Graph Regularized Nonlinear Ridge Regression for Remote Sensing Data Analysis

Abstract. Accurate quantification of long-term trends in stratospheric ozone can be challenging due to their sensitivity to natural variability, the quality of the observational datasets, and non-linear changes in forcing processes as well as the statistical methodologies. Multivariate linear regression (MLR) is the most commonly used tool for ozone trend analysis; however, the complex coupling in many atmospheric processes can make it prone to the issue of over-fitting when using the conventional ordinary-least-squares (OLS) approach. To overcome this issue, here we adopt a regularized (ridge) regression method to estimate ozone trends and quantify the influence of individual processes. We use the Stratospheric Water and OzOne Satellite Homogenized (SWOOSH) merged dataset (v2.7) to derive stratospheric ozone profile trends for the period 1984–2020. Besides SWOOSH, we also analyse a machine-learning-based satellite-corrected gap-free global stratospheric ozone profile dataset from a chemical transport model (ML-TOMCAT) and output from a chemical transport model (TOMCAT) simulation forced with European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis. For 1984–1997, we observe smaller negative trends in the SWOOSH stratospheric ozone profile using ridge regression compared to OLS. Except for the tropical lower stratosphere, the largest differences arise in the mid-latitude lowermost stratosphere (>4 % per decade difference at 100 hPa). From 1998 and the onset of ozone recovery in the upper stratosphere, the positive trends estimated using the ridge regression model (∼1 % per decade near 2 hPa) are smaller than those using OLS (∼2 % per decade). In the lower stratosphere, post-1998 negative trends with large uncertainties are observed and ridge-based trend estimates are somewhat smaller and less variable in magnitude compared to the OLS regression. Aside from the tropical lower stratosphere, the largest difference is around 2 % per decade at 100 hPa (with ∼3 % per decade uncertainties for individual trends) in northern mid-latitudes. For both time periods the SWOOSH data produce large negative trends in the tropical lower stratosphere with a correspondingly large difference between the two trend methods. In both cases the ridge method produces a smaller trend. The regression coefficients from both OLS and ridge models, which represent ozone variations associated with natural processes (e.g. the quasi-biennial oscillation, solar variability, El Niño–Southern Oscillation, Arctic Oscillation, Antarctic Oscillation, and Eliassen–Palm flux), highlight the dominance of dynamical processes in controlling lower-stratospheric ozone concentrations. Ridge regression generally yields smaller regression coefficients due to correlated explanatory variables, and care must be exercised when comparing fit coefficients and their statistical significance across different regression methods. Comparing the ML-TOMCAT-based trend estimates with the ERA5-forced model simulation, we find ML-TOMCAT shows significant improvements with much better consistency with the SWOOSH dataset, despite the ML-TOMCAT training period overlapping with SWOOSH only for the Microwave Limb Sounder (MLS) measurement period. The largest inconsistencies with respect to SWOOSH-based trends post-1998 appear in the lower stratosphere where the ERA5-forced model simulation shows positive trends for both the tropics and the mid-latitudes. The large differences between satellite-based data and the ERA5-forced model simulation confirm significant uncertainties in ozone trend estimates, especially in the lower stratosphere, underscoring the need for caution when interpreting results obtained with different regression methods and datasets.

Learning with transductive SVM for semisupervised pixel classification of remote sensing imagery

Based on the fiscal revenue and other relevant economic index data of Beijing from 1995 to 2020, this study uses the research methods of Ridge regression and Lasso regression to explore the influencing factors of Beijing’s fiscal revenue. Considering that the traditional linear regression model will produce strong multicollinearity among many variables. Therefore, ridge regression and Lasso regression model were firstly used to reduce the influence of multicollinearity between variables, and then variable selection was carried out. Finally, the two models were compared according to the analysis results, and the optimal analysis model was selected. The results show that compared with ridge regression model, lasso regression model has better goodness of fit, smaller error and better model. The added value of the second industry, power generation, resident population, urban per capita disposable income and total retail sales of social consumer goods has a positive impact on fiscal revenue, and the whole social fixed assets investment, employment in cities and towns, per capita consumption expenditure of urban households is has a certain negative impact on fiscal income level.

Hyperspectral images (HSIs) obtained from remote sensing contain abundant information of ground objects, and precise analysis of landcover depends on effective and efficient classification of HSIs into homogeneous ground regions. While many advanced algorithms have been developed for HSI classification, it is a challenge for an algorithm to achieve a good balance between its effectiveness and efficiency due to the high dimensionality of HSIs and insufficient labeled training samples. By taking both the rich spectral features and the spatially homogeneous property of land cover distributions, in this paper, we propose a simple and efficient yet effective method for HSI classification. First, features are extracted by using a weighted spatial-spectral and global-local discriminant analysis algorithm, which is proposed to reduce the feature dimension. Then, combining the discriminant information of neighboring pixels, we propose a spatial collaboration nearest neighbor (SC-NN) classifier to make reliable class judgment for the central one. In the SC-NN classifier, the spatially homogeneous property of landcover distribution of HSIs is utilized to effectively reduce the probability of misclassification when only a small number of training samples are available. To further address the issue of a small number of training samples, we adopt an incremental learning strategy by adding the samples with high classification confidence to the training set. Experimental results on four public datasets show that our proposed method outperforms several state-of-the-art methods with high classification accuracy.

Common framework for linear regression

Optimal portfolio selection decisions hinge on the availability of return models which capture important statistical properties of the assets under consideration. In comparison to traditional assets, estimating a return model for hedge funds proves to be much more complex and challenging. Extended factor models, with option returns as additional factors, have been proposed to model index and individual hedge fund returns, see, e.g., Agarwal and Naik (2004), Fung and Hsieh (1997, 2001). Given that typically only a small number of return samples are available, it is very difficult to identify dominant risk exposures in estimation of return models, particularly for individual hedge funds. Assuming a small sample set, we consider a hypothetic market timing investment strategy from a universe of investment assets and use it for evaluating predictive quality of models estimated using different methods. Ordinary least squares, ridge regression, and support vector regression (SVR) methods are compared. We illustrate that, for predicting individual hedge fund returns, the more sophisticated ridge regression and SVR regression methods, which limit generalization error in addition to minimizing empirical error, perform significantly better than simple ordinary least squares methods with a heuristic factor selection. In addition, we compare and contrast the predictive quality of the estimated extended asset-class index factor model with the extended individual asset-based factor models. We illustrate that, using more sophisticated estimation methods, the extended individual-asset based model can perform better than the extended asset-class index based model.

Traditional geological mapping methods, which rely on field observations and rock sample analysis, are inefficient for continuous spatial mapping of geological features such as alteration zones. Deep learning models such as convolutional neural networks (CNNs) have ushered in a transformative era in remote sensing data analysis. CNNs excel in automatically extracting features from image data for classification and regression problems. CNNs have the ability to pinpoint specific mineralogical changes attributed to mineralisation processes by discerning subtle features within remote sensing data. In this study, we deploy CNNs with three sets of remote sensing data, namely Landsat 8, Landsat 9, and ASTER, to delineate diverse alteration zones within a mineral-rich region north of Broken Hill in western New South Wales, Australia. Our methodology involves model training using two distinct sets of training samples generated through ground truth data and a fully automated approach through selective principal component analysis (PCA). We also compare CNNs with conventional machine learning models, including k‑nearest neighbours, support vector machines, and multilayer perceptron. Our findings indicate that training with a ground truth-based dataset produces more reliable alteration maps. Additionally, we find that CNNs perform slightly better when compared to conventional machine learning models, which further demonstrates the ability of CNNs to capture spatial patterns in remote sensing data effectively. We find that Landsat 9 surpasses Landsat 8 in mapping iron oxide areas when employing the CNNs model trained with ground truth data obtained by field surveys. We also observe that using ASTER data with the CNNs model trained on the ground truth-based dataset produces the most accurate maps for two other important types of alteration zones, argillic and propylitic. This underscores the utility of CNNs in enhancing the efficiency and precision of geological mapping, particularly in discerning subtle alterations indicative of mineralisation processes, especially those associated with critical metal resources.

Recently, depth methods have developed rapidly and achieved remarkable achievements in the field of hyperspectral image classification. Deep learning largely depends on high-quality labels. However, for hyperspectral images, obtaining high-quality labels is difficult, expensive and time-consuming. For the problem of the small number of training samples, We propose a Spatial-spectral Siamese network, which randomly selects a number of tasks composed of support sets and query sets on the training set. The network is used to extract spectral and spatial features and fuse them to obtain spatial-spectral features. The fused Spatial-spectral features are trained to optimize the Spatial-spectral Siamese network by contrastive loss, and the similarity loss is used to measure the similarity score between samples to optimize the similarity network. In addition, the cluster labels obtained by clustering are used as supervised information, The performance of network classification is further optimized by monitoring the clustering task and using a large amount of unlabeled sample information. The results of two frequently used hyperspectral data sets show that the proposed method still has good performance and effect in classification accuracy when training samples are very small.

Multimodal Earth observation data fusion: Graph-based approach in shared latent space

This study evaluates the effectiveness of stone bunds in enhancing soil moisture, vegetation health, and crop yields in Ghana’s semi-arid Upper East Region, an important area for agricultural productivity in West Africa. In this region, agricultural practices are heavily impacted by erratic rainfall and poor soil moisture retention, threatening food security. Despite the known benefits of traditional soil conservation practices like stone bunds, their effectiveness in this context has not been fully quantified. Field and remote sensing data were used to evaluate the influence of stone bunds on soil moisture dynamics, vegetation growth, and crop yield. Experimental plots with and without stone bunds were monitored for climate, soil water infiltration, and soil moisture and analyzed using the NDVI from Sentinel-2 satellite imagery over two growing seasons under sorghum production (2022–2023). The results indicated that stone bunds enhanced soil moisture retention and increased infiltration rates. The NDVI analysis consistently revealed higher vegetation health and growth in the plots with stone bunds, particularly during critical growth periods. The intermediate results of the conducted experiment indicated that stone bunds increased sorghum yields by over 35% compared to the control plots. The substantial agronomic benefits of stone bunds as a soil and water conservation strategy were evident, improving soil water infiltration, water retention, vegetation health, and crop yields. The findings support the broader adoption of stone bunds in semi-arid regions to enhance agricultural productivity and resilience against climate variability. Further research is recommended to explore the long-term impacts and the integration of stone bunds with other sustainable farming practices to optimize rainfed agricultural outcomes.

By constructing a correlation network between global sea surface temperature anomalies (SSTAs) and summer precipitation anomalies in the Yunnan–Guizhou Plateau, key SST regions influencing summer precipitation anomalies in the Yunnan–Guizhou Plateau were selected. It was found that spring SSTAs in the Bay of Bengal, southwestern Atlantic, and eastern Pacific are crucial for influencing summer precipitation anomalies in the Yunnan–Guizhou Plateau. Setting SSTAs from these three regions as predictor variables 3 months in advance, we constructed multiple linear regression (MLR), ridge regression (RR), and lasso regression (LR) models to predict summer precipitation anomalies over the Yunnan–Guizhou region. The training phase involved data spanning from 1961 to 2005, which aimed to predict precipitation anomalies in the Yunnan–Guizhou Plateau for the period extending from 2006 to 2022. Based on MLR, RR, and LR models, the correlations between predicted values and observed summer precipitation anomalies in Yunnan–Guizhou were 0.48, 0.46, and 0.46, respectively. These values were all higher than the correlation coefficients of the NCC_CSM model’s predicted and observed values. Additionally, its performance in predicting summer precipitation anomalies over the Yunnan–Guizhou region, based on key SST regions, was assessed using performance metrics such as anomaly correlation coefficient (ACC), anomaly sign consistency rate (PC), and trend anomaly comprehensive score (PS score). The average ACC of MLR, RR, and LR models was higher than that of the NCC_CSM model’s predictions. For MLR, RR, LR, and NCC_CSM models, the PCs exceeding 50% of the year were 14, 14, 11, and 10, respectively. Furthermore, the average PS score for predicting summer precipitation anomalies over the Yunnan–Guizhou region using MLR, RR, and LR was approximately 73 points; 8 higher than the average PS score of the NCC_CSM model. Therefore, predicting summer precipitation anomalies over the Yunnan–Guizhou region based on key SST regions is of great significance for improving the prediction skills of precipitation anomalies in this region.

Remote sensing data analysis in the cloudy area is still a challenging process. Fortunately, remote sensing technology is fast growing. As a result, multitemporal data could be used to overcome the problem of the cloudy area. Using multitemporal data is a common approach to address the cloud problem. However, most methods only use two data, one as the main data and the other as complementary of the cloudy area. In this paper, a method to harness multitemporal remote sensing data for automatically extracting some indices is proposed. In this method, the process of extracting the indices is done without having to mask the cloud. Those indices could be further used for many applications such as the classification of urban built-up. Landsat-8 data that is acquired during 2019 are stacked, therefore each pixel at the same position creates a list. From each list, indices are extracted. In this study, NDVI, NDBI, and NDWI are used to mapping built-up areas. Furthermore, extracted indices are divided into four categories by their value (maximum, quantile 75, median, and mean). Those indices are then combined into a simple formula to mapping built-up to see which produces better accuracy. The Pleiades as high-resolution remote sensing data is used to assist supervised classification for assessment. In this study, the combination of mean NDBI, maximum NDVI, and mean NDWI result highest Kappa coefficient of 0.771.

The detection of degraded soil distribution areas is an urgent task. It is difficult and very time consuming to solve this problem using ground methods. The modeling of degradation processes based on digital elevation models makes it possible to construct maps of potential degradation, which may differ from the actual spatial distribution of degradation. The use of remote sensing data (RSD) for soil degradation detection is very widespread. Most often, vegetation indices (indicative botany) have been used for this purpose. In this paper, we propose a method for constructing soil maps based on a multi-temporal analysis of the bare soil surface (BSS). It is an alternative method to the use of vegetation indices. The detection of the bare soil surface was carried out using the spectral neighborhood of the soil line (SNSL) technology. For the automatic recognition of BSS on each RSD image, computer vision based on deep machine learning (neural networks) was used. A dataset of 244 BSS distribution masks on 244 Landsat 4, 5, 7, and 8 scenes over 37 years was developed. Half of the dataset was used as a training sample (Landsat path/row 173/028). The other half was used as a test sample (Landsat path/row 174/027). Binary masks were sufficient for recognition. For each RSD pixel, value “1” was set when determining the BSS. In the absence of BSS, value “0” was set. The accuracy of the machine prediction of the presence of BSS was 75%. The detection of degradation was based on the average long-term spectral characteristics of the RED and NIR bands. The coefficient Cmean, which is the distance of the point with the average long-term values of RED and NIR from the origin of the spectral plane RED/NIR, was calculated as an integral characteristic of the mean long-term values. Higher long-term average values of spectral brightness served as indicators of the spread of soil degradation. To test the method of constructing soil degradation maps based on deep machine learning, an acceptance sample of 133 Landsat scenes of path/row 173/026 was used. On the territory of the acceptance sample, ground verifications of the maps of the coefficient Cmean were carried out. Ground verification showed that the values of this coefficient make it possible to estimate the content of organic matter in the plow horizon (R2 = 0.841) and the thickness of the humus horizon (R2 = 0.8599). In total, 80 soil pits were analyzed on an area of 649 ha on eight agricultural fields. Type I error (false positive) of degradation detection was 17.5%, and type II error (false negative) was 2.5%. During the determination of the presence of degradation by ground methods, 90% of the ground data coincided with the detection of degradation from RSD. Thus, the quality of machine learning for BSS recognition is sufficient for the construction of soil degradation maps. The SNSL technology allows us to create maps of soil degradation based on the long-term average spectral characteristics of the BSS.

Imaging spectroscopy as a tool to study sediment characteristics on a tidal sandbank in the Westerschelde

Markov random field (MRF) based methods have been widely used in high spatial resolution (HSR) image classification. However, many existing MRF-based methods put more emphasis on pixel level contexts while less on superpixel level contextual information. To cope with this issue, this article presents a novel bilevel contextual MRF framework, named BLC-MRF, for HSR imagery classification. Specifically, pixel and superpixel level dependence are incorporated into the proposed MRF model to fully exploit spectral–spatial contextual information and preserve object boundaries in HSR images. In BLC-MRF, a pixel level MRF model is first performed and then cascaded as an input of a superpixel level MRF. In superpixel level, unary and pairwise potential terms are constructed by using the superpixel probability estimation method and spectral histogram distance, respectively. At last, a contextual MRF model is conducted and the final classification map can be computed by using $\alpha$ -expansion algorithm. The benefits of BLC-MRF are twofold: first, the pixel and superpixel level contextual information can be exploited under MRF framework to preserve object boundaries for improving the classification performance, and, second, the algorithm can provide promising results with a small number of training samples. Experimental results on three HSR datasets demonstrate that the proposed approach outperforms several state-of-the-art methods in terms of the classification performance.