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Real-world data is typically distributed on low-dimensional manifolds embedded in high-dimensional Euclidean spaces. Accurately extracting spatial distribution features on general manifolds that reflect the intrinsic characteristics of data is crucial for effective feature representation. Therefore, we propose a generalized geodesic basis function neural network (G2BFNN) architecture. The generalized geodesic basis functions (G2BF) are defined based on generalized geodesic distances. The generalized geodesic distance metric (G2DM) is obtained by learning the manifold structure. To implement this architecture, a specific G2BFNN, named discriminative local preserving projection-based G2BFNN (DLPP-G2BFNN) is proposed. DLPP-G2BFNN mainly contains two modules, namely the manifold structure learning module (MSLM) and the network mapping module (NMM). In the MSLM module, a supervised adjacency graph matrix is constructed to constrain the learning of the manifold structure. This enables the learned features in the embedding subspace to maintain the manifold structure while enhancing the discriminability. The features and G2DM learned in the MSLM are fed into the NMM. Through the G2BF in the NMM, the spatial distribution features on manifold are obtained. Finally, the output of the network is obtained through the fully connected layer. Compared with the local response neural network based on Euclidean distance, the proposed network can reveal more essential spatial structure characteristics of the data. Meanwhile, the proposed G2BFNN is a generalized network architecture that can be combined with any manifold learning method, showcasing high scalability. The experimental results demonstrate that the proposed DLPP-G2BFNN outperforms existing methods by utilizing fewer kernels while achieving higher recognition performance.

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Objective.We investigated fluctuations of the photoplethysmography (PPG) waveform in patients undergoing surgery. There is an association between the morphologic variation extracted from arterial blood pressure (ABP) signals and short-term surgical outcomes. The underlying physiology could be the numerous regulatory mechanisms on the cardiovascular system. We hypothesized that similar information might exist in PPG waveform. However, due to the principles of light absorption, the noninvasive PPG signals are more susceptible to artifacts and necessitate meticulous signal processing.Approach.Employing the unsupervised manifold learning algorithm, dynamic diffusion map, we quantified multivariate waveform morphological variations from the PPG continuous waveform signal. Additionally, we developed several data analysis techniques to mitigate PPG signal artifacts to enhance performance and subsequently validated them using real-life clinical database.Main results.Our findings show similar associations between PPG waveform during surgery and short-term surgical outcomes, consistent with the observations from ABP waveform analysis.Significance.The variation of morphology information in the PPG waveform signal in major surgery provides clinical meanings, which may offer new opportunity of PPG waveform in a wider range of biomedical applications, due to its non-invasive nature.

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Community detection in multi-layer networks stands as a prominent subject within network analysis research. However, the majority of existing techniques for identifying communities encounter two primary constraints: they lack suitability for high-dimensional data within multi-layer networks and fail to fully leverage additional auxiliary information among communities to enhance detection accuracy. To address these limitations, a novel approach named weighted prior tensor training decomposition (WPTTD) is proposed for multi-layer network community detection. Specifically, the WPTTD method harnesses the tensor feature optimization techniques to effectively manage high-dimensional data in multi-layer networks. Additionally, it employs a weighted flattened network to construct prior information for each dimension of the multi-layer network, thereby continuously exploring inter-community connections. To preserve the cohesive structure of communities and to harness comprehensive information within the multi-layer network for more effective community detection, the common community manifold learning (CCML) is integrated into the WPTTD framework for enhancing the performance. Experimental evaluations conducted on both artificial and real-world networks have verified that this algorithm outperforms several mainstream multi-layer network community detection algorithms.

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Single-cell transcriptomics (scRNA-seq) is revolutionizing biological research, yet it faces challenges such as inefficient transcript capture and noise. To address these challenges, methods like neighbor averaging or graph diffusion are used. These methods often rely on k-nearest neighbor graphs from low-dimensional manifolds. However, scRNA-seq data suffer from the 'curse of dimensionality', leading to the over-smoothing of data when using imputation methods. To overcome this, sc-PHENIX employs a PCA-UMAP diffusion method, which enhances the preservation of data structures and allows for a refined use of PCA dimensions and diffusion parameters (e.g., k-nearest neighbors, exponentiation of the Markov matrix) to minimize noise introduction. This approach enables a more accurate construction of the exponentiated Markov matrix (cell neighborhood graph), surpassing methods like MAGIC. sc-PHENIX significantly mitigates over-smoothing, as validated through various scRNA-seq datasets, demonstrating improved cell phenotype representation. Applied to a multicellular tumor spheroid dataset, sc-PHENIX identified known extreme phenotype states, showcasing its effectiveness. sc-PHENIX is open-source and available for use and modification.

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In this study, the goal was to develop a method for detecting and classifying organophosphorus pesticides (OPPs) in bodies of water. Sixty-five samples with different concentrations were prepared for each of the organophosphorus pesticides, namely chlorpyrifos, acephate, parathion-methyl, trichlorphon, dichlorvos, profenofos, malathion, dimethoate, fenthion, and phoxim, respectively. Firstly, the spectral data of all the samples was obtained using a UV-visible spectrometer. Secondly, five preprocessing methods, six manifold learning methods, and five machine learning algorithms were utilized to build detection models for identifying OPPs in water bodies. The findings indicate that the accuracy of machine learning models trained on data preprocessed using convolutional smoothing + first-order derivatives (SG + FD) outperforms that of models trained on data preprocessed using other methods. The backpropagation neural network (BPNN) model exhibited the highest accuracy rate at 99.95%, followed by the support vector machine (SVM) and convolutional neural network (CNN) models, both at 99.92%. The extreme learning machine (ELM) and K-nearest neighbors (KNN) models demonstrated accuracy rates of 99.84% and 99.81%, respectively. Following the application of a manifold learning algorithm to the full-wavelength data set for the purpose of dimensionality reduction, the data was then visualized in the first three dimensions. The results demonstrate that the t-distributed domain embedding (t-SNE) algorithm is superior, exhibiting dense clustering of similar clusters and clear classification of dissimilar ones. SG + FD-t-SNE-SVM ranks highest among the feature extraction models in terms of performance. The feature extraction dimension was set to 4, and the average classification accuracy was 99.98%, which slightly improved the prediction performance over the full-wavelength model. As shown in this study, the ultraviolet-visible (UV-visible) spectroscopy system combined with the t-SNE and SVM algorithms can effectively identify and classify OPPs in waterbodies.

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BACKGROUND: To progress adolescent mental health research beyond our present achievements - a complex account of brain and environmental risk factors without understanding neurobiological embedding in the environment - we need methods to unveil relationships between the developing brain and real-world environmental experiences. METHODS: We investigated associations among brain function, environments, and emotional and behavioral problems using participants from the Adolescent Brain and Cognitive Development Study (N=2,401 female). We applied manifold learning, a promising technique for uncovering latent structure from high-dimensional biomedical data like functional magnetic resonance imaging (fMRI). Specifically, we developed exogenous PHATE (E-PHATE) to model brain-environment interactions. We used E-PHATE embeddings of participants' brain activation during emotional and cognitive processing to predict individual differences in cognition and emotional and behavioral problems, both cross-sectionally and longitudinally. RESULTS: E-PHATE embeddings of participants' brain activation and environments at baseline show moderate-to-large associations with total, externalizing, and internalizing problems at baseline, across several subcortical regions and large-scale cortical networks, relative to the zero-to-small effects achieved by voxel or PHATE methods. E-PHATE embeddings of the brain and environment at baseline also relate to emotional and behavioral problems two years later. These longitudinal predictions show a consistent, moderate effect in the frontoparietal and attention networks. CONCLUSIONS: Adolescent brain's embedding in the environment yields enriched insight into emotional and behavioral problems. Using E-PHATE, we demonstrate how the harmonization of cutting-edge computational methods with longstanding developmental theories advances detection and prediction of adolescent emotional and behavioral problems.

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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.

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Monitoring urban structure and development requires high-quality data at high spatio-temporal resolution. While traditional censuses have provided foundational insights into demographic and socio-economic aspects of urban life, their pace may not always align with the pace of urban development. To complement these traditional methods, we explore the potential of analysing alternative big-data sources, such as human mobility data. However, these often noisy and unstructured big data pose new challenges. Here, we propose a method to extract meaningful explanatory variables and classifications from such data. Using movement data from Beijing, which are produced as a by-product of mobile communication, we show that meaningful features can be extracted, revealing, for example, the emergence and absorption of subcentres. This method allows the analysis of urban dynamics at a high-spatial resolution (here 500 m) and near real-time frequency, and high computational efficiency, which is especially suitable for tracing event-driven mobility changes and their impact on urban structures.

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Out-of-distribution (OOD) detection is crucial for enhancing the reliability of machine learning models when confronted with data that differ from their training distribution. In the image domain, we hypothesize that images inhabit manifolds defined by latent properties such as color, position, and shape. Leveraging this intuition, we propose a novel approach to OOD detection using a diffusion model to discern images that deviate from the in-domain distribution. Our method involves training a diffusion model using in-domain images. At inference time, we lift an image from its original manifold using a masking process, and then apply a diffusion model to map it towards the in-domain manifold. We measure the distance between the original and mapped images, and identify those with a large distance as OOD. Our experiments encompass comprehensive evaluation across various datasets characterized by differences in color, semantics, and resolution. Our method demonstrates strong and consistent performance in detecting OOD images across the tested datasets, highlighting its effectiveness in handling images with diverse characteristics. Additionally, ablation studies confirm the significant contribution of each component in our framework to the overall performance.

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With the rapid advancement of remote-sensing technology, the spectral information obtained from hyperspectral remote-sensing imagery has become increasingly rich, facilitating detailed spectral analysis of Earth's surface objects. However, the abundance of spectral information presents certain challenges for data processing, such as the "curse of dimensionality" leading to the "Hughes phenomenon", "strong correlation" due to high resolution, and "nonlinear characteristics" caused by varying surface reflectances. Consequently, dimensionality reduction of hyperspectral data emerges as a critical task. This paper begins by elucidating the principles and processes of hyperspectral image dimensionality reduction based on manifold theory and learning methods, in light of the nonlinear structures and features present in hyperspectral remote-sensing data, and formulates a dimensionality reduction process based on manifold learning. Subsequently, this study explores the capabilities of feature extraction and low-dimensional embedding for hyperspectral imagery using manifold learning approaches, including principal components analysis (PCA), multidimensional scaling (MDS), and linear discriminant analysis (LDA) for linear methods; and isometric mapping (Isomap), locally linear embedding (LLE), Laplacian eigenmaps (LE), Hessian locally linear embedding (HLLE), local tangent space alignment (LTSA), and maximum variance unfolding (MVU) for nonlinear methods, based on the Indian Pines hyperspectral dataset and Pavia University dataset. Furthermore, the paper investigates the optimal neighborhood computation time and overall algorithm runtime for feature extraction in hyperspectral imagery, varying by the choice of neighborhood k and intrinsic dimensionality d values across different manifold learning methods. Based on the outcomes of feature extraction, the study examines the classification experiments of various manifold learning methods, comparing and analyzing the variations in classification accuracy and Kappa coefficient with different selections of neighborhood k and intrinsic dimensionality d values. Building on this, the impact of selecting different bandwidths t for the Gaussian kernel in the LE method and different Lagrange multipliers λ for the MVU method on classification accuracy, given varying choices of neighborhood k and intrinsic dimensionality d, is explored. Through these experiments, the paper investigates the capability and effectiveness of different manifold learning methods in feature extraction and dimensionality reduction within hyperspectral imagery, as influenced by the selection of neighborhood k and intrinsic dimensionality d values, identifying the optimal neighborhood k and intrinsic dimensionality d value for each method. A comparison of classification accuracies reveals that the LTSA method yields superior classification results compared to other manifold learning approaches. The study demonstrates the advantages of manifold learning methods in processing hyperspectral image data, providing an experimental reference for subsequent research on hyperspectral image dimensionality reduction using manifold learning methods.

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Effectively utilizing information from multiple sources and fewer labeled operating condition samples from a sucker-rod pumping system for oil production can improve the recognition effects and engineering practicability. Nevertheless, this is a challenging energy environment scientific application research subject, and therefore, this study proposes an operating state recognition scheme that relies on multisource nonlinear kernel learning and p-Laplacian high-order manifold regularization logistic regress. Specifically, three measured features are selected and extracted, i.e., wellhead temperature signal, electrical power signal, and ground dynamometer cards, based on mechanism analysis, expert experience, and prior knowledge. Finally, we establish the operating condition recognition model to recognize by the multisource p-Laplacian regularization kernel logistic regress algorithm. The experimental data are derived from 60 wells of a common high-pressure and low-permeability thin oil reservoir block of an oil field in China. The corresponding trials highlight that our scheme outperforms traditional recognition methods by exploiting single-source and multiple-feature data. In the context of fewer labeled samples, the proposed method has a greater recognition effect, engineering practicability, and better model robustness than the existing schemes based on other high-order manifold learning, verifying our method's effectiveness.

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Facial age recognition has been widely used in real-world applications. Most of current facial age recognition methods use deep learning to extract facial features to identify age. However, due to the high dimension features of faces, deep learning methods might extract a lot of redundant features, which is not beneficial for facial age recognition. To improve facial age recognition effectively, this paper proposed the deep manifold learning (DML), a combination of deep learning and manifold learning. In DML, deep learning was used to extract high-dimensional facial features, and manifold learning selected age-related features from these high-dimensional facial features for facial age recognition. Finally, we validated the DML on Multivariate Observations of Reactions and Physical Health (MORPH) and Face and Gesture Recognition Network (FG-NET) datasets. The results indicated that the mean absolute error (MAE) of MORPH is 1.60 and that of FG-NET is 2.48. Moreover, compared with the state of the art facial age recognition methods, the accuracy of DML has been greatly improved.

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The expressive power of deep neural networks is manifested by their remarkable ability to approximate multivariate functions in a way that appears to overcome the curse of dimensionality. This ability is exemplified by their success in solving high-dimensional problems where traditional numerical solvers fail due to their limitations in accurately representing high-dimensional structures. To provide a theoretical framework for explaining this phenomenon, we analyze the approximation of Hölder functions defined on a d-dimensional smooth manifold M embedded in RD, with d≪D, using deep neural networks. We prove that the uniform convergence estimates of the approximation and generalization errors by deep neural networks with ReLU activation functions do not depend on the ambient dimension D of the function but only on its lower manifold dimension d, in a precise sense. Our result improves existing results from the literature where approximation and generalization errors were shown to depend weakly on D.

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Background: To progress adolescent mental health research beyond our present achievements - a complex account of brain and environmental risk factors without understanding neurobiological embedding in the environment - we need methods to unveil relationships between the developing brain and real-world environmental experiences. Methods: We investigated associations among brain function, environments, and emotional and behavioral problems using participants from the Adolescent Brain and Cognitive Development Study (N=2,401 female). We applied manifold learning, a promising technique for uncovering latent structure from high-dimensional biomedical data like functional magnetic resonance imaging (fMRI). Specifically, we developed exogenous PHATE (E-PHATE) to model brain-environment interactions. We used E-PHATE embeddings of participants' brain activation during emotional and cognitive processing to predict individual differences in cognition and emotional and behavioral problems, both cross-sectionally and longitudinally. Results: E-PHATE embeddings of participants' brain activation and environments at baseline show moderate-to-large associations with total, externalizing, and internalizing problems at baseline, across several subcortical regions and large-scale cortical networks, relative to the zero-to-small effects achieved by voxel or PHATE methods. E-PHATE embeddings of the brain and environment at baseline also relate to emotional and behavioral problems two years later. These longitudinal predictions show a consistent, moderate effect in the frontoparietal and attention networks. Conclusions: Adolescent brain's embedding in the environment yields enriched insight into emotional and behavioral problems. Using E-PHATE, we demonstrate how the harmonization of cutting-edge computational methods with longstanding developmental theories advances detection and prediction of adolescent emotional and behavioral problems.

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The early detection of colorectal cancer (CRC) through medical image analysis is a pivotal concern in healthcare, with the potential to significantly reduce mortality rates. Current Domain Adaptation (DA) methods strive to mitigate the discrepancies between different imaging modalities that are critical in identifying CRC, yet they often fall short in addressing the complexity of cancer's presentation within these images. These conventional techniques typically overlook the intricate geometrical structures and the local variations within the data, leading to suboptimal diagnostic performance. This study introduces an innovative application of the Discriminative Manifold Distribution Alignment (DMDA) method, which is specifically engineered to enhance the medical image diagnosis of colorectal cancer. DMDA transcends traditional DA approaches by focusing on both local and global distribution alignments and by intricately learning the intrinsic geometrical characteristics present in manifold space. This is achieved without depending on the potentially misleading pseudo-labels, a common pitfall in existing methodologies. Our implementation of DMDA on three distinct datasets, involving several unique DA tasks, has consistently demonstrated superior classification accuracy and computational efficiency. The method adeptly captures the complex morphological and textural nuances of CRC lesions, leading to a significant leap in domain adaptation technology. DMDA's ability to reconcile global and local distributional disparities, coupled with its manifold-based geometrical structure learning, signals a paradigm shift in medical imaging analysis. The results obtained are not only promising in terms of advancing domain adaptation theory but also in their practical implications, offering the prospect of substantially improved diagnostic accuracy and faster clinical workflows. This heralds a transformative approach in personalized oncology care, aligning with the pressing need for early and accurate CRC detection.

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Eating behavior is highly heterogeneous across individuals and cannot be fully explained using only the degree of obesity. We utilized unsupervised machine learning and functional connectivity measures to explore the heterogeneity of eating behaviors measured by a self-assessment instrument using 424 healthy adults (mean ± standard deviation [SD] age = 47.07 ± 18.89 years; 67% female). We generated low-dimensional representations of functional connectivity using resting-state functional magnetic resonance imaging and estimated latent features using the feature representation capabilities of an autoencoder by nonlinearly compressing the functional connectivity information. The clustering approaches applied to latent features identified three distinct subgroups. The subgroups exhibited different levels of hunger traits, while their body mass indices were comparable. The results were replicated in an independent dataset consisting of 212 participants (mean ± SD age = 38.97 ± 19.80 years; 35% female). The model interpretation technique of integrated gradients revealed that the between-group differences in the integrated gradient maps were associated with functional reorganization in heteromodal association and limbic cortices and reward-related subcortical structures such as the accumbens, amygdala, and caudate. The cognitive decoding analysis revealed that these systems are associated with reward- and emotion-related systems. Our findings provide insights into the macroscopic brain organization of eating behavior-related subgroups independent of obesity.

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Elucidating protein conformational changes is essential because conformational changes are closely related to the functions of proteins. Cryo-electron microscopy (cryo-EM) experiment can be used to reconstruct protein conformational changes via a method that involves using the experimental data (two-dimensional protein images). In this study, a reconstruction method, referred to as the "four-dimensional imaging," was proposed. In our four-dimensional imaging technique, the protein conformational change was obtained using the two-dimensional protein images (the three-dimensional electron density maps used in previously proposed techniques were not used). The protein conformation for each two-dimensional protein image was obtained using our original protocol with molecular dynamics simulations. Using a manifold-learning technique and two-dimensional protein images, the protein conformations were arranged according to the conformational change of the protein. By arranging the protein conformations according to the arrangement of the protein images, four-dimensional imaging is constructed. A simulation for a cryo-EM experiment demonstrated the validity of our four-dimensional imaging technique.

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This study delves into the crucial aspect of network topology in artificial neural networks (NNs) and its impact on model performance. Addressing the need to comprehend how network structures influence learning capabilities, the research contrasts traditional multilayer perceptrons (MLPs) with models built on various complex topologies using novel network generation techniques. Drawing insights from synthetic datasets, the study reveals the remarkable accuracy of complex NNs, particularly in high-difficulty scenarios, outperforming MLPs. Our exploration extends to real-world datasets, highlighting the task-specific nature of optimal network topologies and unveiling trade-offs, including increased computational demands and reduced robustness to graph damage in complex NNs compared to MLPs. This research underscores the pivotal role of complex topologies in addressing challenging learning tasks. However, it also signals the necessity for deeper insights into the complex interplay among topological attributes influencing NN performance. By shedding light on the advantages and limitations of complex topologies, this study provides valuable guidance for practitioners and paves the way for future endeavors to design more efficient and adaptable neural architectures across various applications.

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Early detection of colorectal cancer is crucial for improving outcomes and reducing mortality. While there is strong evidence of effectiveness, currently adopted screening methods present several shortcomings which negatively impact the detection of early stage carcinogenesis, including low uptake due to patient discomfort. As a result, developing novel, non-invasive alternatives is an important research priority. Recent advancements in the field of breathomics, the study of breath composition and analysis, have paved the way for new avenues for non-invasive cancer detection and effective monitoring. Harnessing the utility of Volatile Organic Compounds in exhaled breath, breathomics has the potential to disrupt colorectal cancer screening practices. Our goal is to outline key research efforts in this area focusing on machine learning methods used for the analysis of breathomics data, highlight challenges involved in artificial intelligence application in this context, and suggest possible future directions which are currently considered within the framework of the European project ONCOSCREEN.

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Single-cell techniques like Patch-seq have enabled the acquisition of multimodal data from individual neuronal cells, offering systematic insights into neuronal functions. However, these data can be heterogeneous and noisy. To address this, machine learning methods have been used to align cells from different modalities onto a low-dimensional latent space, revealing multimodal cell clusters. The use of those methods can be challenging without computational expertise or suitable computing infrastructure for computationally expensive methods. To address this, we developed a cloud-based web application, MANGEM (multimodal analysis of neuronal gene expression, electrophysiology, and morphology). MANGEM provides a step-by-step accessible and user-friendly interface to machine learning alignment methods of neuronal multimodal data. It can run asynchronously for large-scale data alignment, provide users with various downstream analyses of aligned cells, and visualize the analytic results. We demonstrated the usage of MANGEM by aligning multimodal data of neuronal cells in the mouse visual cortex.