Gaussian Mixture Model Research Articles

A-167 Hematologic setpoints are a deep physiologic phenotype which enable personalized blood count reference intervals

Abstract Background The complete blood count (CBC) is an important screening tool for healthy adults, commonly ordered at periodic physical exams. However, test results are typically interpreted using one-size-fits-all reference intervals (RIs), which don’t account for the low index-of-individuality of most CBC markers. This undermines the goal of precision medicine - to tailor patient care based on individual characteristics. Methods Here we utilize a database of >50,000 healthy outpatients with yearly CBCs, to investigate the value of patient-specific reference intervals (PRIs) for 9 CBC markers. We use Gaussian mixture modelling to calculate each patient’s setpoints, and to construct associated PRIs. Mechanistic drivers of setpoints were investigated through GWAS and via analysis of excess clinical specimens. Clinical outcomes were analyzed by comparing sensitivity of RIs and PRIs for detection of future cytopenia/cythemia and mortality. Results We found healthy adults had patient-specific setpoints that were stable over decades, and distinctly identifiable from 98% of other patients. Setpoints reflected a deep physiologic phenotype, enabling improved detection of genetic determinants of hematologic regulation (Fig1A), including discovery of multiple novel loci via GWAS analysis. Deviation from PRIs was associated with greater risk of cytopenia/cythemia and mortality (Fig1B) than deviation from the RI for all setpoints except MCHC. Setpoints were significantly correlated with long-term all-cause mortality, even when limited to those within the RI (Fig1C). Conclusions We show that hematologic setpoints reflect a deep, patient-specific phenotype. This phenotype can enhance mechanistic studies, and allow for increased diagnostic sensitivity, through calculation of a personalized reference interval. Setpoints are sufficiently stable and patient-specific to help realize the promise of precision medicine for healthy adults.Fig1A.Significance of GWAS hits using setpoints versus single CBCs. Fig1B. 10yr mortality hazard ratio for tests outside the RI and PRI. Fig1C. Association of WBC setpoint with mortality (limited to WBC setpoints inside the RI).

Knowledge-guided Deep Temporal Clustering for Alzheimer's Disease Subtypes in Completed Clinical Trials.

Alzheimer's disease (AD) is a multifaceted neurodegenerative disorder with varied patient progression. We aim to test the hypothesis that AD patients can be categorized into subgroups based on differences in progression. We leveraged data from three randomized clinical trials (RCTs) to develop a knowledge-guided, deep temporal clustering (KG-DTC) framework for AD subtyping. This model combined autoencoders for contextual information capture, k-means clustering for representation formation, and clinical outcome classification for clinical knowledge integration. The derived representations, encompassing demographics, APOE genotype, cognitive assessments, brain volumes, and biomarkers, were clustered using the Gaussian Mixture Model to identify AD subtypes. Our novel KG-DTC framework was developed using placebo data from 2,087 AD patients across three solanezumab clinical trials (EXPEDITION, EXPEDITION2, and EXPEDITION3), achieving high performance in outcome prediction and clustering. The KG-DTC model demonstrated superior clustering structures, especially when combined with k-means clustering loss. External validation with independent clinical trial data showed consistent clustering results, with a 0.33 silhouette score for three clusters. The model's stability was confirmed through a leave-one-out approach, with an average adjusted Rand Index around 0.945. Three distinct AD subtypes were identified, each exhibiting unique patterns of cognitive function, neurodegeneration, and amyloid beta levels. Notably, Subtype 3 (S3) showed rapid cognitive decline across multiple clinical measures (e.g., 0.64 in S1 vs. -1.06 in S2 vs. 15.09 in S3 of average ADAS total change score, p<.001). This innovative approach offers promising insights for understanding variability in treatment outcomes and personalizing AD treatment strategies.

Dynamic uncertainty evaluation of cylindricity error based on Bayesian deep neural network propagation method

Most of the existing methods for measuring and evaluating product geometric tolerances are for static processes, which use lower dimensions, are more complex to calculate, and have poor traceability and dynamic manageability and control of the measurement process. In this paper, a dynamic evaluation model of cylindricity error uncertainty based on the Bayesian deep neural network propagation method is proposed. Firstly, the input random variable sampling sample containing error uncertainty is generated by proposing the improved Monte Carlo sampling method (IMCS), which has the characteristics of homogeneity and validity; then the principle and construction process of a Bayesian neural network model are introduced to generate the propagation model of multidimensional random error variables; further, the Gaussian mixture model is trained by the Monte Carlo method, and the probability density function of the target response is generated by using the Gaussian mixture model. Through numerical experiments, test analysis of bearing outer rings, and comparison with ISO standard methods, the results show that the model based on the dynamic Bayesian deep neural network propagation method can correctly and effectively assess the uncertainty dynamically, and the whole estimation process is stable.

Self-Organizing a Latent Hierarchy of Sketch Patterns for Controllable Sketch Synthesis.

Encoding sketches as Gaussian mixture model (GMM)-distributed latent codes is an effective way to control sketch synthesis. Each Gaussian component represents a specific sketch pattern, and a code randomly sampled from the Gaussian can be decoded to synthesize a sketch with the target pattern. However, existing methods treat the Gaussians as individual clusters, which neglects the relationships between them. For example, the giraffe and horse sketches heading left are related to each other by their face orientation. The relationships between sketch patterns are important messages to reveal cognitive knowledge in sketch data. Thus, it is promising to learn accurate sketch representations by modeling the pattern relationships into a latent structure. In this article, we construct a tree-structured taxonomic hierarchy over the clusters of sketch codes. The clusters with the more specific descriptions of sketch patterns are placed at the lower levels, while the ones with the more general patterns are ranked at the higher levels. The clusters at the same rank relate to each other through the inheritance of features from common ancestors. We propose a hierarchical expectation-maximization (EM)-like algorithm to explicitly learn the hierarchy, jointly with the training of encoder-decoder network. Moreover, the learned latent hierarchy is utilized to regularize sketch codes with structural constraints. Experimental results show that our method significantly improves controllable synthesis performance and obtains effective sketch analogy results.

Probabilistic and explainable modeling of Phase–Phase Cross-Frequency Coupling patterns in EEG. Application to dyslexia diagnosis

This work explores the intricate neural dynamics associated with dyslexia through the lens of Cross-Frequency Coupling (CFC) analysis applied to electroencephalography (EEG) signals evaluated from 48 seven-year-old Spanish readers from the LEEDUCA research platform. The analysis focuses on CFS (Cross-Frequency phase Synchronization) maps, capturing the interaction between different frequency bands during low-level auditory processing stimuli. Then, making use of Gaussian Mixture Models (GMMs), CFS activations are quantified and classified, offering a compressed representation of EEG activation maps. The study unveils promising results specially at the Theta-Gamma coupling (Area Under the Curve = 0.821), demonstrating the method’s sensitivity to dyslexia-related neural patterns and highlighting potential applications in the early identification of dyslexic individuals.

Enhancing Long-Term Water Quality Modeling by Addressing Base Demand, demand Patterns, and Temperature Uncertainty Using Unsupervised Machine Learning Techniques.

Water quality modelling in Water Distribution systems (WDS) is frequently affected by uncertainties in input variables such as base demand and decay constants. When utilizing simulation tools like EPANET, which necessitate exact numerical inputs, these uncertainties can result in inaccurate simulations. This study proposes a novel framework that leverages unsupervised machine learning, specifically a Gaussian Mixture Model (GMMs), to represent and integrate these uncertainties in the simulation. By classifying historical water demand into fuzzy clusters, the framework allows for certain linguistic inputs (e.g., "high" or "low" demand) to be used in water quality simulations. The framework also incorporates representative hourly demand patterns and temperature-dependent chlorine decay constants based on historical data correlations. Validations were conducted on the Anytown network using WNTR-EPANET, comparing simulated chlorine residuals with Validation data from 181 steady-state simulations. The simulation through the framework achieved a Jensen-Shannon Divergence (JSD) of less than 0.008 across all demand clusters, indicating high similarity between predicted and actual probability distributions . In comparison to other simulation scenarios tested, which exhibited increased variability (JSD > 0.18), the proposed framework demonstrated improved accuracy in representing chlorine residual distributions. The methodology is adaptable to other systems, if similar historical datasets containing key variables, such as flow rates and temperature, are provided. While the framework offers a more flexible and accurate approach to handling uncertainties in WDS, its effectiveness is contingent upon the availability of robust historical demand and temperature data for decay constant calibration.

Diffusion model conditioning on gaussian mixture model and negative gaussian mixture gradient

Diffusion models (DMs) are a type of generative model that has had a significant impact on image synthesis and beyond.They can incorporate a wide variety of conditioning inputs—such as text or bounding boxes—to guide generation. In this work, we introduce a novel conditioning mechanism that applies Gaussian mixture models (GMMs) for feature conditioning, which helps steer the denoising process in DMs. Drawing on set theory, our comprehensive theoretical analysis reveals that the conditional latent distribution based on features differs markedly from that based on classes. Consequently, feature-based conditioning tends to generate fewer defects than class-based conditioning. Experiments are designed and carried out and the experimental results support our theoretical findings as well as effectiveness of proposed feature conditioning mechanism. Additionally, we propose a new gradient function named the Negative Gaussian Mixture Gradient (NGMG) and incorporate it into the training of diffusion models alongside an auxiliary classifier. We theoretically demonstrate that NGMG offers comparable advantages to the Wasserstein distance, serving as a more effective cost function when learning distributions supported by low-dimensional manifolds, especially in contrast to many likelihood-based cost functions, such as KL divergences.

Empowering High-Throughput High-Content Analysis of Microphysiological Models: Open-Source Software for Automated Image Analysis of Microvessel Formation and Cell Invasion.

The primary aim of this study was to develop an open-source Python-based software for the automated analysis of dynamic cell behaviors in microphysiological models using non-confocal microscopy. This research seeks to address the existing gap in accessible tools for high-throughput analysis of endothelial tube formation and cell invasion in vitro, facilitating the rapid assessment of drug sensitivity. Our approach involved annotating over 1000 2mm Z-stacks of cancer and endothelial cell co-culture model and training machine learning models to automatically calculate cell coverage, cancer invasion depth, and microvessel dynamics. Specifically, cell coverage area was computed using focus stacking and Gaussian mixture models to generate thresholded Z-projections. Cancer invasion depth was determined using a ResNet-50 binary classification model, identifying which Z-planes contained invaded cells and measuring the total invasion depth. Lastly, microvessel dynamics were assessed through a U-Net Xception-style segmentation model for vessel prediction, the DisPerSE algorithm to extract an embedded graph, then graph analysis to quantify microvessel length and connectivity. To further validate our software, we reanalyzed an image set from a high-throughput drug screen involving a chemotherapy agent on a 3D cervical and endothelial co-culture model. Lastly, we applied this software to two naive image datasets from coculture lumen and microvascular fragment models. The software accurately measured cell coverage, cancer invasion, and microvessel length, yielding drug sensitivity IC50 values with a 95% confidence level compared to manual calculations. This approach significantly reduced the image processing time from weeks down to h. Furthermore, the software was able to calculate cell coverage, microvessel length, and invasion depth from two additional microphysiological models that were imaged with confocal microscopy, highlighting the versatility of the software. Our free and open source software offers an automated solution for quantifying 3D cell behavior in microphysiological models assessed using non-confocal microscopy, providing the broader Cellular and Molecular Bioengineering community with an alternative to standard confocal microscopy paired with proprietary software.This software can be found in our GitHub repository: https://github.com/fogg-lab/tissue-model-analysis-tools. The online version contains supplementary material available at 10.1007/s12195-024-00821-2.

Deciphering the Kinematic Substructure of Local Dark Matter with LAMOST K Giants

Numerical simulations indicate that correlations exist between the velocity distributions of stars and dark matter (DM). We study the local DM velocity distribution based on these correlations. We select K giants from LAMOST DR8 cross-matched with Gaia DR3, which have robust measurements of velocity and metallicity, and separate them into the disk, halo substructure, and isotropic halo components in the chemodynamical space utilizing the Gaussian mixture model. The substructure component is highly radially anisotropic and possibly related to the Gaia–Enceladus–Sausage (GES) merger event, while the isotropic halo component is accreted from the earliest mergers following the Maxwell–Boltzmann distribution (standard halo model [SHM]). We find that the GES-like substructure contributes ∼85% of the local nondisk stars in the solar neighborhood, which is nearly invariant when applying different volume cuts or additional angular momentum constraints. Utilizing the metallicity–stellar mass relation and the stellar mass–halo mass relation, we find that ∼25−15+24% of local DM is in the kinematic substructure. Combined with the stellar distributions of nondisk components, we modify the heliocentric velocity distribution of local DM. It shifts to a lower speed with a sharper peak compared to the SHM and updates the detection limits of DM direct detection experiments. We discuss extensively the degeneracies present in the GMM fitting and propose that more kinematic and chemical information such as α abundance could help to break the degeneracy in the future. Our work confirms that the local DM velocity distribution deviates significantly from the SHM and needs to be properly accounted for in the DM detection experiments.

Surface modification of superduplex stainless steel with C and N: Microstructural and nanomechanical insights

In this study, the effect of thermochemical processes, such as nitriding and carburizing, on the microstructural evolution of superdúplex stainless steel is presented. The objective is to find a correlation between the microstructure and the mechanical properties of the constitutive phases of this stainless steel (i.e., austenite and ferrite) and analyze the diffusion elements influence on the precipitation of secondary phases, such as sigma (σ), chi (χ), nitrides, and carbides. Hardness (H) and elastic modulus (E) maps were obtained by using a high-speed nanoindentation technique. H and E values for the individual phases were determined through the application of Gaussian Mixture Model statistical analysis. Assessments of the mechanical properties of the different phases were achieved by overlaying field emission-scanning electron microscopy micrographs. An excellent correlation between microstructure and small-scale mechanical properties was attained. Secondary phases have been detected and nanoindentation statistics have proven their influence on the mechanical properties.

Metallicity-dependent kinematics and orbits in the Milky Way’s nuclear stellar disc

Context. The nuclear stellar disc (NSD) is a flat and dense stellar structure at the centre of the Milky Way. Previous work has identified the presence of metal-rich and metal-poor stars in the NSD, suggesting that they have different origins. The recent publication of photometric, metallicity, proper motion, and orbital catalogues allows the NSD stellar population to be characterised with unprecedented detail. Aims. We aim to explore the proper motions and orbits of NSD stars with different metallicities to assess whether they have different origins and to better understand the metallicity distribution in the NSD. Methods. We distinguished between metal-rich and metal-poor stars by applying a Gaussian mixture model, as done in previous work, and analysed the proper motions, orbits, and spatial distribution of stars with different metallicities. Results. We find that metal-rich stars exhibit a lower velocity dispersion, suggesting that they trace a kinematically cooler component compared to metal-poor ones. Furthermore, z-tube orbits are predominant among metal-rich stars, while chaotic/box orbits are more common among metal-poor ones. We also find that metal-rich and metal-poor stars show a similar extinction and are present throughout the analysed regions. As a secondary result, we detected a metallicity gradient in the metal-rich population with higher metallicity towards the centre of the NSD and a tentative gradient for the metal-poor stars, which is consistent with previous studies that did not distinguish between the two populations. Conclusions. Our results suggest that metal-rich stars trace the NSD, whereas metal-poor ones are related to the Galactic bar and probably constitute Galactic bar interlopers and/or are NSD stars that originated from accreted clusters. The detected metallicity gradients aligns with the currently accepted inside-out formation of the NSD.

Unsupervised health indicator construction by a new Gaussian-student’s t-distribution mixture model and its application

The equipment’s remaining useful life (RUL) must be accurately estimated to guarantee its reliable operation. As a crucial part of data-driven RUL prediction, the health indicator (HI) construction method employing the distribution discrepancies can represent the variation trend of health conditions. However, the existing Gaussian mixture model based HI construction method cannot accurately estimate the long-tail distribution characteristics in some degradation data. Moreover, it cannot comprehensively mine the distribution characteristics of degradation data by leveraging different types of distributions. A novel Gaussian-student’s t-distribution mixture model (GSMM) that simultaneously considers Gaussian distribution and student’s t-distribution is developed in this work to estimate the distributions of normal and degradation data. Next, the distribution contact ratio metric (DCRM) is applied to measure the discrepancies between the baseline distribution of normal data and the distributions of test data at different moments. The bearing HI can be constructed with the acquired DCRMs. Finally, the effectiveness and merit of the developed HI construction approach are validated by two bearing life-cycle datasets. The experimental results illustrate that the GSMM-based HI performs better than other classical and state-of-the-art HIs. Additionally, the constructed HI is more suitable for bearing RUL prediction.

Modeling and prediction of set‑up errors in breast cancer image‑guided radiotherapy using the Gaussian mixture model.

The aim of the present study was to develop a prediction model for set-up error distribution in breast cancer image-guided radiotherapy (IGRT) using a Gaussian mixture model (GMM). To achieve this, the image-guided set-up errors data of 80 patients with breast cancer were selected, and the GMM was used to develop the set-up errors distribution prediction model. The predicted error center points, covariance and probability were calculated and compared with the planning target volume (PTV) margin formula. A total of 1,200 sets of set-up errors in IGRT for breast cancer were collected. The results of the Gaussian model parameters showed that the set-up errors were mainly in the direction of µ1-µ4 center points. All the raw errors in the lateral, longitudinal and vertical directions were -6.30-4.60, -5.40-1.47 and -2.70-1.70 mm, respectively. According to the probability of each center, the set-up error was most likely to shift in the µ1 direction, reaching 0.53. The set-up errors of the other three centers, µ2, µ3 and µ4, were 0.11, 0.34 and 0.12, respectively. According to the covariance parameters of the GMM, the maximum statistical standard deviation of the set-up errors reached 29.06. In conclusion, the results of the present study demonstrated that the GMM can be used to quantitatively describe and predict the distribution of set-up errors in IGRT for breast cancer, and these findings could be useful as a reference for set-up error control and tumor PTV expansion in breast cancer radiotherapy without routine, daily IGRT.

Joint Deconvolution of Astronomical Images in the Presence of Poisson Noise

We present a new framework for joint likelihood deconvolution (Jolideco) of a set of astronomical observations of the same sky region in the presence of Poisson noise. The observations may be obtained from different instruments with different resolution, and different point-spread functions (PSFs). Jolideco reconstructs a single flux image by optimizing the posterior distribution based on the joint Poisson likelihood of all observations under one of several prior distributions. Most notably, we employ a patch-based image prior that is parameterized via a Gaussian mixture model, which we train on high-signal-to-noise astronomical images, including data from the JWST and the GLEAM radio survey. This prior favors correlation structures among the reconstructed pixel intensities that are characteristic of those observed in the training images. It is, however, not informative for the mean or scale of the reconstruction. By applying the method to simulated data, we show that the combination of multiple observations and the patch-based prior leads to much improved reconstruction quality in many different source scenarios and signal-to-noise regimes. We demonstrate that with the patch prior Jolideco yields superior reconstruction quality relative to alternative standard methods such as the Richardson–Lucy method. We illustrate the results of Jolideco applied to example data from the Chandra X-ray Observatory and the Fermi Gamma-ray Space Telescope. By comparing the measured width of a counts-based and the corresponding Jolideco flux profile of an X-ray filament in SNR 1E 0102.2–7219, we find the deconvolved width of 0.″58 ± 0.″02 to be consistent with the theoretical expectation derived from the known width of the PSF.

Pluto: Sample Selection for Robust Anomaly Detection on Polluted Log Data

Log anomaly detection, critical in identifying system failures and preempting security breaches, finds irregular patterns within large volumes of log data. Modern log anomaly detectors rely on training deep learning models on clean anomaly-free log data. However, such clean log data requires expensive and tedious human labeling. In this paper, we thus propose a robust log anomaly detection framework, PlutoNOSPACE, that automatically selects a clean representative sample subset of the polluted log sequence data to train a Transformer-based anomaly detection model. Pluto features three innovations. First, due to localized concentrations of anomalies inherent in the embedding space of log data, Pluto partitions the sequence embedding space generated by the model into regions that then allow it to identify and discard regions that are highly polluted by our pollution level estimation scheme, based on our pollution quantification via Gaussian mixture modeling. Second, for the remaining more slightly polluted regions, we select samples that maximally purify the eigenvector spectrum, which can be transformed into the NP-hard facility location problem; allowing us to leverage its greedy solution with a (1-(1/e)) approximation guarantee in optimality. Third, by iteratively alternating between the above subset selection, a model re-training on the latest subset, and a subset filtering using dynamic training artifacts generated by the latest model, the data selected is progressively refined. The final sample set is used to retrain the final anomaly detection model. Our experiments on four real-world log benchmark datasets demonstrate that by retaining 77.7% (BGL) to 96.6% (ThunderBird) of the normal sequences while effectively removing 90.3% (BGL) to 100.0% (ThunderBird, HDFS) of the anomalies, Pluto provides a significant absolute F-1 improvement up to 68.86% (2.16% → 71.02%) compared to the state-of-the-art sample selection methods. The implementation of this work is available at https://github.com/LeiMa0324/Pluto-SIGMOD25.

Clinical outcome-guided deep temporal clustering for disease progression subtyping

ObjectiveComplex diseases exhibit heterogeneous progression patterns, necessitating effective capture and clustering of longitudinal changes to identify disease subtypes for personalized treatments. However, existing studies often fail to design clustering-specific representations or neglect clinical outcomes, thereby limiting the interpretability and clinical utility. MethodWe design a unified framework for subtyping longitudinal progressive diseases. We focus on effectively integrating all data from disease progressions and improving patient representation for downstream clustering. Specifically, we propose a clinical Outcome-Guided Deep Temporal Clustering (OG-DTC) that generates representations informed by clustering and clinical outcomes. A GRU-based seq2seq architecture captures the temporal dynamics, and the model integrates k-means clustering and outcome regression to facilitate the formation of clustering structures and the integration of clinical outcomes. The learned representations are clustered using a Gaussian mixture model to identify distinct subtypes. The clustering results are extensively validated through reproducibility, stability, and significance tests. ResultsWe demonstrated the efficacy of our framework by applying it to three Alzheimer’s Disease (AD) clinical trials. Through the AD case study, we identified three distinct subtypes with unique patterns associated with differentiated clinical declines across multiple measures. The ablation study revealed the contributions of each component in the model and showed that jointly optimizing the full model improved patient representations for clustering. Extensive validations showed that the derived clustering is reproducible, stable, and significant. ConclusionOur temporal clustering framework can derive robust clustering applicable for subtyping longitudinal progressive diseases and has the potential to account for subtype variability in clinical outcomes.

Learning Underwater Intervention Skills Based on Dynamic Movement Primitives

Improving the autonomy of underwater interventions by remotely operated vehicles (ROVs) can help mitigate the impact of communication delays on operational efficiency. Currently, underwater interventions for ROVs usually rely on real-time teleoperation or preprogramming by operators, which is not only time-consuming and increases the cognitive burden on operators but also requires extensive specialized programming. Instead, this paper uses the intuitive learning from demonstrations (LfD) approach that uses operator demonstrations as inputs and models the trajectory characteristics of the task through the dynamic movement primitive (DMP) approach for task reproduction as well as the generalization of knowledge to new environments. Unlike existing applications of DMP-based robot trajectory learning methods, we propose the underwater DMP (UDMP) method to address the problem that the complexity and stochasticity of underwater operational environments (e.g., current perturbations and floating operations) diminish the representativeness of the demonstrated trajectories. First, the Gaussian mixture model (GMM) and Gaussian mixture regression (GMR) are used for feature extraction of multiple demonstration trajectories to obtain typical trajectories as inputs to the DMP method. The UDMP method is more suitable for the LfD of underwater interventions than the method that directly learns the nonlinear terms of the DMP. In addition, we improve the commonly used homomorphic-based teleoperation mode to heteromorphic mode, which allows the operator to focus more on the end-operation task. Finally, the effectiveness of the developed method is verified by simulation experiments.

Mangrove mapping in China using Gaussian mixture model with a novel mangrove index (SSMI) derived from optical and SAR imagery

As an important shoreline vegetation and highly productive ecosystem, mangroves play an essential role in the protection of coastlines and ecological diversity. Accurate mapping of the spatial distribution of mangroves is crucial for the protection and restoration of mangrove ecosystems. Supervised classification methods rely on large sample sets and complex classifiers and traditional thresholding methods that require empirical thresholds, given the problems that limit the feasibility and stability of existing mangrove identification and mapping methods on large scales. Thus, this paper develops a novel mangrove index (spectral and SAR mangrove index, SSMI) and Gaussian mixture model (GMM) mangrove mapping method, which does not require training samples and can automatically and accurately map mangrove boundaries by utilizing only single-scene Sentinel-1 and single-scene Sentinel-2 images from the same time period. The SSMI capitalizes on the fact that mangroves are differentiated from other land cover types in terms of optical characteristics (greenness and moisture) and backscattering coefficients of SAR images and ultimately highlights mangrove forest information through the product of three expressions (f(S) = red egde/SWIR1, f(B) = 1/(1 + e-VH), f(W)=(NIR-SWIR1)/(NIR+SWIR1)). The proposed SSMI was tested in six typical mangrove distribution areas in China where climatic conditions and mangrove species vary widely. The results indicated that the SSMI was more capable of mapping mangrove forests than the other mangrove indices (CMRI, NDMI, MVI, and MI), with overall accuracys (OA) higher than 0.90 and F1 scores as high as 0.93 for the other five areas except for the Maowei Gulf (S5). Moreover, the mangrove maps generated by the SSMI were highly consistent with the reference maps (HGMF_2020、LASAC_2018 and IMMA). In addition, the SSMI achieves stable performance, as shown by the mapping results of the other two classification methods (K-means and Otsu’s algorithm). Mangrove mapping in six typical mangrove distribution areas in China for five consecutive years (2019–2023) and experiments in three Southeast Asian countries with major mangrove distributions (Thailand, Vietnam, and Indonesia) demonstrated that the SSMIs constructed in this paper are highly stable across time and space. The SSMI proposed in this paper does not require reference samples or predefined parameters; thus, it has great flexibility and applicability in mapping mangroves on a large scale, especially in cloudy areas.

A novel cross-entropy-based importance sampling method for cumulative time-dependent failure probability function

Cumulative time-dependent failure probability function (C-T-FPF) can reflect the effects of distribution parameters of random inputs and the upper bound of service time interval, which vary in their design domains, on time-dependent failure probability. However, solving C-T-FPF involves a time-consuming triple-layer framework. Thus, we propose an efficient method by combining cross-entropy-based importance sampling (IS) with adaptive Kriging model (CE-IS-AK). The innovations of CE-IS-AK include two aspects. Firstly, we construct a space augmented by both distribution parameters and the upper bound of service time interval, on which the triple-layer framework is decoupled to a single-layer one. And in the augmented space, an optimal IS density is proposed to reduce the required candidate sample size for estimating C-T-FPF. Secondly, we employ Gaussian mixture model (GMM) to approximate the optimal IS density, and the parameters in GMM are determined by minimizing the cross entropy of GMM and the optimal IS density. Moreover, to reduce the model evaluations in the proposed method, Kriging model is adaptively embedded to replace the actual model, and a first failure instant based learning function is proposed to train Kriging model adaptively. Due to the proposed single-layer framework and IS strategy assisted by the Kriging model, the efficiency is greatly improved for estimating C-T-FPF, which is validated by several examples.

Impacts of landscape configurations on ecosystem services and their trade-offs across different landscape compositions

Landscape sustainability depends on the design of landscape patterns that can be guided by ecosystem services (ESs). Clarifying the impacts of landscape configurations on ESs and their trade-offs will facilitate landscape planning and management to achieve the best design without changing most landscape compositions. However, limited work has focused on these impacts, and whether these impacts are the same on different compositions remains unexplored. Thus, this study analyzes the impacts of landscape configurations on ESs and their trade-offs for different compositions. In this analysis, Gaussian mixture model was used to cluster the landscape by compositions, five important ESs (crop production, water yield, carbon storage, soil retention, and outdoor recreation) were quantified, and the constraint line was used to analyze the impact, taking the Xiangjiang River Basin as an example. Results showed that three clusters of landscape compositions, which are similar to the urban–rural–natural gradient, were identified. Furthermore, the impacts of landscape configurations on ESs and their trade-offs had largely the same direction in different compositions. However, change in landscape composition makes the high correlations among them weaker or shift to constraint impacts. Based on the results of the study, we can not only contribute to local landscape development but also argue three general approaches for landscape planning and management. First, considering the trade-offs and making a choice adapted to local conditions. Second, adjusting landscape configurations with virtually no changes of compositions. Third, external intervention based on rational landscape configurations.