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Application of multinomial logistic regression to Model the Impact of Rainfall Genesis on the Performance of Storm Overflows: Case Study

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WATER RESOURCES MANAGEMENT 2022年第10期36卷 3699-3714页

作者： Szelag, Bartosz Suligowski, Roman Majewski, Grzegorz Kowal, Przemyslaw Bralewski, Adrian Bralewska, Karolina Aniol, Ewa Rogula-Kozlowska, Wioletta De Paola, Francesco Kielce Univ Technol 7 Aleja Tysiaclecia Panstwa Polskiego St PL-25314 Kielce Poland Jan Kochanowski Univ Humanities & Sci 7 Uniwersytecka St PL-25406 Kielce Poland Warsaw Univ Life Sci 166 Nowoursynowska St PL-02776 Warsaw Poland Gdansk Univ Technol 11-12 Narutowicza St PL-80233 Gdansk Poland Main Sch Fire Serv 52-54 Slowackiego St PL-01629 Warsaw Poland Univ Naples Federico II Via Claudio 21 I-80125 Naples Italy

In this study, a mathematical model was proposed to analyze the performance of storm overflows. The model included the influence of rainfall genesis on the duration of storm overflow, its volume, and the maximum instantaneous flow. The multinomial logistic regression model, which has not been used so far to model objects located in a stormwater system, was proposed to simulate the duration of storm overflow. The Iman-Conover method, using the theoretical cumulative distributions determined on the basis of 45 - year rainfall sequences, was adopted to simulate the rainfall characteristics describing the overflow performance (total and maximum 30-min rainfall depth and duration). The simulations showed a significant impact of rainfall genesis on the parameters of the storm overflow. The model and the results presented in this study can be used at the stage of dimensioning storm overflows and to create an early warning system against undesirable phenomena in the stormwater system within urban catchments.

关键词： Storm overflow multinomial logistic regression Rainfall genesis Iman-conover method

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Sparse multinomial logistic regression: Fast algorithms and generalization bounds

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2005年第6期27卷 957-968页

作者： Krishnapuram, B Carin, L Figueiredo, MAT Hartemink, AJ Siemens Med Solut USA Inc Comp Aided Diag & Therapy Grp Malvern PA 19355 USA Duke Univ Dept Elect Engn Durham NC 27708 USA Inst Super Tecn Dept Elect & Comp Engn Inst Telecommun P-1049001 Lisbon Portugal Duke Univ Dept Comp Sci Durham NC 27708 USA

Recently developed methods for learning sparse classifiers are among the state-of-the-art in supervised learning. These methods learn classifiers that incorporate weighted sums of basis functions with sparsity-promoting priors encouraging the weight estimates to be either significantly large or exactly zero. From a learning-theoretic perspective, these methods control the capacity of the learned classifier by minimizing the number of basis functions used, resulting in better generalization. This paper presents three contributions related to learning sparse classifiers. First, we introduce a true multiclass formulation based on multinomial logistic regression. Second, by combining a bound optimization approach with a component-wise update procedure, we derive fast exact algorithms for learning sparse multiclass classifiers that scale favorably in both the number of training samples and the feature dimensionality, making them applicable even to large data sets in high-dimensional feature spaces. To the best of our knowledge, these are the first algorithms to perform exact multinomial logistic regression with a sparsity-promoting prior. Third, we show how nontrivial generalization bounds can be derived for our classifier in the binary case. Experimental results on standard benchmark data sets attest to the accuracy, sparsity, and efficiency of the proposed methods.

关键词： supervised learning classification sparsity Bayesian inference multinomial logistic regression bound optimization expectation maximization (EM) learning theory generalization bounds

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Unilateral sensorineural hearing loss identification based on double-density dual-tree complex wavelet transform and multinomial logistic regression

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INTEGRATED COMPUTER-AIDED ENGINEERING 2019年第4期26卷 411-426页

作者： Wang, Shui-Hua Zhang, Yu-Dong Yang, Ming Liu, Bin Ramirez, Javier Manuel Gorriz, Juan Henan Polytech Univ Sch Comp Sci & Technol Jiaozuo 454000 Henan Peoples R China Nanjing Univ Med Sch Affiliated Hosp Dept Rheumatol & ImmunolNanjing Drum Tower Hosp Nanjing 210008 Jiangsu Peoples R China Univ Leicester Dept Informat Leicester Leics England Nanjing Med Univ Childrens Hosp Dept Radiol Nanjing 210008 Jiangsu Peoples R China Southeast Univ Zhong Da Hosp Dept Radiol Nanjing 210009 Jiangsu Peoples R China Univ Granada Dept Signal Theory Networking & Commun Granada Spain Univ Cambridge Dept Psychiat Robinson Way Cambridge England Univ Leicester Dept Math Leicester Leics England

AIM: Unilateral sensorineural hearing loss is a brain disease, which causes slight morphology changes within brain structure. Traditional manual method may ignore this change. METHOD: In this work, we developed a novel method, based on the double-density dual-tree complex (DDDTCWT), and radial basis function kernel principal component analysis (RKPCA) and multinomial logistic regression (MLR) for the magnetic resonance imaging scanning. We first used DDDTCWT to extract features. Afterwards, we used RKPCA to reduce feature dimensionalities. Finally, MLR was employed to be the classifier. RESULT: The 10 times of 10-fold stratified cross validation showed our method achieved an overall accuracy of 96.44 +/- 0.88%. The sensitivities of detecting left-sided sensorineural hearing loss, right-sided sensorineural hearing loss, and healthy controls were 96.67 +/- 2.72%, 96.67 +/- 3.51%, and 96.00 +/- 4.10%, respectively. CONCLUSION: Our method performed better than both raw and improved AlexNet, and eight state-of-the-art methods via a stringent statistical 10 x 10-fold stratified cross validation. The MLR gives better classification performance than decision tree, support vector machine, and back-propagation neural network.

关键词： Unilateral sensorineural hearing loss dual-tree complex wavelet transform kernel principal component analysis multinomial logistic regression double-density dual-tree complex wavelet transform magnetic resonance imaging alexNet

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Rank-k 2-D multinomial logistic regression for Matrix Data Classification

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018年第8期29卷 3524-3537页

作者： Song, Kun Nie, Feiping Han, Junwei Li, Xuelong Northwestern Polytech Univ Sch Automat Xian 710072 Shaanxi Peoples R China Northwestern Polytech Univ Sch Comp Sci Ctr Opt Imagery Anal & Learning Xian 710072 Shaanxi Peoples R China Chinese Acad Sci Inst Opt & Precis Mech Xian 710119 Shaanxi Peoples R China

The amount of matrix data has increased rapidly nowadays. How to classify matrix data efficiently is an important issue. In this paper, by discovering the shortages of 2-D linear discriminant analysis and 2-D logistic regression, a novel 2-D framework named rank-k 2-D multinomial logistic regression (2DMLR-RK) is proposed. The 2DMLR-RK is designed for a multiclass matrix classification problem. In the proposed framework, each category is modeled by a left projection matrix and a right projection matrix with rank k. The left projection matrices capture the row information of matrix data, and the right projection matrices acquire the column information. We identify the parameter k plays the role of balancing the capacity of learning and generalization of the 2DMLR-RK. In addition, we develop an effective framework for solving the proposed non-convex optimization problem. The convergence, initialization, and computational complexity are discussed. Extensive experiments on various types of data sets are conducted. Comparing with 1-D methods, 2DMLR-RK not only achieves a better classification accuracy, but also costs less computation time. Comparing with other state-of-the-art 2-D methods, the 2DMLR-RK achieves a better performance for matrix data classification.

关键词： 2-D logistic regression (2DLR) matrix analysis matrix data classification multinomial logistic regression

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Evaluating risk factors for endemic human Salmonella Enteritidis infections with different phage types in Ontario, Canada using multinomial logistic regression and a case-case study approach

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BMC PUBLIC HEALTH 2012年第1期12卷 1-10页

作者： Varga, Csaba Middleton, Dean Walton, Ryan Savage, Rachel Tighe, Mary-Kathryn Allen, Vanessa Ahmed, Rafiq Rosella, Laura Univ Guelph Dept Populat Med Guelph ON N1G 2W1 Canada Ontario Minist Agr Food & Rural Affairs Guelph ON N1G 4Y2 Canada Publ Hlth Ontario Toronto ON M5G 1V2 Canada Univ Toronto Dalla Lana Sch Publ Hlth Toronto ON M5T 3M7 Canada Publ Hlth Agcy Canada Natl Microbiol Lab Winnipeg MB Canada

Background: Identifying risk factors for Salmonella Enteritidis (SE) infections in Ontario will assist public health authorities to design effective control and prevention programs to reduce the burden of SE infections. Our research objective was to identify risk factors for acquiring SE infections with various phage types (PT) in Ontario, Canada. We hypothesized that certain PTs (e. g., PT8 and PT13a) have specific risk factors for infection. Methods: Our study included endemic SE cases with various PTs whose isolates were submitted to the Public Health Laboratory-Toronto from January 20th to August 12th, 2011. Cases were interviewed using a standardized questionnaire that included questions pertaining to demographics, travel history, clinical symptoms, contact with animals, and food exposures. A multinomial logistic regression method using the Generalized Linear Latent and Mixed Model procedure and a case-case study design were used to identify risk factors for acquiring SE infections with various PTs in Ontario, Canada. In the multinomial logistic regression model, the outcome variable had three categories representing human infections caused by SE PT8, PT13a, and all other SE PTs (i.e., non-PT8/non-PT13a) as a referent category to which the other two categories were compared. Results: In the multivariable model, SE PT8 was positively associated with contact with dogs (OR=2.17, 95% CI 1.01-4.68) and negatively associated with pepper consumption (OR=0.35, 95% CI 0.13-0.94), after adjusting for age categories and gender, and using exposure periods and health regions as random effects to account for clustering. Conclusions: Our study findings offer interesting hypotheses about the role of phage type-specific risk factors. multinomial logistic regression analysis and the case-case study approach are novel methodologies to evaluate associations among SE infections with different PTs and various risk factors.

关键词： Health Region multinomial logistic regression Phage Type Animal Contact Public Health Unit

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Widen NomoGram for multinomial logistic regression: an application to staging liver fibrosis in chronic hepatitis C patients

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STATISTICAL METHODS IN MEDICAL RESEARCH 2017年第2期26卷 823-838页

作者： Ardoino, Ilaria Lanzoni, Monica Marano, Giuseppe Boracchi, Patrizia Sagrini, Elisabetta Gianstefani, Alice Piscaglia, Fabio Biganzoli, Elia M. Univ Milan Dept Clin Sci & Community Hlth Milan Italy Osped Maggiore Policlin Fdn IRCCS CaGranda Milan Italy Fdn IRCCS Ist Nazl Tumori Milan Italy Univ & Gen Hosp Dept Clin Med Bologna Italy

The interpretation of regression models results can often benefit from the generation of nomograms, user friendly' graphical devices especially useful for assisting the decision-making processes. However, in the case of multinomial regression models, whenever categorical responses with more than two classes are involved, nomograms cannot be drawn in the conventional way. Such a difficulty in managing and interpreting the outcome could often result in a limitation of the use of multinomial regression in decision-making support. In the present paper, we illustrate the derivation of a non-conventional nomogram for multinomial regression models, intended to overcome this issue. Although it may appear less straightforward at first sight, the proposed methodology allows an easy interpretation of the results of multinomial regression models and makes them more accessible for clinicians and general practitioners too. Development of prediction model based on multinomial logistic regression and of the pertinent graphical tool is illustrated by means of an example involving the prediction of the extent of liver fibrosis in hepatitis C patients by routinely available markers.

关键词： Categorical outcome multinomial logistic regression prediction nomogram

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Modelling built-up expansion and densification with multinomial logistic regression, cellular automata and genetic algorithm

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COMPUTERS ENVIRONMENT AND URBAN SYSTEMS 2018年 67卷 147-156页

作者： Mustafa, Ahmed Heppenstall, Alison Omrani, Hichem Saadi, Ismail Cools, Mario Teller, Jacques Univ Liege Urban & Environm Engn Dept LEMA Liege Belgium Purdue Univ Dept Comp Sci 305 N Univ St W Lafayette IN 47907 USA Univ Leeds Sch Geog Leeds W Yorkshire England LISER Urban Dev & Mobil Dept Luxembourg Luxembourg Univ Liege Allee Decouverte 9Quartier Polytech 1 B-4000 Liege Belgium

This paper presents a model to simulate built-up expansion and densification based on a combination of a non ordered multinomial logistic regression (MLR) and cellular automata (CA). 'The probability for built-up development is assessed based on (i) a set of built-up development causative factors and (ii) the land-use of neighboring cells. The model considers four built-up classes: non built-up, low-density, medium-density and high density built-up. Unlike the most commonly used built-up/urban models which simulate built-up expansion, our approach considers expansion and the potential for densification within already built-up areas when their present density allows it. The model is built, calibrated, and validated for Wallonia region (Belgium) using cadastral data. Three 100 x 100 m raster-based built-up maps for 1990, 2000, and 2010 are developed to define one calibration interval (1990-2000) and one validation interval (2000 2010). The causative factors are calibrated using MLR whereas the CA neighboring effects are calibrated based on a multi-objective genetic algoritlun. The calibrated model is applied to simulate the built-up pattern in 2010. The simulated map in 2010 is used to evaluate the model's performance against the actual 2010 map by means of fuzzy set theory. According to the findings, land-use policy, slope, and distance to roads are the most important determinants of the expansion process. The densification process is mainly driven by zoning, slope, distance to different roads and richness index. The results also show that the densification generally occurs where there are dense neighbors whereas areas with lower densities retain their densities over time.

关键词： Built-up density Cellular automata multinomial logistic regression Multi-objective genetic algorithm

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multinomial logistic regression for prediction of vulnerable road users risk injuries based on spatial and temporal assessment

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International Journal for Consumer and Product Safety 2019年第4期26卷 379-390页

Urban area’s rapid growth often leads to adverse effects such as traffic congestion and increasing accident risks due to the expansion in transportation systems. In the frame of smart cities, active modes are expected to be promoted to improve living conditions. To achieve this goal, it is necessary to reduce the number of vulnerable road users (VRUs) injuries. Considering injury severity levels from crashes involving VRUs, this article seeks spatial and temporal patterns between cities and presents a model to predict the likelihood of VRUs to be involved in a crash. Kernel Density Estimation was applied to identify blackspots based on injury severity levels. A multinomial logistic regression model was developed to identify statistically significant variables to predict the occurrence of these crashes. Results show that target spatial and temporal variables influence the number and severity of crashes involving VRUs. This approach can help to enhance road safety policies.

关键词： Road crashes injury severity kernel density estimation multinomial logistic regression vulnerable road users

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Fault diagnosis of rolling element bearing by using multinomial logistic regression and wavelet packet transform

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SOFT COMPUTING 2014年第2期18卷 255-266页

作者： Pandya, D. H. Upadhyay, S. H. Harsha, S. P. Indian Inst Technol Roorkee Dept Mech & Ind Engn Vibrat & Noise Control Lab Roorkee 247667 Uttar Pradesh India

This paper is focused on comparison of effectiveness of artificial intelligence (AI) techniques in fault diagnosis of rolling element bearings. The features for classification are extracted through wavelet packet decomposition using RBIO 5.5 wavelet. The whole classification is done using two features: energy and Kurtosis. The data samples for classification are taken with reference to a healthy bearing, thus, minimizing the errors from the experimental set-up. Four bearing conditions such as bearing with outer race defect, inner race defect, ball defect and combined defect on outer race, inner race and ball have been used in this paper. Localized defects of micron level are induced through laser machining. The effectiveness of three AI techniques viz. ANN, SVM and multinomial logistic regression are compared. The results show that the logistic regression technique is the more effective than other two techniques as ANN and SVM.

关键词： Energy Kurtosis Wavelet packet decomposition ANN SVM multinomial logistic regression

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Categorical missing data imputation for software cost estimation by multinomial logistic regression

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JOURNAL OF SYSTEMS AND SOFTWARE 2006年第3期79卷 404-414页

作者： Sentas, P Angelis, L Aristotle Univ Thessaloniki Dept Informat Thessaloniki 54124 Greece

A common problem in software cost estimation is the manipulation of incomplete or missing data in databases used for the development of prediction models. In such cases, the most popular and simple method of handling missing data is to ignore either the projects or the attributes with missing observations. This technique causes the loss of valuable information and therefore may lead to inaccurate cost estimation models. On the other hand, there are various imputation methods used to estimate the missing values in a data set. These methods are applied mainly on numerical data and produce continuous estimates. However, it is well known that the majority of the cost data sets contain software projects with mostly categorical attributes with many missing values. It is therefore reasonable to use some estimating method producing categorical rather than continuous values. The purpose of this paper is to investigate the possibility of using such a method for estimating categorical missing values in software cost databases. Specifically, the method known as multinomial logistic regression (MLR) is suggested for imputation and is applied on projects of the ISBSG multi-organizational software database. Comparisons of NILR with other techniques for handling missing data, such as listwise deletion (LD), mean imputation (MI), expectation maximization (EM) and regression imputation (RI) under different patterns and percentages of missing data, show the high efficiency of the proposed method. (C) 2005 Elsevier Inc. All rights reserved.

关键词： software effort prediction cost estimation missing data imputation multinomial logistic regression

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