Pairwise Matrix Research Articles

Unsupervised Data Labeling on Graphs by Self‐Assignment Flows

AbstractThis paper extends the recently introduced assignment flow approach for supervised image labeling to unsupervised scenarios where no labels are given. The resulting self‐assignment flow takes a pairwise data affinity matrix as input data and maximizes the correlation with a low‐rank matrix that is parametrized by the variables of the assignment flow, which entails an assignment of the data to themselves through the formation of latent labels (feature prototypes). A single user parameter, the neighborhood size for the geometric regularization of assignments, drives the entire process. By smooth geodesic interpolation between different normalizations of self‐assignment matrices on the positive definite matrix manifold, a one‐parameter family of self‐assignment flows is defined. Accordingly, our approach can be characterized from different viewpoints, e.g. as performing spatially regularized, rank‐constrained discrete optimal transport, or as computing spatially regularized normalized spectral cuts. Regarding combinatorial optimization, our approach successfully determines completely positive factorizations of self‐assignments in large‐scale scenarios, subject to spatial regularization. Various experiments including the unsupervised learning of patch dictionaries using a locally invariant distance function, illustrate the properties of the approach.

A Scalable Optimization Mechanism for Pairwise Based Discrete Hashing.

Maintaining the pairwise relationship among originally high-dimensional data into a low-dimensional binary space is a popular strategy to learn binary codes. One simple and intuitive method is to utilize two identical code matrices produced by hash functions to approximate a pairwise real label matrix. However, the resulting quartic problem in term of hash functions is difficult to directly solve due to the non-convex and non-smooth nature of the objective. In this paper, unlike previous optimization methods using various relaxation strategies, we aim to directly solve the original quartic problem using a novel alternative optimization mechanism to linearize the quartic problem by introducing a linear regression model. Additionally, we find that gradually learning each batch of binary codes in a sequential mode, i.e. batch by batch, is greatly beneficial to the convergence of binary code learning. Based on this significant discovery and the proposed strategy, we introduce a scalable symmetric discrete hashing algorithm that gradually and smoothly updates each batch of binary codes. To further improve the smoothness, we also propose a greedy symmetric discrete hashing algorithm to update each bit of batch binary codes. Moreover, we extend the proposed optimization mechanism to solve the non-convex optimization problems for binary code learning in many other pairwise based hashing algorithms. Extensive experiments on benchmark single-label and multi-label databases demonstrate the superior performance of the proposed mechanism over recent state-of-the-art methods on two kinds of retrieval tasks: similarity and ranking order. The source codes are available on https://github.com/xsshi2015/Scalable-Pairwise-based-Discrete-Hashing.

Flash flood hazard mapping based on AHP with GIS and satellite information in Kampong Speu Province, Cambodia

Purpose Cambodia is considered one of the countries that are most vulnerable to adverse effects of climate change, particularly floods and droughts. Kampong Speu Province is a frequent site of calamitous flash floods. Reliable sources of flash flood information and analysis are critical in efforts to minimize the impact of flooding. Unfortunately, Cambodia does not yet have a comprehensive program for flash flood hazard mapping, with many places such as Kampong Speu Province having no such information resources available. The purpose of this paper is, therefore, to determine flash flood hazard levels across all of Kampong Speu Province using analytical hierarchy process (AHP) and geographical information system (GIS) with satellite information. Design/methodology/approach The integrated AHP–GIS analysis in this study encompasses ten parameters in the assessment of flash flood hazard levels across the province: rainfall, geology, soil, elevation, slope, stream order, flow direction, distance from drainage, drainage density and land use. The study uses a 10 × 10 pairwise matrix in AHP to compare the relative importance of each parameter and find each parameter’s weight. Finally, a flash flood hazard map is developed displaying all areas of Kampong Speu Province classified into five levels, with Level 5 being the most hazardous. Findings This study reveals that high and very high flash flood hazard levels are identified in the northwest part of Kampong Speu Province, particularly in Aoral, Phnum Srouch and Thpong districts and along Prek Thnot River and streams. Originality/value The flash flood hazard map developed here provides a wealth of information that can be invaluable for implementing effective disaster mitigation, improving disaster preparedness and optimizing land use.

Reply by Authors.

You have accessJournal of UrologyLetters to the Editor/Errata1 Oct 2020Reply by Authorsis a reply to letterRe: Delayed Radical Prostatectomy is Not Associated with Adverse Oncological Outcomes: Implications for Men Experiencing Surgical Delay Due to the COVID-19 Pandemic K. B. Ginsburg, G. L. Curtis, R. E. Timar, A. K. George, and M. L. Cher K. B. GinsburgK. B. Ginsburg More articles by this author , G. L. CurtisG. L. Curtis More articles by this author , R. E. TimarR. E. Timar More articles by this author , A. K. GeorgeA. K. George More articles by this author , and M. L. CherM. L. Cher More articles by this author View All Author Informationhttps://doi.org/10.1097/JU.0000000000001193AboutPDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareFacebookTwitterLinked InEmail Rosen et al raise important statistical considerations that we indeed took into account while designing this analysis and interrogating the models included in the article. Regarding collinearity, as suggested, a pairwise correlation matrix was used to assess for correlation of variables included in the models. The risk of collinearity rises with a correlation coefficient above 0.8. None of the combinations of variables included in our models approached this threshold, thus reducing the risk. Rosen et al also cite a very useful publication by Bujang et al4 regarding general rules for logistic regression models while raising the issue of overfitting the models.4 They mention that 10 to 15 events are needed per independent variable included in the model and an estimated sample size of 100 + 50 × (number of independent variables) patients to support an adequately powered logistic regression model. According to this formula, the minimum number of patients needed for a model with 37 predictors would be 1,950, with approximately 370 to 555 events. The sample size afforded to us by the National Cancer Database allowed for an adequately powered analysis of all of the models presented in the article, as our smallest subgroup contained more than 17,000 patients with more than 2,000 events. Regarding the relationship between the other predictors in the models and the outcomes of interest, we purposely omitted this information for brevity. We presented a large volume of data, and we did not want to distract from the relationship between treatment delay and oncologic outcomes by creating multiple lengthy tables including the ORs, 95% CIs and p values for all of the other covariates. We believe the data presented in our study are congruent with previously published reports and are intuitive regarding what we know about the slow natural history of prostate cancer. A common mantra of many academics, which is credited to George Box, comes to mind: “All models are wrong, but some are useful.”5 Acknowledging the limitations of these data, we believe our work may be beneficial to patients and clinicians alike while discussing the implications of unintentional treatment delay and optimal timing for treatment of prostate cancer amid the current COVID-19 environment and waves or surges in the future. References 4. : Sample size guidelines for logistic regression from observational studies with large population: emphasis on the accuracy between statistics and parameters based on real life clinical data.Malays J Med Sci 2018; 25: 122. Google Scholar 5. : Science and statistics. J Am Stat Assoc 1976; 71: 791. Google Scholar © 2020 by American Urological Association Education and Research, Inc.FiguresReferencesRelatedDetailsRelated articlesJournal of Urology1 Jul 2020Re: Delayed Radical Prostatectomy is Not Associated with Adverse Oncological Outcomes: Implications for Men Experiencing Surgical Delay Due to the COVID-19 Pandemic Volume 204Issue 4October 2020Page: 845-845 Advertisement Copyright & Permissions© 2020 by American Urological Association Education and Research, Inc.MetricsAuthor Information K. B. Ginsburg More articles by this author G. L. Curtis More articles by this author R. E. Timar More articles by this author A. K. George More articles by this author M. L. Cher More articles by this author Expand All Advertisement Advertisement PDF downloadLoading ...

Simultaneous autoregressive models for spatial extremes

AbstractMotivated by the widespread use of large gridded data sets in the atmospheric sciences, we propose a new model for extremes of areal data that is inspired by the simultaneous autoregressive (SAR) model in classical spatial statistics. Our extreme SAR model extends recent work on transformed‐linear operations applied to regularly varying random vectors, and is unique among extremes models in being directly analogous to a classical linear model. An additional appeal is its simplicity; given a proximity matrix W, spatial dependence is described by a single parameter . We develop an estimation method that minimizes the discrepancy between the tail pairwise dependence matrix (TPDM) for the fitted model and the estimated TPDM. Applying this method to simulated data demonstrates that it is able to produce good estimates of extremal spatial dependence even in the case of model misspecification, and additionally produces reasonable estimates of uncertainty. We also apply the method to gridded precipitation observations for a study region over northeast Colorado, and find that a single‐parameter extreme SAR model paired with a neighborhood structure which accounts for longer range dependence effectively models spatial dependence in these data.

An Information-Theoretic Approach to Unsupervised Feature Selection for High-Dimensional Data

In this paper, we propose an information-theoretic approach to design the functional representations to extract the hidden common structure shared by a set of random variables. The main idea is to measure the common information between the random variables by Watanabe's total correlation, and then find the hidden attributes of these random variables such that the common information is reduced the most given these attributes. We show that these attributes can be characterized by an exponential family specified by the eigen-decomposition of some pairwise joint distribution matrix. Then, we adopt the log-likelihood functions for estimating these attributes as the desired functional representations of the random variables, and show that such representations are informative to describe the common structure. Moreover, we design both the multivariate alternating conditional expectation (MACE) algorithm to compute the proposed functional representations for discrete data, and a novel neural network training approach for continuous or high-dimensional data. Furthermore, we show that our approach has deep connections to existing techniques, such as Hirschfeld-Gebelein-R\'{e}nyi (HGR) maximal correlation, linear principal component analysis (PCA), and consistent functional map, which establishes insightful connections between information theory and machine learning. Finally, the performances of our algorithms are validated by numerical simulations.

PPM10 CORRELATION AND HIEARCHICAL CLUSTERING ORDER ANALYSIS OF TOP 25 CO-OCCURRING GENOMIC ALTERATIONS IN NON-SMALL CELL LUNG CANCER

The study was designed to analyze co-occurrence pattern of top 25 genomic alterations in patients with non-small cell lung cancer (NSCLC) to inform future research. The Flatiron Clinico-Genomic Database (CGDB) is a linked data source including electronic medical record and genomics data from Foundation Medicine, Inc. Patients with advanced or metastatic NSCLC were eligible for this study if they received anti-cancer therapy within 180 days after diagnosis. The 25 biomarkers with highest alteration rate were identified. Correlation matrix and cluster analysis were used. Of 5807 eligible patients, 5536 (95.3%) had at least one of 25 top biomarkers, among which the top 5 highest are TP53(65.1%), KRAS (29.7%), CDKN2A (26.7%), PDL1 (18.4%), and EGFR (17.9%). There are 1404 (24.2%) patients had two co-occurring biomarkers, 1317 (22.7%) three co-occurring biomarkers, 998 (17.2%) four co-occurring biomarkers, and 591 (10.2%) had five co-occurring biomarkers. The pairwise correlation matrix indicated strong and significant correlations occurs between CDKN2B and CDKNN2A (ρ=0.725, p<0.0001); NFKBIA and NKX2-1 (ρ=0.796, p<0.0001), SOX2 and PIK3CA (ρ=0.479, p<0.0001). Medium correlation was observed between RB1 and TP53 (ρ=0.14, p<0.0001), KRAS and STK11 (ρ=0.169, p<0.0001), KRAS and RBM10 (ρ=0.133, p<0.0001). Further hierarchical clustering order analysis show 6 co-occurrence patterns among SMARCA4, STK11 AND KEAP1, ATM, KRAS and RBM10, ARID1A and LRP1B, PTEN, MLL2, PIK3CA, SOX2, TP53, and RB1, ERBB2, CDKN2A, and CDKN2B, EGFR, MDM2, MYC, NKX2-1 and NFKBIA. The genomic alterations in NSCLC patients are very heterogeneous and reflect the underlying tumor biology. Strong co-occurrence among certain genes may exist and graphic presentation may help identify patterns.

Application of fuzzy preference relations method in AHP to improve judgment matrix consistency

Most issues when using AHP is the difficulty of getting the consistency of a judgment matrix. It can be affected due to decision-making subjectivity. This study proposes the usage of the fuzzy Preference Relations (FPR) method to ensure a judgment in decision-making is acceptable and high objectively due to its obstacle for satisfying consistent judgment matrix from decision-makers in AHP. Improving the consistency of decision matrix can be done through the following steps, namely: 1) Transform pairwise comparison matrix of A=(a_ij) into FPR R=(r_ij ), 2) construct a new consistency matrix of FRP which satisfies the additive consistency, and 3) compose a new consistent pairwise matrix. As a result, the consistency index value was acceptable (< 0.10). Moreover, the procedure is applied in the determination of agro-industries based SMEs development.

Visual Approaches for Exploratory Data Analysis: A Survey of the Visual Assessment of Clustering Tendency (VAT) Family of Algorithms

Exploratory data analysis (EDA) using data clustering is extremely important for understanding the basic characteristics of a novel data set before developing complex statistical models and testing the various hypotheses. A preliminary step to clustering is deciding whether the data contain any clusters and, if so, how many clusters to seek. This is the clustering-tendency-assessment problem, which has not received much attention in the pattern-recognition literature. An important category of algorithms in this domain includes visual approaches, represented here by the visual assessment of tendency (VAT) algorithm, which reorders the pairwise dissimilarity matrix and then generates a reordered dissimilarity image (RDI) or cluster heat map that shows possible clusters in the data by dark blocks along the diagonal.

Analyzing Urban Sprawl and Sustainable Development in Dhaka, Bangladesh

The paper examines the impact of urban sprawl on sustainable development in Dhaka megacity, applying a comprehensive analysis. The study selected the greater Dhaka region as the study area. Besides quantitative analysis, the paper also used the widely accepted definition of sprawl to confirm the existence of sprawl in the context of Dhaka. It also employed the Pairwise Ranking Matrix (PRM) to determine the most contributing factors of urban sprawl in Dhaka. The ArcGIS and Remote Sensing tools were used to investigate and indicate urban sprawl patterns and land-use change from 1990 to 2017. The findings confirmed that Dhaka was slowly experiencing processes of urban sprawl, particularly in Southern, Western, and Eastern local regions. As policy tools, this paper contributed to the designing of effective spatial planning and strategies for planned urban growth and sustainable development. Keywords: Urban sprawl; Sustainable development; Dhaka; Spatial planning; ArcGIS DOI: 10.7176/JESD/11-6-02 Publication date: March 31 st 2020

Quasi-Periodic Time Series Clustering for Human Activity Recognition

This paper analyses the periodic signals in the time series to recognize human activity by using a mobile accelerometer. Each point in the timeline corresponds to a segment of historical time series. This segments form a phase trajectory in phase space of human activity. The principal components of segments of the phase trajectory are treated as feature descriptions at the point in the timeline. The paper introduces a new distance function between the points in new feature space. To reval changes of types of the human activity the paper proposes an algorithm. This algorithm clusters points of the timeline by using a pairwise distances matrix. The algorithm was tested on synthetic and real data. This real data were obtained from a mobile accelerometer.

Pairwise sparse + low-rank models for variables of mixed type

Factor models have been proposed for a broad range of observed variables such as binary, Gaussian, and variables of mixed types. They typically model a pairwise interaction parameter matrix with a low-rank and a diagonal component. The low-rank component can be interpreted as the effect of a few latent quantitative variables which are common in social science applications. Another line of research has investigated graphical models for the same types of observed variables, where the pairwise interactions are usually assumed to be sparse. Sparse network structures are often found in the natural sciences. Still overall, while factor and sparse models are suitable for many applications, they sometimes might not be expressive enough to fit certain data well. This has motivated the confluence of factor and graphical models, yielding models where the interaction parameters are decomposed into respectively sparse and low-rank components. Up to now, this has only been done separately for observed Gaussian and for observed binary variables, but never jointly. The present work accomplishes a unified treatment of pairwise sparse and low-rank models. It does so by simultaneously allowing observed binary and quantitative (conditional Gaussian) variables. The model parameters of the joint model can be estimated using a convex regularized likelihood optimization problem. We show that the resulting estimator has consistency properties in the high-dimensional setting.

Hierarchical Clustering Analyses of Plasma Proteins in Subjects With Cardiovascular Risk Factors Identify Informative Subsets Based on Differential Levels of Angiogenic and Inflammatory Biomarkers.

Agglomerative hierarchical clustering analysis (HCA) is a commonly used unsupervised machine learning approach for identifying informative natural clusters of observations. HCA is performed by calculating a pairwise dissimilarity matrix and then clustering similar observations until all observations are grouped within a cluster. Verifying the empirical clusters produced by HCA is complex and not well studied in biomedical applications. Here, we demonstrate the comparability of a novel HCA technique with one that was used in previous biomedical applications while applying both techniques to plasma angiogenic (FGF, FLT, PIGF, Tie-2, VEGF, VEGF-D) and inflammatory (MMP1, MMP3, MMP9, IL8, TNFα) protein data to identify informative subsets of individuals. Study subjects were diagnosed with mild cognitive impairment due to cerebrovascular disease (MCI-CVD). Through comparison of the two HCA techniques, we were able to identify subsets of individuals, based on differences in VEGF (p < 0.001), MMP1 (p < 0.001), and IL8 (p < 0.001) levels. These profiles provide novel insights into angiogenic and inflammatory pathologies that may contribute to VCID.

Flexible Multi-modal Hashing for Scalable Multimedia Retrieval

Multi-modal hashing methods could support efficient multimedia retrieval by combining multi-modal features for binary hash learning at the both offline training and online query stages. However, existing multi-modal methods cannot binarize the queries, when only one or part of modalities are provided. In this article, we propose a novel Flexible Multi-modal Hashing (FMH) method to address this problem. FMH learns multiple modality-specific hash codes and multi-modal collaborative hash codes simultaneously within a single model. The hash codes are flexibly generated according to the newly coming queries, which provide any one or combination of modality features. Besides, the hashing learning procedure is efficiently supervised by the pair-wise semantic matrix to enhance the discriminative capability. It could successfully avoid the challenging symmetric semantic matrix factorization and O ( n 2 ) storage cost of semantic matrix. Finally, we design a fast discrete optimization to learn hash codes directly with simple operations. Experiments validate the superiority of the proposed approach.

PrefMap: Visualization of fuzzy pairwise preference structures

Fuzzy pairwise preferences are an important model to specify and process expert opinions. A fuzzy pairwise preference matrix contains degrees of preference of each option over each other option. Such degrees of preference are often numerically specified by domain experts. In decision processes it is highly desirable to be able to analyze such preference structures, in order to answer questions like: Which objects are most or least preferred? Are there clusters of options with similar preference? Are the preferences consistent or partially contradictory? An important approach for such analysis is visualization. The goal is to produce good visualizations of preference matrices in order to better understand the expert opinions, to easily identify favorite or less favorite options, to discuss and address inconsistencies, or to reach consensus in group decision processes. Standard methods for visualization of preferences are matrix visualization and chord diagrams, which are not suitable for larger data sets, and which are not able to visualize clusters or inconsistencies. To overcome this drawback we propose PrefMap, a new method for visualizing preference matrices. Experiments with nine artificial and real–world preference data sets indicate that PrefMap yields good visualizations that allow to easily identify favorite and less favorite options, clusters, and inconsistencies, even for large data sets.

Effect of Financial Leverage on Firm Value: Evidence From Selected Firms Quoted on the Nigerian Stock Exchange

This study examined the effect of financial leverage on firm value with evidence from a sample of selected companies quoted on the Nigerian Stock Exchange. The study adopts a panel data analysis using secondary data obtained from the financial statements of the selected companies over the period 2014-2018. The sample of 18 firms studied was selected through the convenient sampling technique. The level of financial leverage was denominated by long term debt to equity ratio. This work is the first Nigerian study to utilize the Tobin’s q ratio as a proxy of firm value. Other variables proven in literature to be of importance when considering firm value such as Total Asset, Return on Asset and the Number of years for which the firm has been in operation, were utilized as control variables in presenting the Tobin’s Q model of firm valuation. Data obtained were analyzed by E-VIEWS to determine the extent of the causal and correlational relationships between the dependent variable and the regressors. The study determined the degree of causality using the Pooled Ordinary Least Squares (POLS), Random Effect Panel Data Model(REM) and Fixed Effect Panel Model(FEM) estimation techniques. The correlation coefficients were estimated using the pairwise correlation matrix to determine the extent to which financial leverage can predict firm value In line with the findings of Akani & Kenn-Ndubuisi (2017); the regression results showed that financial leverage has a significantly negative effect on firm value while the result of the pairwise correlation showed that there is no significant linear relationship between leverage and firm value. The Management of these companies were advised to take less long term debts and instead such firms should consider issuing more equity to reduce the level of financial leverage to thereby attain the optimal capital structure. Financial leverage has proven to be a weak predictor of firm value; hence the management should not rely on the levels of financial leverage to predict future firm value. Future studies may consider the use of a larger sample and a random sample selection method which will group the firms based on their level of capitalization into mid, low and high-capitalization companies so which will help to ascertain the average optimal capital structure for each of the three classes. Finally, future studies can consider a longer time span. Keywords : Firm value, Tobin’s q, Financial Leverage, REM JEL Classification: G11; G32; M21 DOI : 10.7176/EJBM/12-3-16 Publication date: January 31 st 2020

Implementation of multi-criteria decision method for selection of suitable material for development of horizontal wind turbine blade for sustainable energy generation

The material selection process for producing a horizontal axis wind turbine blade for sustainable energy generation is a vital issue when using Nigeria as a case study. Due to the challenge faced with the low wind speed variations. However, this paper focuses on implementing MCDM for the material selection process for a suitable material for developing a horizontal wind turbine blade. This paper used a quantitative research approach using AHP and TOPSIS multi-criteria decision method. The study put into consideration the environmental conditions for the material selection process when designing the questionnaire. The authors extracted the data used for the selection process from the 130 research questionnaire distributed to materials engineers and renewable energy professionals. This research considered four alternatives that is, aluminum alloy, stainless steel, glass fiber, and mild steel to determine the best material for the wind turbine blade. Also, the model has four criteria and eight sub-criteria used for developing the pair-wise matrix and the performance score used for the ranking process of the alternatives. The result shows that a consistency index of 0.056 and a consistency ratio of 0.062 gotten via the AHP method is workable for material selection practice. 78%, 43%, 67%, and 25% are the performance scores for the four alternatives via the TOPSIS techniques. In conclusion, aluminum alloy is the best material, followed by glass fibre. Therefore, the decision-makers recommended aluminum alloy; hence, manufacturers should apply aluminum alloy to develop the wind turbine blade for sustainable energy generation.

Crop-Industry Relevance Index: Assessment Model for Tanzania

The interdependence between agriculture and industry sectors has increased in developing countries where smallholder farmers dominate agricultural production. However, methodology for assessing the contribution of smallholder farmers to the industrialization is lacking. The current paper presents the developed crop-industry relevance index (CIRI) framework used to analyze crop production and gauge the contribution of smallholder farming in industrial development in Tanzania. The study employed the Analytic Hierarchy Process (AHP) to derive weights for constructing the CIRI. The study defined five criteria that represents characteristics of crop types defining the crop industry relevance. The pairwise matrix representing value judgement on the contribution of different crop types to the industrialization were established. The normalization procedure resulted to derivation of weights. Consistency analysis performed to check the consistency in the value judgement on role of different crop types on industrialization. The results are that, the consistency ratio was 0.0318 implying robust weight values. Finding are that, the contribution of smallholder farmers to the production of industrial relevant crops is estimated to be 20% in year 2014. The estimated industrial value is mainly contributed by maize, paddy, cassava, cotton, sugarcane and sunflower. The implication is that while maize, cassava and paddy are produced primarily for food, there is emerging importance in the industrial development. Effort to enhance crop production focusing these crops beers dual benefits in the country.

Active ranking from pairwise comparisons and when parametric assumptions do not help

We consider sequential or active ranking of a set of $n$ items based on noisy pairwise comparisons. Items are ranked according to the probability that a given item beats a randomly chosen item, and ranking refers to partitioning the items into sets of prespecified sizes according to their scores. This notion of ranking includes as special cases the identification of the top-$k$ items and the total ordering of the items. We first analyze a sequential ranking algorithm that counts the number of comparisons won, and uses these counts to decide whether to stop, or to compare another pair of items, chosen based on confidence intervals specified by the data collected up to that point. We prove that this algorithm succeeds in recovering the ranking using a number of comparisons that is optimal up to logarithmic factors. This guarantee does depend on whether or not the underlying pairwise probability matrix, satisfies a particular structural property, unlike a significant body of past work on pairwise ranking based on parametric models such as the Thurstone or Bradley–Terry–Luce models. It has been a long-standing open question as to whether or not imposing these parametric assumptions allows for improved ranking algorithms. For stochastic comparison models, in which the pairwise probabilities are bounded away from zero, our second contribution is to resolve this issue by proving a lower bound for parametric models. This shows, perhaps surprisingly, that these popular parametric modeling choices offer at most logarithmic gains for stochastic comparisons.

Multi-criteria decision-making for the analysis of flash floods: A case study of Awlad Toq-Sherq, Southeast Sohag, Egypt

The multi-criteria method is a widely used technique to study and analyze the impact and causes of natural hazards. Our study area, that forms a part of the governorate of Sohag, lies in Southeast Sohag and is one of the most flash flood prone regions of Egypt's Eastern Desert. In the last decades, this area of Sohag has suffered from frequent flash floods, with some flood events resulting in human casualties. In our study, we use a multi-criteria process combined with geographical information system (GIS) and remotely sensed data to produce a flash flood susceptibility map. In addition, we discuss the various factors related to flash flooding such as elevation, slope, drainage network, lithology, topographic wetness index, as well as land use, and reclassify these based on their contribution and their effect on flood probability. To calculate the weighted factor for each raster, a pairwise matrix was constructed. Results from our multi-criteria analysis for flash flooding indicate that approximately 5% of the total study area is at a very high risk of flooding, 10% at a high risk, and 25% at a moderate flood risk. Furthermore, our results highlight the areas at risk of flooding and the need for the development of relevant warning systems. Our results also indicate that the southeastern part of the study area is most susceptible to flash floods and we suggest that the necessary focus be given to this region as well as the implementation of a flood warning system. A consistency index was used to determine the accuracy of our model and was calculated to be 0.058, indicating a well-performing model.