Uncertainties of landslide susceptibility prediction:influences of different study area scales and mapping unit scales

This study aims to investigate the effects of different mapping unit scales and study area scales on the uncertainty rules of landslide susceptibility prediction(LSP).To illustrate various study area scales,Ganzhou City in China,its eastern region(Ganzhou East),and Ruijin County in Ganzhou East were chosen.Different mapping unit scales are represented by grid units with spatial resolution of 30 and 60 m,as well as slope units that were extracted by multi-scale segmentation method.The 3855 landslide locations and 21 typical environmental factors in Ganzhou City are first determined to create spatial datasets with input-outputs.Then,landslide susceptibility maps(LSMs)of Ganzhou City,Ganzhou East and Ruijin County are pro-duced using a support vector machine(SVM)and random forest(RF),respectively.The LSMs of the above three regions are then extracted by mask from the LSM of Ganzhou City,along with the LSMs of Ruijin County from Ganzhou East.Additionally,LSMs of Ruijin at various mapping unit scales are generated in accordance.Accuracy and landslide suscepti-bility indexes(LSIs)distribution are used to express LSP uncertainties.The LSP uncertainties under grid units significantly decrease as study area scales decrease from Ganzhou City,Ganzhou East to Ruijin County,whereas those under slope units are less affected by study area scales.Of course,attentions should also be paid to the broader representativeness of large study areas.The LSP accuracy of slope units increases by about 6%–10%compared with those under grid units with 30 m and 60 m resolution in the same study area's scale.The significance of environmental factors exhibits an averaging trend as study area scale increases from small to large.The importance of environmental factors varies greatly with the 60 m grid unit,but it tends to be consistent to some extent in the 30 m grid unit and the slope unit.

Common Fixed Point Theorems for Sequences of φ-type Contraction Set-valued Mappings

In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings are also obtained.

Formal Concept Analysis Based on Set-valued Mapping

Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, etc. In this paper, it is shown that a formal context T is equivalent to a set-valued mapping S ： G → P（М）, and formal concepts could be defined in the set-valued mapping S. It is known that the topology and set-valued mapping are linked. Hence, the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology.

Natural Mappings on Set-valued Mapping Spaces

In this paper,we discuss the continuities of some natural mappings on pointcompact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings,set-valued diagonal mappings,induced mappings,set-valued evaluation mappings,set-valued topological sum mappings and set-valued topological product mappings.

Proximal point algorithm for a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings

We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.

Iterative Processes with Errors for Generalized Set-Valued φ-Hemi-contractive Mapping in Banach Spaces

A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.

Iterative Approximation with Errors for Generalized Set-Valued Strongly Accretive Mapping in Banach Spaces

A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et al. was proved. The results presented in this paper improve and extend the earlier results obtained by Huang et al.

A survey of ergodicity on the set-valued mappings

In this paper, we give a survey on the PhD thesis of the first author. There theexistence and ergodicity on invariant measures of set-valued mappings are discused.

IMIBSE与ISOMAP在旋转机械故障诊断中的应用

针对基本熵的区域划分标准不理想,导致无法有效测量振动信号的复杂度,使故障诊断的准确率不佳这一问题,提出了一种基于改进多尺度改进基本熵(IMIBSE)、等距特征映射(ISOMAP)和随机森林(RF)的旋转机械故障诊断方法。首先,采用基于方差的区域划分准则对基本熵进行了改进,结合改进的粗粒化处理,提出了IMIBSE,并将其用于提取故障特征;随后,利用ISOMAP对原始故障特征进行了特征降维,选择了对分类贡献最大的一组特征作为故障敏感特征;最后,基于RF建立了多故障分类器,将故障敏感特征输入至RF模型进行了训练和测试,实现了旋转机械的故障识别,利用齿轮箱和离心泵两种故障数据集将IMIBSE方法与复合多尺度基本熵、多尺度改进基本熵、多尺度基本熵进行了比较和分析。研究结果表明:IMIBSE不仅具有最佳的可视化效果,而且取得的识别准确率最高,二者均达到了100%,而二者的平均分类准确率分别为100%和99.8%;相较于其他故障诊断方法,IMIBSE方法的准确率更高,而且适用于小样本的故障识别问题。

Mapping landslide susceptibility at the Three Gorges Reservoir, China, using gradient boosting decision tree,random forest and information value models

This work was to generate landslide susceptibility maps for the Three Gorges Reservoir(TGR) area, China by using different machine learning models. Three advanced machine learning methods, namely, gradient boosting decision tree(GBDT), random forest(RF) and information value(InV) models, were used, and the performances were assessed and compared. In total, 202 landslides were mapped by using a series of field surveys, aerial photographs, and reviews of historical and bibliographical data. Nine causative factors were then considered in landslide susceptibility map generation by using the GBDT, RF and InV models. All of the maps of the causative factors were resampled to a resolution of 28.5 m. Of the 486289 pixels in the area,28526 pixels were landslide pixels, and 457763 pixels were non-landslide pixels. Finally, landslide susceptibility maps were generated by using the three machine learning models, and their performances were assessed through receiver operating characteristic(ROC) curves, the sensitivity, specificity,overall accuracy(OA), and kappa coefficient(KAPPA). The results showed that the GBDT, RF and In V models in overall produced reasonable accurate landslide susceptibility maps. Among these three methods, the GBDT method outperforms the other two machine learning methods, which can provide strong technical support for producing landslide susceptibility maps in TGR.

Landslide susceptibility mapping using hybrid random forest with GeoDetector and RFE for factor optimization

The present study aims to develop two hybrid models to optimize the factors and enhance the predictive ability of the landslide susceptibility models.For this,a landslide inventory map was created with 406 historical landslides and 2030 non-landslide points,which was randomly divided into two datasets for model training(70%)and model testing(30%).22 factors were initially selected to establish a landslide factor database.We applied the GeoDetector and recursive feature elimination method(RFE)to address factor optimization to reduce information redundancy and collinearity in the data.Thereafter,the frequency ratio method,multicollinearity test,and interactive detector were used to analyze and evaluate the optimized factors.Subsequently,the random forest(RF)model was used to create a landslide susceptibility map with original and optimized factors.The resultant hybrid models GeoDetector-RF and RFE-RF were evaluated and compared by the area under the receiver operating characteristic curve(AUC)and accuracy.The accuracy of the two hybrid models(0.868 for GeoDetector-RF and 0.869 for RFE-RF)were higher than that of the RF model(0.860),indicating that the hybrid models with factor optimization have high reliability and predictability.Both RFE-RF GeoDetector-RF had higher AUC values,respectively 0.863 and 0.860,than RF(0.853).These results confirm the ability of factor optimization methods to improve the performance of landslide susceptibility models.

A universal algorithm to generate pseudo-random numbers based on uniform mapping as homeomorphism

A specific uniform map is constructed as a homeomorphism mapping chaotic time series into [0,1] to obtain sequences of standard uniform distribution. With the uniform map, a chaotic orbit and a sequence orbit obtained are topologically equivalent to each other so the map can preserve the most dynamic properties of chaotic systems such as permutation entropy. Based on the uniform map, a universal algorithm to generate pseudo random numbers is proposed and the pseudo random series is tested to follow the standard 0-1 random distribution both theoretically and experimentally. The algorithm is not complex, which does not impose high requirement on computer hard ware and thus computation speed is fast. The method not only extends the parameter spaces but also avoids the drawback of small function space caused by constraints on chaotic maps used to generate pseudo random numbers. The algorithm can be applied to any chaotic system and can produce pseudo random sequence of high quality, thus can be a good universal pseudo random number generator.

ON THE GENERALIZED FRITZ JOHN OPTIMALITY CONDITIONS OF VECTOR OPTIMIZATION WITH SET-VALUED MAPS UNDER BENSON PROPER EFFICIENCY

A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.

Benson proper efficiency for vector optimization of generalized subconvexlike set-valued maps in ordered linear spaces

Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency.

ε-super Effcient Solutions of Optimization Problems with Set-valued Maps in Locally Convex Space

In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,used new methods,the scalarization theorem and Lagrange multiplier theorem for ε-super effcient solution are established.

Set-Valued Non-Linear Random Implicit Quasivariational Inclusions

In this paper, we propose iterative algorithms for set valued nonlinear random implicit quasivariational inclusions. We define the related random implicit proximal operator equations and establish an equivalence between them. Finally, we prove the existence and convergence of random iterative sequences generated by random iterative algorithms.

A Strong Law of Large Numbers for Set-Valued Random Variables in Gα Space

In this paper, we shall represent a strong law of large numbers (SLLN) for weighted sums of set- valued random variables in the sense of the Hausdorff metric dH, based on the result of single-valued random variable obtained by Taylor [1].

Strong Laws of Large Numbers for Fuzzy Set-Valued Random Variables in Gα Space

In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of d∞H . The results are based on the result of single-valued random variables obtained by Taylor [1] and set-valued random variables obtained by Li Guan [2].

Topological Stability and Entropy for Certain Set-valued Maps

In this paper,the dynamics(including shadowing property,expansiveness,topological stability and entropy)of several types of upper semi-continuous set-valued maps are mainly considered from differentiable dynamical systems points of view.It is shown that(1)if f is a hyperbolic endomorphism then for eachε>0 there exists a C^(1)-neighborhood U of f such that the induced set-valued map F_(f,U)has theε-shadowing property,and moreover,if f is an expanding endomorphism then there exists a C^(1)-neighborhood U of f such that the induced set-valued map F_(f,U)has the Lipschitz shadowing property;(2)when a set-valued map F is generated by finite expanding endomorphisms,it has the shadowing property,and moreover,if the collection of the generators has no coincidence point then F is expansive and hence is topologically stable;(3)if f is an expanding endomorphism then for eachε>0 there exists a C^(1)-neighborhood U of f such that h(F_(f,U,ε))=h(f);(4)when F is generated by finite expanding endomorphisms with no coincidence point,the entropy formula of F is given.Furthermore,the dynamics of the set-valued maps based on discontinuous maps on the interval are also considered.

Mapping regional cropping patterns by using GF-1 WFV sensor data

The successful launched Gaofen satellite no. 1 wide field-of-view （GF-1 WFV） camera is characterized by its high spatial resolution and may provide some potential for regional crop mapping. This study, taking the Bei＇an City, Northeast China as the study area, aims to investigate the potential of GF-1 WFV images for crop identification and explore how to fully use its spectral, textural and temporal information to improve classification accuracy. In doing so, an object-based and Random Forest （RF） algorithm was used for crop mapping. The results showed that classification based on an optimized single temporal GF-1 image can achieve an overall accuracy of about 83%, and the addition of textural features can im- prove the accuracy by 8.14%. Moreover, the multi-temporal GF-1 data can produce a classification map of crops with an overall accuracy of 93.08% and the introduction of textural variables into multi-temporal GF-1 data can only increase the accuracy by about 1%, which suggests the importance of temporal information of GF-1 for crop mapping in comparison with single temporal data. By comparing classification results of GF-1 data with different feature inputs, it is concluded that GF-1 WFV data in general can meet the mapping efficiency and accuracy requirements of regional crop. But given the unique spectral characteristics of the GF-1 WFV imagery, the use of textual and temporal information is needed to yield a satisfactory accuracy.