Markov Chain Random Field Research Articles

Workload prediction for enhancing power efficiency of cloud data centers using optimized self‐attention‐based progressive generative adversarial network

SummaryNowadays, future workload prediction is an important requirement in cloud data centers to maintain flexibility and scalability of resources. However, due to unexpected peaks, drops in workload, noise, and redundancy in user requests, there is a considerable variance in resource demands, making it difficult to accurately predict workloads. Therefore, a self‐attention‐based progressive generative adversarial network (SAPGAN) optimized with Giza Pyramids Construction Algorithm (GPCA)‐based workload prediction is proposed for Sustainable Cloud Data Centers (CDC). At first, redundant data in historical data obtained through CDC are filtered utilizing Markov chain random field (MCRF) co‐simulation method. These pre‐processed historical data are supplied to the SAPGAN. The SAPGAN weight parameters are optimized by GPCA. The proposed method is analyzed using 2 benchmark datasets: HTTP traces from Saskatchewan and NASA. The simulation is implemented in JAVA. The performance metrics is examined to verify the efficacy of the proposed technique. The performance of the proposed approach provides 28.70%, 11.87%, and 14.79% higher accuracy; 30.15%, 11.72%, and 18.34% lesser energy consume for the dataset of NASA; and 5.32%, 2.45%, and 5.67% higher accuracy; 12.36%, 24.24%, and 34.16% lesser energy consume for the dataset of Saskatchewan HTTP traces compared with existing methods, such as auto‐adaptive learning in a dynamic cloud environment (AADEA‐WLP‐CDC), a neural network model depending on biphase adaptive learning for anticipating cloud data center workload (BALNN‐WLP‐CDC) and multiple scale ensemble of deep learning framework for multistep‐ahead cloud workload prediction (EMD‐LSTM‐GAN‐WLP‐CDC).

Self-attention generative adversarial capsule network optimized with atomic orbital search algorithm based sentiment analysis for online product recommendation

Self-Attention based Generative Adversarial Capsule Network optimized with Atomic orbital search algorithm based Sentiment Analysis is proposed in this manuscript for Online Product Recommendation (SFA-AGCN-AOSA-SA-OPR). Here, Collaborative filtering (CF) and product-product (P-P) similarity method is utilized for designing the new recommendation system. CF is employed for predicting the best shops and P-P similarity method is employed to predict the better product. Initially, the datas are gathered via Amazon Product recommendation dataset. After that, the datas are given to pre-processing. During pre-processing, Markov chain random field (MCRF) co-simulation is used to remove the unwanted content and filtering relevant text. The preprocessing output is fed to feature extraction. The features, like manufacturing date, Manufacturing price, discounts, offers, quality ratings, and suggestions or reviews are extracted using Gray level co-occurrence matrix (GLCM) window adaptive algorithm based feature extraction method. Finally, Self-Attention based Generative Adversarial Capsule Network (SFA-AGCN) categorizes the product recommendation as excellent, good, very good, bad, very bad. Atomic orbital search algorithm optimizes the SFA-AGCN weight parameters. The performance metrics, like accuracy, precision, sensitivity, recall, F-measure, mean absolute error (MAE), mean squared error (MSE), mean absolute percentage error (MAPE) is examined. The efficiency of the proposed method provides higher mean absolute percentage error 98.23%, 88.34%, 90.35% and 78.96% and lower Mean squared error 92.15%, 90.25%, 89.64% and 92.48% compared to the existing methods, such as sentiment analysis of online product reviews using DLMNN and future prediction of online product using IANFIS (DLMNN-IANFIS-SA-OPR), intelligent sentiment analysis approach using edge computing based deep learning technique (DCNN-SA-OPR), sentiment analysis for online product reviews in Chinese depending on sentiment lexicon and deep learning (CNN-BiGRU-SA-OPR) and sentiment analysis on product reviews depending on weighted word embedding and deep neural networks (CNN-LSTM-SA-OPR) respectively.

Vulnerability-based regionalization for disaster management considering storms and earthquakes

Existing approaches to risk assessment in natural disasters usually suffer from information specificity and data density. For example, road vulnerability assessment requires disaster information on the neighbors of all road segments, but weather stations may be far from such locations. The widely used intensity–duration–frequency analysis is too rough to overcome the tradeoff between estimation accuracy and reliability for assessing road vulnerability. Therefore, this study proposes a machine learning method to replace the frequency-style vulnerability with an intelligent measure, which will enhance the assessment by predicting the missing weather information at all road segments. Compared with conventional interpolation methods, our Markov chain random field kriging can reliably estimate the ungauged information when available stations are distributed asymmetrically. Therefore, our model contributes to the assessment methods by providing accurate and reliable vulnerability information for the transportation network under contemporary changing weather conditions. Through elaborate proofs to demonstrate the theoretical validity of our mathematical results, empirical results are also presented for application to practical governance. The empirical accuracy of 0.3 normalized root mean square error for disasters of storms and earthquakes is sufficient to convince local authorities to change their existing methods. The resulting regionalization in road network vulnerability is also tailor-made for practical applicability.

Markov chain random field kriging for estimating extreme precipitation at unevenly distributed sites

Delineating a homogeneous region is a standard procedure for rainfall frequency analysis in predicting precipitation in ungauged basins (PUB) in vast unpopulated areas. However, for data about the extreme weather events measured at stations that are asymmetrically distributed, the use of conventional regionalization techniques for forecasting is challenging. Vast depopulated zones, such as high-mountain catchment areas, basins, and swamps, are rich in features that influence precipitation, but they contain few stations. Hence, data from the populated area must be used to estimate data for the unpopulated areas. Accordingly, this study developed a novel spatial imputation approach for simulating spatial precipitation over a planar grid. In this approach, the Markov chain random field (MCRF) technique is used to estimate the parameters of the stochastic process of ungauged sites at all grid points from versatile juxtapositional directions. The probability learning-based MCRF approach differs from most traditional interpolation approaches, which may fail in unevenly distributed situations. After completing the training, the predicted precipitation in the mountainous areas was validated through a third-party dataset. Despite the quality of third-party data, our accuracy is confirmed both in standard metric and visual inspections. The normalized root mean square errors between the predicted values and the validation values were below 0.321, demonstrating that the MCRF step can effectively estimate the precipitation at unevenly distributed sites.

Precipitation Modeling for Extreme Weather Based on Sparse Hybrid Machine Learning and Markov Chain Random Field in a Multi-Scale Subspace

This paper proposes to apply a Markov chain random field conditioning method with a hybrid machine learning method to provide long-range precipitation predictions under increasingly extreme weather conditions. Existing precipitation models are limited in time-span, and long-range simulations cannot predict rainfall distribution for a specific year. This paper proposes a hybrid (ensemble) learning method to perform forecasting on a multi-scaled, conditioned functional time series over a sparse l1 space. Therefore, on the basis of this method, a long-range prediction algorithm is developed for applications, such as agriculture or construction works. Our findings show that the conditioning method and multi-scale decomposition in the parse space l1 are proved useful in resisting statistical variation due to increasingly extreme weather conditions. Because the predictions are year-specific, we verify our prediction accuracy for the year we are interested in, but not for other years.

Markov chain random fields in the perspective of spatial Bayesian networks and optimal neighborhoods for simulation of categorical fields

The Markov chain random field (MCRF) model/theory provides a non-linear spatial Bayesian updating solution at the neighborhood nearest data level for simulating categorical spatial variables. In the MCRF solution, the spatial dependencies among nearest data and the central random variable is a probabilistic directed acyclic graph that conforms to a neighborhood-based Bayesian network on spatial data. By selecting different neighborhood sizes and structures, applying the spatial conditional independence assumption to nearest neighbors, or incorporating ancillary information, one may construct specific MCRF models based on the MCRF general solution for various application purposes. Simplified MCRF models based on assuming the spatial conditional independence of nearest data involve only spatial transition probabilities, and one can implement them easily in sequential simulations. In this article, we prove the spatial Bayesian network characteristic of MCRFs, and test the optimal neighborhoods under the spatial conditional independence assumption. The testing results indicate that the quadrantal (i.e., one nearest datum per quadrant) neighborhood is generally the best choice for the simplified MCRF solution, performing better than other sectored neighborhoods and non-sectored neighborhoods with regard to simulation accuracy and pattern rationality.

Mapping imbalanced soil classes using Markov chain random fields models treated with data resampling technique

Class imbalance is a problem in spatial predictive models; it occurs when classes with a large number of observations dominate the prediction and classes with much less number of observations are not predicted at all. It is a crucial topic as imbalanced distribution of soil classes occurs naturally. In this study, we address this problem using Markov chain random field modeling combined with a data resampling technique, i.e., random oversampling. The study area is about 12,000 ha with imbalanced distribution of eight soil great groups located in the northwest of Iran. Four algorithms were used to interpolate class observations, including fixed-path and random-path Markov chain random fields (FPth and RPth, respectively), indicator kriging simulation (IKS) and Markovian-type categorical simulation (MCS). All of the models provide prediction and simulation as outputs. The random oversampling technique was applied to the minority soil classes prior to modeling. Using original data that have imbalanced classes for mapping resulted in loss of the minority classes and relatively low Kappa agreement values for some models. Data oversampling increased overall accuracy and Kappa coefficient for FPth and RPth models. In addition, it led to the maintenance of one or two minority classes in the resulting maps. Overall, RPth model showed the highest overall accuracy and Kappa coefficient both in prediction (overall = 50%, K = 0.33) and simulation (overall = 52%, K = 0.36) outputs after data oversampling. Markov chain models combined with data oversampling technique can be used for mapping imbalanced soil classes.

A Comparison of Markov Chain Random Field and Ordinary Kriging Methods for Calculating Soil Texture in a Mountainous Watershed, Northwest China

Accurate mapping the spatial distribution of different soil textures is important for eco-hydrological studies and water resource management. However, it is quite a challenge to map the soil texture in data scarce, hard to access mountainous watersheds. This paper compares a nonlinear method, the Markov chain random field (MCRF) with a classical linear method, ordinary kriging (OK) for calculating the soil texture at different search radiuses in the upstream region of the Heihe River Watershed. Results show that soil texture values that were calculated by the OK method tends to predict soil texture values within a certain range (sand (12.098~40.317), silt (47.847~71.231), and clay (12.781~19.420)) because of the smoothing effect, thus leading to greater accuracy in predicting the major soil texture type (silt loam). Nonetheless, the MCRF method considers the interclass relationships between sampling points, leading to greater accuracy in predicting minor types (loam and sandy loam). Meanwhile, the OK method performed best for all the types at the radius of 65 km influenced by the densities of all the sampling points, while the best performance of the MCRF method differs with radiuses as the largest densities varying for different soil types. For loam and sandy loam, the OK method ignored them, thus the MCRF method is more suitable in mountainous areas with high soil heterogeneity.

A framework of experimental transiogram modelling for Markov chain geostatistical simulation of landscape categories

Experimental transiogram modelling, especially joint modelling, is crucial for Markov chain random field (MCRF) simulation of categorical spatial variables with multiple classes. Experimental transiogram estimation of landscape categorical variables in a non-visual context and manual model fitting are tedious and time-consuming tasks if the number of classes is large. This study presented a framework which integrated the linear interpolation method and the mathematical model fitting method for transiogram joint modelling to facilitate the whole modelling procedure. The framework was developed as a tool, entitled TGRAM. The tool provides several advanced characteristics and functions which greatly improve the efficiency of transiogram joint modelling. Two case studies were provided to demonstrate the feasibility of the tool. The modelling results can directly provide parameters (i.e., transition probability values at continuous lags in the required pixel size) for further MCRF simulations in related research areas, such as land cover/land use classification, soil and lithofacies mapping, and urban growth detection.

Analyzing horizontal and vertical urban expansions in three East Asian megacities with the SS-coMCRF model

A recently proposed method based on the spectral similarity-enhanced Markov chain random field cosimulation (SS-coMCRF) model has provided a practical approach for estimating both horizontal and vertical urban expansion of megacities using Landsat images. Estimating vertical urban growth – the area change of mid-rise or taller buildings (MTBs) – makes it possible to gain some new insights into the urban expansion of megacities. This study makes use of the new approach to examine the horizontal and vertical urban expansion of three capital megacities (Beijing, Seoul, and Tokyo) in East Asia during the late 1980s to the mid-2010s. In contrast to previous studies that only assessed horizontal urban growth, which usually showed almost no increase in urban area in some highly developed cities, this study indicates some different findings: (1) Both horizontal and vertical urban expansion had been happening in the three megacities during the studied period, especially with respect to vertical urban expansion. During the studied period there were 20.7 km2, 11.3 km2, and 6.8 km2 MTB area increases in Beijing, Seoul, and Tokyo, respectively. (2) Different cities showed some differences in growth patterns, mainly because they were at different urban development stages and impacted by different local situations in terms of geography, population, and development policies. (3) A similarity is that the three megacities all tended to horizontally expand initially and then grow vertically in the already developed areas. This study may provide a useful new perspective on the urban expansion of megacities.

Parallel computing solutions for Markov chain spatial sequential simulation of categorical fields

ABSTRACTThe Markov chain random field (MCRF) model is a spatial statistical approach for modeling categorical spatial variables in multiple dimensions. However, this approach tends to be computationally costly when dealing with large data sets because of its sequential simulation processes. Therefore, improving its computational efficiency is necessary in order to run this model on larger sizes of spatial data. In this study, we suggested four parallel computing solutions by using both central processing unit (CPU) and graphics processing unit (GPU) for executing the sequential simulation algorithm of the MCRF model, and compared them with the nonparallel computing solution on computation time spent for a land cover post-classification. The four parallel computing solutions are: (1) multicore processor parallel computing (MP), (2) parallel computing by GPU-accelerated nearest neighbor searching (GNNS), (3) MP with GPU-accelerated nearest neighbor searching (MP-GNNS), and (4) parallel computing by GPU-accelerated approximation and GPU-accelerated nearest neighbor searching (GA-GNNS). Experimental results indicated that all of the four parallel computing solutions are at least 1.8× faster than the nonparallel solution. Particularly, the GA-GNNS solution with 512 threads per block is around 83× faster than the nonparallel solution when conducting a land cover post-classification with a remotely sensed image of 1000 × 1000 pixels.

Improving Object-Based Land Use/Cover Classification from Medium Resolution Imagery by Markov Chain Geostatistical Post-Classification

Land use/land cover maps derived from remotely sensed imagery are often insufficient in quality for some quantitative application purposes due to a variety of reasons such as spectral confusion. Although object-based classification has some advantages over pixel-based classification in identifying relatively homogeneous land use/cover areas from medium resolution remotely sensed images, the classification accuracy is usually still relatively low. In this study, we aimed to test whether the recently proposed Markov chain random field (MCRF) post-classification method, that is, the spectral similarity-enhanced MCRF co-simulation (SS-coMCRF) model, can effectively improve object-based land use/cover classifications on different landscapes. Four study areas (Cixi, Yinchuan and Maanshan in China and Hartford in USA) with different landscapes and classification schemes were chosen for case studies. Expert-interpreted sample data (0.087% to 0.258% of total pixels) were obtained for each study area from the original Landsat images used in object-based pre-classification and other sources (e.g., Google satellite imagery). Post-classification results showed that the overall classification accuracies of the four cases were obviously improved over the corresponding pre-classification results by 14.1% for Cixi, 5% for Yinchuan, 11.8% for Maanshan and 5.6% for Hartford, respectively. At the meantime, SS-coMCRF also reduced the noise and minor patches contained in pre-classifications. This means that the Markov chain geostatistical post-classification method is capable of improving the accuracy and quality of object-based land use/cover classification from medium resolution remotely sensed imagery in various landscape situations.

Detecting horizontal and vertical urban growth from medium resolution imagery and its relationships with major socioeconomic factors

ABSTRACTUrban growth consists of horizontal and vertical expansions. An integrative framework for estimating horizontal and vertical expansions of city urban areas using Landsat images was presented. It includes following steps: (1) a spectrum-based classifier (here Support Vector Machine) is first used to preclassify Landsat images; (2) the spectral similarity-enhanced Markov chain random field cosimulation model is then applied to postclassify the preclassified images and detect building shadows; and (3) a morphological operator based on spatial logic reasoning is used to estimate mid-rise or taller buildings (MTBs) from detected shadows. Both horizontal urban growth and vertical urban growth in the main city area of Guangzhou for the time period of 1993–2013 were detected. The accuracy of identified MTBs by shadows was validated to be 78.1% on average for 2013. The case study indicates that Guangzhou had undergone both horizontal and vertical urban growth from 1993 to 2013, and vertical urban growth followed horizontal urban growth successively. The relationships between the horizontal and vertical urban growth and three major socioeconomic factors during the studied period were analysed. Results indicate that both the total area of built-up areas and the total area of detected MTBs are significantly correlated with population density, real gross domestic product, and fixed investment (i.e. investment in fixed assets such as land, buildings), respectively. While population density is the major driving force of horizontal urban expansion, fixed investment is the major driving force of vertical urban expansion for the city as a whole. Although the method is not perfect currently in detecting MTBs in various situations and the case study is mainly exploratory, the proposed framework and the case study can be helpful in quantitatively exploring the horizontal urban growth and vertical urban growth of a city and their causes.

Incorporating Spectral Similarity Into Markov Chain Geostatistical Cosimulation for Reducing Smoothing Effect in Land Cover Postclassification

Spatial statistics provides useful methods for incorporating spatial dependence into land cover classification. However, the geometric features of land cover classes are difficult to be captured by geostatistical models due to smoothing effect. The objective of this study is to incorporate spectral similarity into the Markov chain random field (MCRF) cosimulation (coMCRF) model, that is, to propose a spectral similarity-enhanced MCRF cosimulation (SS-coMCRF) model, for land cover postclassification so that postclassification will cause less geometric loss. Two mutually complementary spectral similarity measures, Jaccard index and the spectral correlation measure, were employed as a constraining factor in SS-coMCRF. One medium spatial resolution scene with a complex landscape and one very high spatial resolution scene with an urban landscape were selected for case studies. Neural network classifier and support vector machine classifier were used to conduct land cover preclassifications. Both coMCRF and SS-coMCRF were used to postprocess preclassified images based on expert-interpreted sample datasets from multiple data sources. Compared with preclassified results that depend on only spectral information of pixels, postclassifications by both models achieved similar significant improvements in overall accuracy. However, compared with coMCRF, the SS-coMCRF model apparently improved postclassified land cover patterns by effectively capturing some geometric features (e.g., boundaries and linear stripes) and more details of land cover classes. In general, incorporating spectral similarity into land cover postclassification through SS-coMCRF may contribute significantly to the “shape” or geometric accuracy of classified land cover classes.

Spatial hidden Markov chain models for estimation of petroleum reservoir categorical variables

Indicator variograms and transition probabilities are used to measure spatial continuity of petroleum reservoir categorical variables. Variogram-based Kriging variants are symmetric geostatistical methods, which cannot completely capture the complex reservoir spatial heterogeneity structure. The asymmetric spatial Markov chain (SMC) approaches employ transition probabilities to incorporate proportion, length and juxtaposition relation information in subsurface reservoir structures. Secondary data in petroleum geology, however, cannot be reasonably aggregated. We propose a spatial hidden Markov chain (SHMC) model to tackle these issues. This method integrates well data and seismic data by using Viterbi algorithm for reservoir forecasting. The classified sonic impedance is used as auxiliary data, directly in some kind of Bayesian updating process via a hidden Markov model. The SMC embedded in SHMC has been redefined according to first-order neighborhood with different lag in three-dimensional space. Compared with traditional SMC in Markov chain random field theory, the SHMC method performs better in prediction accuracy and reflecting the geological sedimentation process by integrating auxiliary information.

Land cover post-classifications by Markov chain geostatistical cosimulation based on pre-classifications by different conventional classifiers

ABSTRACTThe recently proposed Bayesian Markov chain random field (MCRF) cosimulation approach, as a new non-linear geostatistical cosimulation method, for land cover classification improvement (i.e. post-classification) may significantly increase classification accuracy by taking advantage of expert-interpreted data and pre-classified image data. The objective of this study is to explore the performance of the MCRF post-classification method based on pre-classification results from different conventional classifiers on a complex landscape. Five conventional classifiers, including maximum likelihood (ML), neural network (NN), Support Vector Machine (SVM), minimum distance (MD), and k-means (KM), were used to conduct land cover pre-classifications of a remotely sensed image with a 90,000 ha area and complex landscape. A sample dataset (0.32% of total pixels) was first interpreted based on expert knowledge from the image and other related data sources, and then MCRF cosimulations were performed conditionally on the expert-interpreted sample dataset and the five pre-classified image datasets, respectively. Finally, MCRF post-classification maps were compared with corresponding pre-classification maps. Results showed that the MCRF method achieved obvious accuracy improvements (ranging from 4.6% to 16.8%) in post-classifications compared to the pre-classification results from different pre-classifiers. This study indicates that the MCRF post-classification method is capable of improving land cover classification accuracy over different conventional classifiers by making use of multiple data sources (expert-interpreted data and pre-classified data) and spatial correlation information, even if the study area is relatively large and has a complex landscape.

Theoretical generalization of Markov chain random field from potential function perspective

The inner relationship between Markov random field (MRF) and Markov chain random field (MCRF) is discussed. MCRF is a special MRF for dealing with high-order interactions of sparse data. It consists of a single spatial Markov chain (SMC) that can move in the whole space. Generally, the theoretical backbone of MCRF is conditional independence assumption, which is a way around the problem of knowing joint probabilities of multi-points. This so-called Naive Bayes assumption should not be taken lightly and should be checked whenever possible because it is mathematically difficult to prove. Rather than trap in this independence proving, an appropriate potential function in MRF theory is chosen instead. The MCRF formulas are well deduced and the joint probability of MRF is presented by localization approach, so that the complicated parameter estimation algorithm and iteration process can be avoided. The MCRF model is then applied to the lithofacies identification of a region and compared with triplex Markov chain (TMC) simulation. Analyses show that the MCRF model will not cause underestimation problem and can better reflect the geological sedimentation process.

Bayesian Markov Chain Random Field Cosimulation for Improving Land Cover Classification Accuracy

This study introduces a Bayesian Markov chain random field (MCRF) cosimulation approach for improving land-use/land-cover (LULC) classification accuracy through integrating expert-interpreted data and pre-classified image data. The expert-interpreted data are used as conditioning sample data in cosimulation, and may be interpreted from various sources. The pre-classification can be performed using any convenient conventional method. The approach uses the recently suggested MCRF cosimulation algorithm (Co-MCSS) to take a pre-classified image as auxiliary data while performing cosimulations conditioned on expert-interpreted data. It was tested using a series of expert-interpreted data sets and an image data set pre-classified by the supervised maximum likelihood (SML) algorithm. Results show that with the density of the interpreted data (pixel labels) increasing from 0 to 1.81 % of total pixels, the accuracy of optimal classification maps from Co-MCSS improves by 8.49 to 20.96 %, being much higher than that generated by SML and those purely conditioned on expert-interpreted data. This means that expert-interpreted data may largely contribute to the accuracy of LULC classification from remotely sensed imagery, and inversely the pre-classified image data also can largely contribute to the accuracy of LULC classes simulated by the MCRF approach based on expert-interpreted data. Therefore, the proposed approach can improve classification accuracy of pre-classified maps as long as some expert-interpreted data are available. The main advantage of this approach is that it may comprehensively utilize a variety of available information seamlessly to LULC classification through expert interpretation and spatial cosimulation.

Some further clarification on Markov chain random fields and transiograms

The Markov chain random field (MCRF) theory and the transiogram spatial measure were proposed several years ago. Basic sequential simulation algorithms based on simple MCRF models such as the Markov chain sequential simulation algorithm and the Markov chain sequential co-simulation algorithm have been developed and used in a series of application studies. However, misunderstanding of these two ideas and the geostatistical approach built on them arose recently among some researchers in geostatistics. The purpose of this article is to further clarify some issues related to these two ideas, so as to avoid further misunderstanding. For those issues already clarified, trivial, or obviously irrelevant, we do not talk about them here.

Updating categorical soil maps using limited survey data by Bayesian Markov chain cosimulation.

Updating categorical soil maps is necessary for providing current, higher-quality soil data to agricultural and environmental management but may not require a costly thorough field survey because latest legacy maps may only need limited corrections. This study suggests a Markov chain random field (MCRF) sequential cosimulation (Co-MCSS) method for updating categorical soil maps using limited survey data provided that qualified legacy maps are available. A case study using synthetic data demonstrates that Co-MCSS can appreciably improve simulation accuracy of soil types with both contributions from a legacy map and limited sample data. The method indicates the following characteristics: (1) if a soil type indicates no change in an update survey or it has been reclassified into another type that similarly evinces no change, it will be simply reproduced in the updated map; (2) if a soil type has changes in some places, it will be simulated with uncertainty quantified by occurrence probability maps; (3) if a soil type has no change in an area but evinces changes in other distant areas, it still can be captured in the area with unobvious uncertainty. We concluded that Co-MCSS might be a practical method for updating categorical soil maps with limited survey data.