Linear Embedding Research Articles

Primary Modes of Northern Hemisphere Snowfall Particle Size Distributions

Abstract A comprehensive understanding of snowfall microphysics is crucial for enhancing the accuracy of remote sensing snowfall retrievals. However, variations in regional and seasonal snow particle size distributions (PSDs) contribute substantial uncertainty. Here, we examine snowfall PSDs from across the Northern Hemisphere, applying Principal Component Analysis (PCA) to disdrometer observations with the aim of identifying dominant modes of variability across varying regional climates. The PCA revealed three Empirical Orthogonal Functions (EOFs) that account for a combined 95% of the variability across the dataset, which are attributed to latent linear embeddings of snowfall intensity (EOF1), snowfall character (EOF2) and snowfall regime (EOF3). Examining point clusters with the highest combined EOF values reveals six distinct modes of variability (i.e., Principal Component [PC] groups) with unique PSD traits. These groups are then correlated with environmental factors using data from collocated vertically pointing radar, surface meteorology, and reanalysis to assist in assigning physical attributes. The first and second PC groups, linked to EOF1’s intensity embedding, are described by their PSD intercepts, snowfall rates, and reflectivity and Doppler velocity values, representing low and high intensity snowfall modes, respectively. The third and fourth PC groups, associated with EOF2’s character embedding, are defined by temperature, fall speed, and density, indicative of cold, fluffy snowfall and warm, dense snowfall, respectively. The fifth and sixth PC groups, related to EOF3’s regime embedding, are distinguished by their PSD slope, snowfall rate, and reflectivity profiles, signifying shallow, weak convective systems with small particles, and deep, stratiform snowfall events with large aggregates, respectively.

Enhanced Hessian locally linear embedding method for rolling bearing fault diagnosis based upon novel variational mode decomposition

Due to the plenty of redundant information contained in the fault feature sets of the original vibration signals of rolling bearings, the diagnostic accuracy is reduced and computational complexity is increased, making it very difficult to achieve accurate and fast fault recognition. So as to address the hard issue, this article develops an Enhanced Hessian Locally Linear Embedding (EHLLE) method for rolling bearing fault diagnosis based upon Novel Variational Mode Decomposition (NVMD). Firstly, NVMD method is utilized to denoise sample vibration signals and the sensitive modes containing main fault information are obtained. Secondly, some time-domain and frequency-domain statistical features are used to construct sample high-dimensional features, the dimensionality of which is reduced by EHLLE. Ultimately, K-Means algorithm is employed to cluster the low-dimensional features, which are utilized to train Support Vector Machine (SVM), and then the trained SVM is applied to the recognition of testing sample low-dimensional features. Two experiments of rolling bearing fault diagnosis demonstrate the effectiveness of NVMD-EHLLE method. Additionally, the superiority of the developed method is verified by comparing with other three typical methods.

Trace Ratio Based Manifold Learning With Tensor Data

ABSTRACTIn this article, we propose an extension of trace ratio based Manifold learning methods to deal with multidimensional data sets. Based on recent progress on the tensor‐tensor product, we present a generalization of the trace ratio criterion by using the properties of the t‐product. This will conduct us to introduce some new concepts such as Laplacian tensor and we will study formally the trace ratio problem by discussing the conditions for the existence of solutions and optimality. Next, we will present a tensor Newton QR decomposition algorithm for solving the trace ratio problem. Manifold learning methods such as Laplacian eigenmaps, linear discriminant analysis and locally linear embedding will be formulated in a tensor representation and optimized by the proposed algorithm. Finally, we will evaluate the performance of the different studied dimension reduction methods on several synthetic and real world data sets.

Hybrid Model Integrating Locally Linear Embedding and LightGBM for Predicting Sulfur Content in Electroslag Remelting

This study proposes a model for predicting the sulfur content in the electroslag remelting (ESR) process, by integrating locally linear embedding (LLE) and the LightGBM algorithm. The LLE dimensionality reduction method is employed to preprocess the factors influencing the sulfur content, preserving the local relationships between samples while reducing the data dimensionality. Subsequently, five models are established, including LLE‐LightGBM, LLE‐RR, LLE‐RF, LLE‐XGBoost, and LLE‐CatBoost. Bayesian optimization is used to tune the hyperparameters of these models, which are then trained and validated using production data. The results demonstrate that the integration of LLE and Bayesian optimization improved the performance of all five models. The incorporation of LLE enhanced the models’ understanding and predictive capabilities of the data, thereby improving their performance and robustness. Among the five models, the LLE‐LightGBM model exhibits the best performance, with the following metrics: MSE = 0, = 0.9894, MAE = 0, MEDAE = 0, EVS = 0.9895, and ME = 1.8 × 10−5. Therefore, the LLE‐LightGBM model can accurately predict the sulfur content in the ESR process, providing valuable guidance for end‐point control and decision‐making, and offering a new approach toward the intelligent automation of the ESR process.

Cardiovascular disease detection from cardiac arrhythmia ECG signals using artificial intelligence models with hyperparameters tuning methodologies

Cardiovascular disease (CVD) is connected with irregular cardiac electrical activity, which can be seen in ECG alterations. Due to its convenience and non-invasive aspect, the ECG is routinely exploited to identify different arrhythmias and automatic ECG recognition is needed immediately. In this paper, enhancement for the detection of CVDs such as Ventricular Tachycardia (VT), Premature Ventricular Contraction (PVC) and ST Change (ST) arrhythmia using different dimensionality reduction techniques and multiple classifiers are presented. Three-dimensionality reduction methods, such as Local Linear Embedding (LLE), Diffusion Maps (DM), and Laplacian Eigen (LE), are employed. The dimensionally reduced ECG samples are further feature selected with Cuckoo Search (CS) and Harmonic Search Optimization (HSO) algorithms. A publicly available MIT-BIH (Physionet) - VT database, PVC database, ST Change database and NSR database were used in this work. The cardiac vascular disturbances are classified by using seven classifiers such as Gaussian Mixture Model (GMM), Expectation Maximization (EM), Non-linear Regression (NLR), Logistic Regression (LR), Bayesian Linear Discriminant Analysis (BDLC), Detrended Fluctuation Analysis (Detrended FA), and Firefly. For different classes, the average overall accuracy of the classification techniques is 55.65 % when without CS and HSO feature selection, 64.36 % when CS feature selection is used, and 75.39 % when HSO feature selection is used. Also, to improve the performance of classifiers, the hyperparameters of four classifiers (GMM, EM, BDLC and Firefly) are tuned with the Adam and Grid Search Optimization (GSO) approaches. The average accuracy of classification for the CS feature-based classifiers that used GSO and Adam hyperparameter tuning was 79.92 % and 85.78 %, respectively. The average accuracy of classification for the HSO feature-based classifiers that used GSO and Adam hyperparameter tuning was 86.87 % and 93.77 %, respectively. The performance of the classifier is analyzed based on the accuracy parameter for both with and without feature selection methods and with hyperparameter tuning techniques. In the case of ST vs. NSR, a higher accuracy of 98.92 % is achieved for the LLE dimensionality reduction with HSO feature selection for the GMM classifier with Adam's hyperparameter tuning approach. The GMM classifier with the Adam hyperparameter tuning approach with 98.92 % accuracy in detecting ST vs. NSR cardiac disease is outperforming all other classifiers and methodologies.

Exploratory techniques to analyse Ecuador's tourism industry

Abstract The analysis of the operation of tourism companies will provide valid information for the design of policies to reactivate the tourism industry, which has been strongly affected during the pandemic generated by COVID-19. The objective of this paper is to use soft computing techniques to analyse tourism companies in Ecuador. First of all, dimensionality reduction methods are applied: principal component analysis, isometric feature mapping and locally linear embedding, on data of tourism enterprises in Ecuador for the year 2015. In addition, to verify the trend of operational variables, the data of tourism companies in Ecuador in 2019 and 2020 are analysed with dimensionality reduction methods that improve the interpretation by minimizing the loss of information. The data sets are analysed with k-means, k-medoids and Hierarchical Clustering, generating groups according to similar characteristics. The optimal number of clusters is determined with the following: Elbow Method, Silhouette Coefficient, Davies-Bouldin Index and Dunn Index. In addition, an analysis of the operation of tourism companies in the year 2020 concerning previous years is included. The study allows exploring Soft Computing techniques to identify important information for the definition of strategies that contribute to an effective reactivation of the tourist industry of Ecuador.

Manifold learning-based reduced-order model for full speed flow field

Reduced-order models (ROMs) can effectively balance the accuracy and efficiency of computational fluid dynamics (CFD). The nonlinear flow field characteristics cannot be captured accurately by traditional ROMs, such as proper orthogonal decomposition (POD). Combining isometric mapping (ISOMAP) and local linear embedding (LLE), a novel manifold learning method (ISOMAP-Local LLE) is proposed, performing global and accurate reconstruction of the nonlinear flow field. First, the nonlinear dimensionality reduction is derived by considering the global isometric characteristic and the local reconstruction relationship simultaneously. Then, the local interpolation model is constructed to improve the interpolation accuracy introduced by the global interpolation model. Finally, the flow field reconstruction is accomplished based on the inverse mapping. Furthermore, the criteria of hyperparameters have been established to achieve high-precision prediction. Several examples covering full speed flow field are carried out to demonstrate the accuracy and efficiency of ISOMAP-Local LLE. The proposed manifold learning-based ROM achieves prediction accuracy that surpasses that of other ROMs (such as POD, ISOMAP, LLE, etc.), resulting in significant time cost savings for CFD simulations.

Natural gas pipeline leak diagnosis based on manifold learning

Natural gas pipeline leakage is a common safety hazard, which can have a great impact on the economy and the environment. This paper proposed a novel manifold learning-enabled feature extraction method for natural gas pipeline leakage diagnosis. Firstly, the natural gas pipeline working condition signal is decomposed and denoised by Variational mode decomposition (VMD). Secondly, the denoised pipeline signals were constructed into a form expressed by the Symmetric positive definite matrix (SPD) using the VMD reconstruction technique, and the geodesic distance measurement method was applied to the SPD matrix to make the data located on the SPD manifold. Then feature extraction is carried out by Local linear embedding (LLE) method based on asymmetric distance. Finally, pattern recognition of the features extracted in this paper by Support vector machine (SVM) can achieve 100% recognition accuracy. By enabling faster and more accurate leak detection, the method minimizes gas loss, as well as mitigating the environmental risks caused by this potent greenhouse gas.

Sea Ice Detection from GNSS-R Data Based on Local Linear Embedding

Sea ice plays a critical role in the Earth’s climate system, and its variations affect ecosystem stability. This study introduces a novel method for detecting sea ice in the Arctic Ocean using bidirectional radar reflections from the Global Navigation Satellite System (GNSS). Utilizing delay-Doppler maps (DDM) from the UK TechDemoSat-1 (TDS-1) satellite mission and surface data from the U.S. National Oceanic and Atmospheric Administration (NOAA), we employ the local linear embedding (LLE) algorithm for feature extraction. This approach notably reduces training costs and enhances real-time performance, while maintaining a high accuracy and robust noise immunity level. Focusing on the region above 70° north latitude throughout 2018, we aimed to distinguish between sea ice and seawater. The extracted DDM features via LLE are input into a support vector machine (SVM) for classification. The results indicate that our method achieves an accuracy of over 99% for selected low-noise data and a monthly average accuracy of 92.74% for data containing noise, while the CNN method has a monthly average accuracy of only 77.31% for noisy data. A comparative analysis between the LLE-SVM approach and the convolutional neural network (CNN) method demonstrated the superior anti-interference capabilities of the former. Additionally, the impact of the sea ice melting period on detection accuracy was analyzed.

Few-Shot Steel Defect Detection Based on a Fine-Tuned Network with Serial Multi-Scale Attention

Detecting defects on a steel surface is crucial for the quality enhancement of steel, but its effectiveness is impeded by the limited number of high-quality samples, diverse defect types, and the presence of interference factors such as dirt spots. Therefore, this article proposes a fine-tuned deep learning approach to overcome these obstacles in unstructured few-shot settings. Initially, to address steel surface defect complexities, we integrated a serial multi-scale attention mechanism, concatenating attention and spatial modules, to generate feature maps that contain both channel information and spatial information. Further, a pseudo-label semi-supervised learning algorithm (SSL) based on a variant of the locally linear embedding (LLE) algorithm was proposed, enhancing the generalization capability of the model through information from unlabeled data. Afterwards, the refined model was merged into a fine-tuned few-shot object detection network, which applied extensive base class samples for initial training and sparsed new class samples for fine-tuning. Finally, specialized datasets considering defect diversity and pixel scales were constructed and tested. Compared with conventional methods, our approach improved accuracy by 5.93% in 7-shot detection tasks, markedly reducing manual workload and signifying a leap forward for practical applications in steel defect detection.

Envelopes in Banach spaces

We introduce the notion of isometric envelope of a subspace in a Banach space, establishing its connections with several key elements: (a) we explore its relation to the mean ergodic projection on fixed points within a semigroup of contractions, (b) we draw parallels with Korovkin sets from the 1970s, (c) we investigate its impact on the extension properties of linear isometric embeddings. We use this concept to address the recent conjecture that the Gurarij space and the spaces Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_p$$\\end{document}, p∉2N+4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p \ otin 2{\\mathbb {N}}+4$$\\end{document} are the only separable approximately ultrahomogeneous Banach spaces (a certain multidimensional transitivity of the action of the linear isometry group). The similar conjecture for Fraïssé Banach spaces (a strengthening of the approximately homogeneous property) is also considered. We characterize the Hilbert space as the only separable reflexive space in which any closed subspace coincides with its envelope; and we show that the Gurarij space satisfies the same property. We compute some envelopes in the case of Lebesgue spaces, showing that the reflexive Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_p$$\\end{document}-spaces are the only reflexive rearrangement invariant spaces on [0, 1] for which all 1-complemented subspaces are envelopes. We also identify the isometrically unique “full” quotient space of Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_p$$\\end{document} by a Hilbertian subspace, for appropriate values of p, as well as the associated topological group embedding of the unitary group into the isometry group of Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_p$$\\end{document}.

Explicit unsupervised feature selection based on structured graph and locally linear embedding

Numerous redundant and irrelevant features are usually contained in high-dimensional data whose presence, if ignored, can bring detrimental effects on the performance of data processing tasks. Unsupervised feature selection (UFS) as a trending topic in a great deal of domains has been greatly concerned, which can effectively filter out redundant and irrelevant features in the unlabeled data. The majority of existing UFS methods mainly focus on building the parameterized model in the original feature space or some certain low-dimensional feature subspace, which cannot fully capture the information of the target space. In this work, we propose a novel UFS method that unifies the explicit feature selective matrix and structured graph into a learning framework. An explicit selection matrix, whose scale, bound of the elements and structure are considered, is tailored for UFS. Furthermore, we take into account the local consistency so that the low dimensional manifold structures can be preserved to a better degree. Instead of using the pre-defined similarity matrix to construct graph, we make use of the way of learning to obtain the adaptive graph. Besides, for the purpose of exploiting the cluster structure of data, we impose a rank constraint on the graph. Notably, both the explicit selection matrix and intrinsic structure are learned in the target feature subspace, and thus the proposed methodology is more straightforward and effective. We present an effective and efficient algorithm for the resulting problem based on alternative optimization strategy, and establish its convergence and computational complexity analysis. The experimental results show that our proposed approach has improved by over 5.28% and 5.79% on average in terms of clustering accuracy (ACC) and Normalized Mutual Information (NMI) compared with comparison methods, which demonstrates its superiority.

A residual autoencoder-based transformer for fault detection of multivariate processes

The complexity of high-dimensional and noisy process signals reduces the effectiveness of conventional fault detection methods in industrial processes. Based on the hypothesis that data collected from normal and faulty processes has different characteristics, unsupervised deep neural networks, e.g., autoencoders, have been widely applied in process fault detection and achieved good performance. Many variants have been proposed to improve feature learning by combining different network structures. In this paper, a new transformer model, residual autoencoder-based transformer, is proposed for process fault detection. Firstly, autoencoder and transformer are integrated for better unsupervised feature learning of process signals. Secondly, linear embedding and attention mechanisms with bias are proposed to generate effective features from process signals. Finally, residual connections are constructed between the encoder and decoder of RATransformer to address overfitting in training. Four industrial cases are used to test the performance of RATransformer for process fault detection. The results show that the fault detection rate of RATransformer is at least 1 % higher than other comparison methods. Moreover, the testing results show that the model structure improves the fault detection performance of RATransformer. The complex models like RATransformer can be used in the industrial process when sufficient normal process data is available. An end-to-end training method can be further developed to improve the applicability of RATransformer in process fault detection in the future.

Integration of Manifold Learning and Density Estimation for Fine-Tuned Face Recognition

With the rapid advancements in data analysis and the increasing complexity of high-dimensional datasets, traditional dimensionality reduction techniques like Local Linear Embedding (LLE) often face challenges in maintaining accuracy and efficiency. This research aims to overcome the limitations of LLE, specifically its reliance on the nearest neighbor concept, its inability to distinguish differences among manifold points, and its underutilization of data discrimination information. To address these issues, we propose an advanced LLE algorithm that integrates decision tree-based neighbor recognition with Gaussian kernel density estimation. Decision trees accurately determine neighboring relationships, which are then optimized using Gaussian kernel density estimation to better reflect the distribution of sample points on the manifold. The algorithm also incorporates data discrimination information to enhance classification accuracy and efficiency. Evaluations in facial recognition tasks using SVM classifiers demonstrate significant improvements. Integrating decision trees (LLE-DT) yielded accuracy gains, with LFW at 98.75%, CFP 96.10%, and Olivetti 92.18%. Gaussian density estimation (LLE-GDE) achieved further enhancements, especially in LFW (99.13%), with CFP at 96.85%, and Olivetti at 91.82%. Combining both methods (LLE-DT-GDE) led to substantial improvements: LFW 99.61%, CFP 97.23%, and Olivetti 93.56%, highlighting the synergy between decision trees and Gaussian estimation. This advanced LLE algorithm effectively addresses the limitations of traditional approaches, showing promising results in complex data processing tasks such as facial recognition. These findings suggest its potential for broader applications in fields requiring robust data analysis and classification.

Privacy-preserving outsourcing scheme of face recognition based on locally linear embedding

Face recognition is a biometric-based technology that identifies or verifies a person’s identity by analyzing and comparing patterns in their facial features. Among kinds of face recognition algorithms, Locally Linear Embedding (LLE) algorithm has the advantage of preserving the local structure of face data. However, the LLE algorithm requires some computationally intensive matrix calculations, which might introduce latency to the device. In this paper, we propose a privacy-preserving outsourcing scheme of face recognition based on LLE algorithm for the first time. By outsourcing matrix multiplication, linear equations, and eigenvalue decomposition of the LLE algorithm to a cloud server, we reduce the computational load on the client device. To ensure data security, we generate a novel type of sparse orthogonal matrix through square root application and random permutation of diagonal elements, used as secret keys to blind the client’s data. Meanwhile, due to the sparsity of key matrices, the complexity of client-side computation complexity is reduced from O(n3) to O(n2). The experimental results show that our proposed scheme reduces computational costs while maintaining almost identical face recognition accuracy as the original LLE-based algorithm.

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.

Dimensionality Reduction in Structural Health Monitoring: A Case Study on Damaged Wind Turbine Blades

AbstractIn recent years, advances in structural health monitoring (SHM) of composite materials have been observed, driven by the adoption of intelligent diagnostic techniques. Vibration signals, which embed valuable structural health information, have been increasingly utilized in SHM. However, the high dimensionality of this data has necessitated significant computational resources and has made the differentiation between health states more complex. Highlighting the need for effective feature extraction and dimensionality reduction (DR), a study is conducted. In this research, advanced DR techniques, i.e., principal component analysis (PCA), locally linear embedding (LLE), t‐distributed stochastic neighbors embedding (t‐SNE), and uniform manifold approximation and projection (UMAP), are applied to an experimental dataset from a wind turbine blade under various health and environmental conditions (controlled‐environment vibration signals). The extracted features are then processed for the classification phase, and it is found that UMAP provides the best performance, albeit with a slightly increased computational demand. The findings from this research offer invaluable insights for researchers and engineers, assisting in the selection of the most appropriate DR method for SHM, and weighing up accuracy against computational time.

Analysis of Manifold and its Application

Manifold learning is a field of study in machine learning and statistics that is closely associated with dimensionality reduction algorithmic techniques is gaining popularity these days. There are two types of manifold learning approaches: linear and nonlinear. Principal component analysis (PCA) and multidimensional scaling (MDS) are two examples of linear techniques that have long been staples in the statistician's arsenal for evaluating multivariate data. Nonlinear manifold learning, which encompasses diffusion maps, Laplacian Eigenmaps, Hessian Eigenmaps, Isomap, and local linear embedding, has seen a surge in research effort recently. A few of these methods are nonlinear extensions of linear approaches. A nearest search, the definition of distances or affinities between points (a crucial component of these methods' effectiveness), and an Eigen problem for embedding high-dimensional points into a lower dimensional space make up the algorithmic process of the majority of these techniques. The strengths and weaknesses of the new method are briefly reviewed in this article. In the field of computer graphics, we utilize a particular manifold learning method was first presented in statistics and machine learning to create a global, Spectral-based shape descriptor.

Machine Learning Model in Obesity to Predict Weight Loss One Year after Bariatric Surgery: A Pilot Study.

Roux-en-Y gastric bypass (RYGB) is a treatment for severe obesity. However, many patients have insufficient total weight loss (TWL) after RYGB. Although multiple factors have been involved, their influence is incompletely known. The aim of this exploratory study was to evaluate the feasibility and reliability of the use of machine learning (ML) techniques to estimate the success in weight loss after RYGP, based on clinical, anthropometric and biochemical data, in order to identify morbidly obese patients with poor weight responses. We retrospectively analyzed 118 patients, who underwent RYGB at the Hospital Clínico Universitario of Valencia (Spain) between 2013 and 2017. We applied a ML approach using local linear embedding (LLE) as a tool for the evaluation and classification of the main parameters in conjunction with evolutionary algorithms for the optimization and adjustment of the parameter model. The variables associated with one-year postoperative %TWL were obstructive sleep apnea, osteoarthritis, insulin treatment, preoperative weight, insulin resistance index, apolipoprotein A, uric acid, complement component 3, and vitamin B12. The model correctly classified 71.4% of subjects with TWL < 30% although 36.4% with TWL ≥ 30% were incorrectly classified as "unsuccessful procedures". The ML-model processed moderate discriminatory precision in the validation set. Thus, in severe obesity, ML-models can be useful to assist in the selection of patients before bariatric surgery.

Multi-view data visualisation via manifold learning

Non-linear dimensionality reduction can be performed by manifold learning approaches, such as stochastic neighbour embedding (SNE), locally linear embedding (LLE) and isometric feature mapping (ISOMAP). These methods aim to produce two or three latent embeddings, primarily to visualise the data in intelligible representations. This manuscript proposes extensions of Student’s t-distributed SNE (t-SNE), LLE and ISOMAP, for dimensionality reduction and visualisation of multi-view data. Multi-view data refers to multiple types of data generated from the same samples. The proposed multi-view approaches provide more comprehensible projections of the samples compared to the ones obtained by visualising each data-view separately. Commonly, visualisation is used for identifying underlying patterns within the samples. By incorporating the obtained low-dimensional embeddings from the multi-view manifold approaches into the K-means clustering algorithm, it is shown that clusters of the samples are accurately identified. Through extensive comparisons of novel and existing multi-view manifold learning algorithms on real and synthetic data, the proposed multi-view extension of t-SNE, named multi-SNE, is found to have the best performance, quantified both qualitatively and quantitatively by assessing the clusterings obtained. The applicability of multi-SNE is illustrated by its implementation in the newly developed and challenging multi-omics single-cell data. The aim is to visualise and identify cell heterogeneity and cell types in biological tissues relevant to health and disease. In this application, multi-SNE provides an improved performance over single-view manifold learning approaches and a promising solution for unified clustering of multi-omics single-cell data.