The fuzzy broad learning system (FBLS) is a recently proposed neuro-fuzzy model that shares the similar structure of a BLS. It shows high accuracy in both classification and regression tasks and inherits the fast computational nature of a BLS. However, the ensemble of several fuzzy subsystems in an FBLS decreases the possibility for people to understand the fuzzy model since the fuzzy rules from different fuzzy systems are difficult to combine together while keeping the consistence. To balance the model accuracy and complexity, a synthetically simplified FBLS, named compact FBLS (CFBLS), is developed, which can generate much fewer and more explainable fuzzy rules for understanding. There is only one traditional Takagi-Sugeno-Kang fuzzy system in the feature layer of a CFBLS, and the input universe of discourse is equally partitioned to obtain the fuzzy sets with proper linguistic labels accordingly. The random feature selection matrix and rule combination matrix are employed to reduce the total number of fuzzy rules and avoid the ``curse of dimensionality''. The enhancement layer is kept in the CFBLS that helps to add a nonlinear transformation of input features to the traditional first-order polynomial used in the consequent part of a fuzzy rule. The pseudoinverse is also used to determine the parameters of CFBLS, guaranteeing its fast computational nature. The experiments on the popular UCI and KEEL data sets indicate that the CFBLS can generate a smaller set of comprehensible fuzzy rules and achieve much higher accuracy than some state-of-the-art neuro-fuzzy models. Moreover, the advantage of CFBLS is also verified in a real-world application.

Broad learning system (BLS) is proposed as a competitor to deep neural network, which is constructed using only single hidden layer instead of multilayered structure. It also manages incremental learning with intelligible mathematical derivation by pseudoinverse. Despite its empirical success, the limitations of BLS cannot be overlooked, especially for its sensibility to the number of feature nodes. For this reason, large model is required in training, which may easily cause overfitting. In this paper, a probabilistic model called sparse Bayesian broad learning system (SBBLS) is proposed to dispose of this defect by linearly-weighting a small group of basis functions from an enormous number of candidates within Bayesian framework. Outstanding sparsity and generalization can be observed in SBBLS. More distinctively, SBBLS is capable of outputting probabilistic estimation of prediction for further decision analysis while maintaining inherent properties of BLS simultaneously. Experimental results demonstrate that the proposed SBBLS model could achieve comparable performance to BLS both in regression and classification with probabilistic interpretability.

Urban sensing has become prevalent for monitoring dynamic urban status due to the development of intelligent computing. Fast sensing and accurate analyzing of soil quality promote to make data-driven urban planning and management. Soil contamination hiders the sustainable development of the city environmental ecology. Decentralized sensing based on an Internet of Things (IoT) architecture is a state-of-art technology. Portable spectral detection serves for immediate quantitative analysis of target components. In this case, portable sensing combined with federated learning simply shares the informative features extracted from the IoT-based spectral sensing data. However, the modeling technique for the analysis of spectroscopic sensing data faces several challenges due to the emerge of the big data problem in IoT-based sceneries. The consideration of possible federal learning of multi-node collective data should ask for deep studies of modeling methodologies. In this paper, we built up an IoT-based portable spectral sensing system for simultaneous sensing and detecting the soil data at distributed sensing places. The collaborate training model was established for dealing with the dynamic sensing data, by the fusion design of a broad learning network (BLN) and a fuzzy partial least square (fPLS) model. The BLN output feature variables are produced from the scalable pseudo input layer with training linking weights adaptively, and the number of fuzzy rules is scalable. In experiment, the decentralized sensing system and the fusion modeling framework carry out the model optimization for the portable near-infrared spectroscopic sensing data of heavy metal in soil samples. The quantification of two elements demonstrated that the proposed framework yielded superior prediction results to the conventional PLS model for the training and evaluating on the dynamic sensing data. In interaction with the IoT architecture, the framework is prospectively expected as an advanced intelligent technical support for fast analysis of the portable spectroscopic sensing data.

Curve approximation is a challenging issue to precisely depict exquisite shapes of natural phenomena, in which the piecewise Bézier curve is one of the most widely utilized tools due to its beneficial properties. It is essential to determine the quantity and location of control points through the process of generating the mathematical representation of desired objects. This paper presents a new algorithm called adaptive extension fitting scheme (AEFS) to determine a piecewise Bézier curve that best fits a given sequence of data points as well as locate the coordinates of the connecting points between the pieces adaptively. Taking full advantage of the scalability of the Bézier curve segment, AEFS is effective in sequential knot searching within an impressively small computational consumption. The capability of the proposed stepwise extension strategy is deduced from rigorous theoretical proof, resulting in proper connecting points together with well-fitted Bézier curves. The proposed algorithm is evaluated by some popular benchmarks for curve fitting, and compared with several state-of-the-art approaches. Experimental results indicate that AEFS outperforms other models involved in terms of execution time, fitting accuracy, number of segments, and the authenticity of shape contours.

Zhouqu County is located at the intersection of two active structural belts in the east of the Qinghai-Tibet Plateau, which is a rare, high-incidence area of landslides, debris flow, and earthquakes on a global scale. The complex regional geological background, the fragile ecological environment, and the significant tectonic activities have caused great difficulties for the dynamic susceptibility assessment and prediction of landslides in the study area. Specifically, Zhouqu is a typical alpine-canyon region in geomorphology; currently there is still a lack of a landslide susceptibility assessment study for this particular type of area. Therefore, the development of landslide susceptibility mapping (LSM) in this area is of great significance for quickly grasping the regional landslide situation and formulating disaster reduction strategies. In this article, we propose a graph-represented learning algorithm named GBLS within a broad framework in order to better extract the spatially relevant characteristics of the geographical data and to quickly obtain the change pattern of landslide susceptibility according to the frequent variation (increase or decrease) of the data. Based on the broad structure, we construct a group of graph feature nodes through graph-represented learning to make better use of geometric correlation of data to upgrade the precision. The proposed method maintains the efficiency and effectiveness due to its broad structure, and even better, it is able to take advantage of incremental data to complete fast learning methodology without repeated calculation, thus avoiding time waste and massive computation consumption. Empirical results verify the excellent performance with high efficiency and generalization of GBLS on the 407 landslides in the study area inventoried by remote sensing interpretation and field investigation. Then, the landslide susceptibility map is drawn to visualize the landslide susceptibility assessment according to the result of GBLS with the highest AUC (0.982). The four most influential factors were ranked out as rainfall, NDVI, aspect, and Terrain Ruggedness Index. Our research provides a selection criterion that can be referenced for future research where GBLS is of great significance in LSM of the alpine-canyon region. It plays an important role in demonstrating and popularizing the research in the same type of landform environment. The LSM would help the government better prevent and confine the risk of landslide hazards in the alpine-canyon region of Zhouqu.

The ecological quality of river basins is significantly influenced by the complex network of river structures and their connectivity. This study measured the temporal and spatial variability of ecological quality, as reflected by remote sensing ecological indices (RSEI), and examined their responses to river network connectivity (RNC). In total, 8 RNC indices, including river structure of river density (D_r), water surface ratio (W_r), edge-node ratio (β), and network connectivity (γ), and node importance indices of betweenness centrality (BC), PageRank (PG_R), out_degree centrality (Out_D), and in_closeness centrality (In_C), were generated at the subbasin scale. Our results highlighted the significance of RNC in influencing both the values and variability of RSEI, and the extent of this influence varied across different time periods. Specifically, three distinct clusters can be extracted from the temporal variability of RSEI, representing wet, near-normal, and dry years. The river structure index of γ significantly influenced the spatial patterns of subbasin RSEIs, particularly in wet years (R² = 0.554), whereas β displayed a pronounced U-shape correlation with subbasin RSEIs in dry years (R² = 0.512). Although node importance indices did not correlate directly with subbasin RSEI levels, as the river structure indices did, they significantly positively affected temporal variability of subbasin RSEIs (EI_SD_t). Higher values of PG_R, Out_D, and In_C were associated with increased subbasin RSEI variability. Based on these correlations, we developed RNC-based RSEI and EI_SD_t models with high adjusted coefficients of determination to facilitate the assessment of ecosystem quality. This study provides essential insights into ecosystem dynamics related to river connectivity within a basin and offers valuable guidance for effective watershed management and conservation efforts aimed at enhancing ecological resilience and sustainability.