely distributed on each cluster of pure HER2 cases; however, the expressions were considerably higher in one of the clusters in cases of Luminal-HER2. The ERBB2 expression in Luminal cases, which included HER2-low status, was lower than that in HER2-positive cases, albeit slight expression was observed. Cell proliferation factors, including IGF, IGF1R, and EGF, were included in the ERBB2-high expression group compared with the ERBB2-low expression group for pathway analysis. Further, we examined typical gene expressions which are associated with markers related to breast cancer, cancer stem cell, and epithelial-to-mesenchymal transition in each case and revealed heterogeneous patterns across patients. [Conclusion] Heterogeneous ERBB2 expression distribution was observed in HER2-positive cases, and slight ERBB2 expression was identified in the Luminal cases. Moreover, Luminal-HER2 cases could be considered a more heterogeneous subtype compared with pure HER2 cases. Additionally, gene expressions of typical gene markers varied across patients. These results indicated that breast cancer displays heterogeneous patterns on each HER2 status not only intra-tumoral heterogeneity but also inter-patient heterogeneity. Citation Format: Sho Shiino, Momoko Tokura, Jun Nakayama, Masayuki Yoshida, Akihiko Suto, Yusuke Yamamoto. Investigation of tumor heterogeneity using integrated single-cell RNA sequence data based on HER2 status in patients with breast cancer [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: Advances in Breast Cancer Research; 2023 Oct 19-22; San Diego, California. Philadelphia (PA): AACR; Cancer Res 2024;84(3 Suppl_1):Abstract nr B063.

Combustion instability analysis in an ethylene-fueled scramjet combustor under various fuel penetration height conditions using an image-based nonlinear dimensionality reduction method

The present study investigates the effects of fuel penetration height on combustion instabilities in an ethylene-fueled scramjet model combustor with a cavity flameholder. Experiments were performed at the stagnation temperature of 1900 K, the stagnation pressure of 0.37 MPa, and the Mach number of 2. Three fuel injection orifice diameters:2.3, 2.4, and 2.5 mm, were tested to elucidate the effects of ethylene penetration height on combustion instabilities. Furthermore, high-speed measurements of CH* chemiluminescence and shadowgraphs were performed with high-speed video cameras. To examine the dynamics of the combustion instabilities, time-resolved CH* chemiluminescence images and shock parameters, extracted from snapshots of shadowgraphs, were analyzed using a non-linear dimensionality reduction algorithm: Gaussian Process Dynamical Model (GPDM). Thereafter, further analyses on the acquired latent variables were conducted with Recurrence Plot (RP). The experimental results showed that the fuel equivalence ratio (ϕ) range for cavity shear-layer combustion mode expanded as d decreased. Furthermore, for ϕ = 0.18, the instability behavior remarkably changed at around d = 2.4 mm. Therefore, the instability dynamics for ϕ = 0.18 were investigated using GPDM and RP including results from our previous study (d = 2, 3, and 4 mm), revealing differences in the instability behaviors. For d = 3 and 4 mm, jet-wake combustion and ram combustion modes were established alternately with a frequency of about 1600 Hz. In contrast, at d = 2.4 and 2.5 mm, although a similar instability in the d = 4 mm case was present at almost the same oscillation frequency, a different instability behavior was also confirmed. This additional instability exhibited an intermediate state between jet-wake combustion and ram combustion modes. These two instabilities emerged aperiodically. For an unstable combustion in shear layer observed for d = 2 and 2.3 mm, corresponding RPs exhibited black patches, indicating that the oscillation amplitude diminished substantially.

Soft sensor for predicting indoor PM2.5 concentration in subway with adaptive boosting deep learning model

Public health depends on indoor air quality (IAQ), hence soft measurement techniques must be implemented in the subway environment for more precise and reliable monitoring of indoor particulate matter concentration levels. Adaptive boosting (AdaBoost), an ensemble learning technique, is simple to code and less prone to overfitting. Compared to a single model, it is better able to take into consideration the intricate elements included in air quality data. It is suggested to use an adaptive boosting of long short-term memory (AdaBoost-LSTM) model and kernel principal component analysis (KPCA) for ensemble learning. The kernel function and PCA are first coupled to create KPCA, which is a nonlinear dimensionality reduction method for IAQ. This removes the negative impacts of noise interference. The learning performance of LSTM is then enhanced using AdaBoost as an ensemble learning technique. The KPCA-AdaBoost-LSTM model can deliver higher modeling performance, according to the results. The R2 reached 0.9007 and 0.8995 when predicting PM2.5 in the hall and platform. SHapley Additive exPlanations (SHAP) analysis was used to interpret the input contributions of the model, enhancing the interpretability and transparency of the proposed soft sensor.

Model-based evaluation of spatiotemporal data reduction methods with unknown ground truth through optimal visualization and interpretability metrics.

Optimizing and benchmarking data reduction methods for dynamic or spatial visualization and interpretation (DSVI) face challenges due to many factors, including data complexity, lack of ground truth, time-dependent metrics, dimensionality bias and different visual mappings of the same data. Current studies often focus on independent static visualization or interpretability metrics that require ground truth. To overcome this limitation, we propose the MIBCOVIS framework, a comprehensive and interpretable benchmarking and computational approach. MIBCOVIS enhances the visualization and interpretability of high-dimensional data without relying on ground truth by integrating five robust metrics, including a novel time-ordered Markov-based structural metric, into a semi-supervised hierarchical Bayesian model. The framework assesses method accuracy and considers interaction effects among metric features. We apply MIBCOVIS using linear and nonlinear dimensionality reduction methods to evaluate optimal DSVI for four distinct dynamic and spatial biological processes captured by three single-cell data modalities: CyTOF, scRNA-seq and CODEX. These data vary in complexity based on feature dimensionality, unknown cell types and dynamic or spatial differences. Unlike traditional single-summary score approaches, MIBCOVIS compares accuracy distributions across methods. Our findings underscore the joint evaluation of visualization and interpretability, rather than relying on separate metrics. We reveal that prioritizing average performance can obscure method feature performance. Additionally, we explore the impact of data complexity on visualization and interpretability. Specifically, we provide optimal parameters and features and recommend methods, like the optimized variational contractive autoencoder, for targeted DSVI for various data complexities. MIBCOVIS shows promise for evaluating dynamic single-cell atlases and spatiotemporal data reduction models.

Trade-offs in the latent representation of microstructure evolution

Characterizing and quantifying microstructure evolution is critical to forming quantitative relationships between material processing conditions, resulting microstructure, and observed properties. Machine-learning methods are increasingly accelerating the development of these relationships by treating microstructure evolution as a pattern recognition problem, discovering relationships explicitly or implicitly. These methods often rely on identifying low-dimensional microstructural fingerprints as latent variables. However, using inappropriate latent variables can lead to challenges in learning meaningful relationships. In this work, we survey and discuss the ability of various linear and nonlinear dimensionality reduction methods including principal component analysis, autoencoders, and diffusion maps to quantify and characterize the learned latent space microstructural representations and their time evolution. We characterize latent spaces by their ability to represent high-dimensional microstructural data in terms of compression achieved as a function of the number of latent dimensions required to represent the data accurately, their accuracy based on their reconstruction performance, and the smoothness of the microstructural trajectories in latent dimension. We quantify these metrics for common microstructure evolution problems in material science including spinodal decomposition of a binary metallic alloy, thin film deposition of a binary metallic alloy, dendritic growth, and grain growth in a polycrystal. This study provides considerations and guidelines for choosing dimensionality reduction methods when considering materials problems that involve high dimensional data and a variety of features over a range of lengths and time scales.

A software defect prediction method based on learnable three-line hybrid feature fusion

Software defect prediction (SDP) plays a crucial role in ensuring the security and quality of software systems. However, it faces challenges posed by high-dimensional features present in software defect datasets and the limited effectiveness of traditional nonlinear dimensionality reduction methods in extracting essential feature information. To address these issues, we propose a novel approach called learnable three-line hybrid feature fusion (LTHFFA), which incorporates the principle of three-line hybrid breeding into feature fusion for the first time. In this method, three distinct dimensionality reduction techniques are initially employed to obtain three separate sets of features. Subsequently, a learnable weight factor feature fusion method is proposed to facilitate automatically learn and dynamically update of feature weights. By integrating the three feature sets based on the principle of three-line hybrid breeding, we derive learnable three-line hybrid fusion features. These features are then utilized in the context of software defect prediction. Experimental results demonstrate the superior performance of LTHFFA compared to nine other dimensionality reduction methods across seventeen publicly available software defect datasets. LTHFFA exhibits the ability to effectively integrate multiple feature sets, reduce feature redundancy, and enhance predictive accuracy. Moreover, statistical analysis using Friedman ranking and Holm's post-hoc test confirms the significant advantage of LTHFFA over alternative dimensionality reduction methods.

Nonlinear dimensionality reduction methods for potentiometric multisensor systems data analysis

AbstractElectrochemical multisensor systems were proven to be a very perspective research direction in modern analytical chemistry. The multisensor approach assumes an employment of cross‐sensitive chemical sensors in combination with multivariate data processing methods. Dimensionality reduction of the data obtained from multisensor systems is a very important step and it is mostly based on the traditional tools of chemometrics, such as Principal Component Analysis (PCA). In case of chemically complex samples, the response of multisensor systems may have a complex nonlinear nature and the use of linear modelling methods does not seem optimal. However, the potential of nonlinear dimensionality reduction methods in the processing of multisensor data has not yet been systematically studied. In this report we aim to fill this gap and assess the performance of various nonlinear dimensionality reduction tools: Isomap, Self‐Organizing Kohonen Maps, and Autoencoder. These methods were explored using three datasets from potentiometric multisensor systems obtained in various real applications. It was shown that nonlinear dimensionality reduction methods give the possibility to obtain additional and more detailed information about the analyzed objects/processes compared to PCA. However, calculation time for nonlinear dimensionality reduction methods essentially exceeds that for PCA, and it can be a limiting factor for application of such algorithms.

Absence of enterotypes in the human gut microbiomes reanalyzed with non-linear dimensionality reduction methods.

Enterotypes of the human gut microbiome have been proposed to be a powerful prognostic tool to evaluate the correlation between lifestyle, nutrition, and disease. However, the number of enterotypes suggested in the literature ranged from two to four. The growth of available metagenome data and the use of exact, non-linear methods of data analysis challenges the very concept of clusters in the multidimensional space of bacterial microbiomes. Using several published human gut microbiome datasets of variable 16S rRNA regions, we demonstrate the presence of a lower-dimensional structure in the microbiome space, with high-dimensional data concentrated near a low-dimensional non-linear submanifold, but the absence of distinct and stable clusters that could represent enterotypes. This observation is robust with regard to diverse combinations of dimensionality reduction techniques and clustering algorithms.

Laplacian-based Cluster-Contractive t-SNE for High-Dimensional Data Visualization

Dimensionality reduction techniques aim at representing high-dimensional data in low-dimensional spaces to extract hidden and useful information or facilitate visual understanding and interpretation of the data. However, few of them take into consideration the potential cluster information contained implicitly in the high-dimensional data. In this article, we propose Lap tSNE, a new graph-layout nonlinear dimensionality reduction method based on t-SNE, one of the best techniques for visualizing high-dimensional data as 2D scatter plots. Specifically, Lap tSNE leverages the eigenvalue information of the graph Laplacian to shrink the potential clusters in the low-dimensional embedding when learning to preserve the local and global structure from high-dimensional space to low-dimensional space. It is nontrivial to solve the proposed model because the eigenvalues of normalized symmetric Laplacian are functions of the decision variable. We provide a majorization-minimization algorithm with convergence guarantee to solve the optimization problem of Lap tSNE and show how to calculate the gradient analytically, which may be of broad interest when considering optimization with Laplacian-composited objective. We evaluate our method by a formal comparison with state-of-the-art methods on seven benchmark datasets, both visually and via established quantitative measurements. The results demonstrate the superiority of our method over baselines such as t-SNE and UMAP. We also provide out-of-sample extension, large-scale extension, and mini-batch extension for our Lap tSNE to facilitate dimensionality reduction in various scenarios.