Parkinson's disease(PD)is a neurodegenerative disorder characterized by motor and non-motor symptoms that significantly impact an individual's quality of life.Voice changes have shown promise as early indicato...Parkinson's disease(PD)is a neurodegenerative disorder characterized by motor and non-motor symptoms that significantly impact an individual's quality of life.Voice changes have shown promise as early indicators of PD,making voice analysis a valuable tool for early detection and intervention.This study aims to assess and detect the severity of PD through voice analysis using the mobile device voice recordings dataset.The dataset consisted of recordings from PD patients at different stages of the disease and healthy control subjects.A novel approach was employed,incorporating a voice activity detection algorithm for speech segmentation and the wavelet scattering transform for feature extraction.A Bayesian optimization technique is used to fine-tune the hyperparameters of seven commonly used classifiers and optimize the performance of machine learning classifiers for PD severity detection.AdaBoost and K-nearest neighbor consistently demonstrated superior performance across various evaluation metrics among the classifiers.Furthermore,a weighted majority voting(WMV)technique is implemented,leveraging the predictions of multiple models to achieve a near-perfect accuracy of 98.62%,improving classification accuracy.The results highlight the promising potential of voice analysis in PD diagnosis and monitoring.Integrating advanced signal processing techniques and machine learning models provides reliable and accessible tools for PD assessment,facilitating early intervention and improving patient outcomes.This study contributes to the field by demonstrating the effectiveness of the proposed methodology and the significant role of WMV in enhancing classification accuracy for PD severity detection.展开更多
Extreme learning machine(ELM)has been proved to be an effective pattern classification and regression learning mechanism by researchers.However,its good performance is based on a large number of hidden layer nodes.Wit...Extreme learning machine(ELM)has been proved to be an effective pattern classification and regression learning mechanism by researchers.However,its good performance is based on a large number of hidden layer nodes.With the increase of the nodes in the hidden layers,the computation cost is greatly increased.In this paper,we propose a novel algorithm,named constrained voting extreme learning machine(CV-ELM).Compared with the traditional ELM,the CV-ELM determines the input weight and bias based on the differences of between-class samples.At the same time,to improve the accuracy of the proposed method,the voting selection is introduced.The proposed method is evaluated on public benchmark datasets.The experimental results show that the proposed algorithm is superior to the original ELM algorithm.Further,we apply the CV-ELM to the classification of superheat degree(SD)state in the aluminum electrolysis industry,and the recognition accuracy rate reaches87.4%,and the experimental results demonstrate that the proposed method is more robust than the existing state-of-the-art identification methods.展开更多
After the celebrations marking the birth of Africa’s newest nation,much work lies ahead for South Sudan by Alphonce Shiundu IN Nairobi,shirtless men,with white body powder sprinkled on their black chests and shoulder...After the celebrations marking the birth of Africa’s newest nation,much work lies ahead for South Sudan by Alphonce Shiundu IN Nairobi,shirtless men,with white body powder sprinkled on their black chests and shoulders,jumped up and down singing and shouting.Not to be left behind,tall dark women in extravagant bright-colored clothes also ululated as they vigorously shook their shoulders in a beautiful,rhythmical dance.展开更多
This paper focuses on improving decision tree induction algorithms when a kind of tie appears during the rule generation procedure for specific training datasets. The tie occurs when there are equal proportions of the...This paper focuses on improving decision tree induction algorithms when a kind of tie appears during the rule generation procedure for specific training datasets. The tie occurs when there are equal proportions of the target class outcome in the leaf node's records that leads to a situation where majority voting cannot be applied. To solve the above mentioned exception, we propose to base the prediction of the result on the naive Bayes (NB) estimate, k-nearest neighbour (k-NN) and association rule mining (ARM). The other features used for splitting the parent nodes are also taken into consideration.展开更多
The Hand Gestures Recognition(HGR)System can be employed to facilitate communication between humans and computers instead of using special input and output devices.These devices may complicate communication with compu...The Hand Gestures Recognition(HGR)System can be employed to facilitate communication between humans and computers instead of using special input and output devices.These devices may complicate communication with computers especially for people with disabilities.Hand gestures can be defined as a natural human-to-human communication method,which also can be used in human-computer interaction.Many researchers developed various techniques and methods that aimed to understand and recognize specific hand gestures by employing one or two machine learning algorithms with a reasonable accuracy.Thiswork aims to develop a powerful hand gesture recognition model with a 100%recognition rate.We proposed an ensemble classification model that combines the most powerful machine learning classifiers to obtain diversity and improve accuracy.The majority voting method was used to aggregate accuracies produced by each classifier and get the final classification result.Our model was trained using a self-constructed dataset containing 1600 images of ten different hand gestures.The employing of canny’s edge detector and histogram of oriented gradient method was a great combination with the ensemble classifier and the recognition rate.The experimental results had shown the robustness of our proposed model.Logistic Regression and Support Vector Machine have achieved 100%accuracy.The developed model was validated using two public datasets,and the findings have proved that our model outperformed other compared studies.展开更多
In order to effectively solve the problem of copyright protection of materials genome engineering data,this paper proposes a method for copyright protection of materials genome engineering data based on zero-watermark...In order to effectively solve the problem of copyright protection of materials genome engineering data,this paper proposes a method for copyright protection of materials genome engineering data based on zero-watermarking technology.First,the important attribute values are selected from the materials genome engineering database;then,use the method of remainder to group the selected attribute values and extract eigenvalues;then,the eigenvalues sequence is obtained by the majority election method;finally,XOR the sequence with the actual copyright information to obtain the watermarking information and store it in the third-party authentication center.When a copyright dispute requires copyright authentication for the database to be detected.First,the zero-watermarking construction algorithm is used to obtain an eigenvalues sequence;then,this sequence is XORed with the watermarking information stored in the third-party authentication center to obtain copyright information to-be-detected.Finally,the ownership is determined by calculating the similarity between copyright information to-be-detected and copyright information that has practical significance.The experimental result shows that the zero-watermarking method proposed in this paper can effectively resist various common attacks,and can well achieve the copyright protection of material genome engineering database.展开更多
Pulmonary diseases are common throughout the world,especially in developing countries.These diseases include chronic obstructive pulmonary diseases,pneumonia,asthma,tuberculosis,fibrosis,and recently COVID-19.In gener...Pulmonary diseases are common throughout the world,especially in developing countries.These diseases include chronic obstructive pulmonary diseases,pneumonia,asthma,tuberculosis,fibrosis,and recently COVID-19.In general,pulmonary diseases have a similar footprint on chest radiographs which makes them difficult to discriminate even for expert radiologists.In recent years,many image processing techniques and artificial intelligence models have been developed to quickly and accurately diagnose lung diseases.In this paper,the performance of four popular pretrained models(namely VGG16,DenseNet201,DarkNet19,and XceptionNet)in distinguishing between different pulmonary diseases was analyzed.To the best of our knowledge,this is the first published study to ever attempt to distinguish all four cases normal,pneumonia,COVID-19 and lung opacity from ChestX-Ray(CXR)images.All models were trained using Chest-X-Ray(CXR)images,and statistically tested using 5-fold cross validation.Using individual models,XceptionNet outperformed all other models with a 94.775%accuracy and Area Under the Curve(AUC)of Receiver Operating Characteristic(ROC)of 99.84%.On the other hand,DarkNet19 represents a good compromise between accuracy,fast convergence,resource utilization,and near real time detection(0.33 s).Using a collection of models,the 97.79%accuracy achieved by Ensemble Features was the highest among all surveyed methods,but it takes the longest time to predict an image(5.68 s).An efficient effective decision support system can be developed using one of those approaches to assist radiologists in the field make the right assessment in terms of accuracy and prediction time,such a dependable system can be used in rural areas and various healthcare sectors.展开更多
This study proposes a convolutional neural network(CNN)-based identity recognition scheme using electrocardiogram(ECG)at different water temperatures(WTs)during bathing,aiming to explore the impact of ECG length on th...This study proposes a convolutional neural network(CNN)-based identity recognition scheme using electrocardiogram(ECG)at different water temperatures(WTs)during bathing,aiming to explore the impact of ECG length on the recognition rate.ECG data was collected using non-contact electrodes at five different WTs during bathing.Ten young student subjects(seven men and three women)participated in data collection.Three ECG recordings were collected at each preset bathtub WT for each subject.Each recording is 18 min long,with a sampling rate of 200 Hz.In total,150 ECG recordings and 150 WT recordings were collected.The R peaks were detected based on the processed ECG(baseline wandering eliminated,50-Hz hum removed,ECG smoothing and ECG normalization)and the QRS complex waves were segmented.These segmented waves were then transformed into binary images,which served as the datasets.For each subject,the training,validation,and test data were taken from the first,second,and third ECG recordings,respectively.The number of training and validation images was 84297 and 83734,respectively.In the test stage,the preliminary classification results were obtained using the trained CNN model,and the finer classification results were determined using the majority vote method based on the preliminary results.The validation rate was 98.71%.The recognition rates were 95.00%and 98.00%when the number of test heartbeats was 7 and 17,respectively,for each subject.展开更多
Results of the 2005 PRPA Survey indicated that the majority of PR professional respondents are interested in going through an accreditation process for better public recognition.
There have been many skewed cancer gene expression datasets in the post-genomic era. Extraction of differential expression genes or construction of decision rules using these skewed datasets by traditional algorithms ...There have been many skewed cancer gene expression datasets in the post-genomic era. Extraction of differential expression genes or construction of decision rules using these skewed datasets by traditional algorithms will seriously underestimate the performance of the minority class, leading to inaccurate diagnosis in clinical trails. This paper presents a skewed gene selection algorithm that introduces a weighted metric into the gene selection procedure. The extracted genes are paired as decision rules to distinguish both classes, with these decision rules then integrated into an ensemble learning framework by majority voting to recognize test examples; thus avoiding tedious data normalization and classifier construction. The mining and integrating of a few reliable decision rules gave higher or at least comparable classification performance than many traditional class imbalance learning algorithms on four benchmark imbalanced cancer gene expression datasets.展开更多
This paper studies the traveling location prediction problem for detecting whether mobile users will leave their living area and where they will go.We investigate the hidden connections between users’behaviors in dif...This paper studies the traveling location prediction problem for detecting whether mobile users will leave their living area and where they will go.We investigate the hidden connections between users’behaviors in different locations and online social interactions.We combine dynamic Bayesian networks with a majority voting model which is based on social interaction information to estimate the users’behaviors and predict the locations.By analyzing Instagram media records,spanning a period of 3 months,we explore rarely visited locations,which are often ignored as noise in previous research.In comparison,our model,using Instagram data with two existing location prediction models,shows that(1)our location prediction is more accurate and robust in both the general location and the location outside the living area;(2)social relations are instrumental in the location prediction as social interaction information can increase the accuracy of the prediction.展开更多
Recent developments of 30 m global land characterization datasets (e.g., land cover, vegetation continues field) represent the finest spatial resolution inputs for global scale studies. Here, we present results from...Recent developments of 30 m global land characterization datasets (e.g., land cover, vegetation continues field) represent the finest spatial resolution inputs for global scale studies. Here, we present results from further improvement to land cover map- ping and impact analysis of spatial resolution on area estimation for different land cover types. We proposed a set of methods to aggregate two existing 30 m resolution circa 2010 global land cover maps, namely FROM-GLC (Finer Resolution Observa- tion and Monitoring-Global Land Cover) and FROM-GLC-seg (Segmentation), with two coarser resolution global maps on development, i.e., Nighttime Light Impervious Surface Area (NL-ISA) and MODIS urban extent (MODIS-urban), to produce an improved 30 m global land cover map-FROM-GLC-agg (Aggregation). It was pos-processed using additional coarse res- olution datasets (i.e., MCD12Q1, GlobCover2009, MOD44W etc.) to reduce land cover type confusion. Around 98.9% pixels remain 30 m resolution after some post-processing to this dataset. Based on this map, majority aggregation and proportion ag- gregation approaches were employed to create a multi-resolution hierarchy (i.e., 250 m, 500 m, 1 km, 5 km, 10 km, 25 km, 50 km, 100 km) of land cover maps to meet requirements for different resolutions from different applications. Through accuracy assessment, we found that the best overall accuracies for the post-processed base map (at 30 m) and the three maps subse- quently aggregated at 250 m, 500 m, 1 km resolutions are 69.50%, 76.65%, 74.65%, and 73.47%, respectively. Our analysis of area-estimation biases for different land cover types at different resolutions suggests that maps at coarser than 5 km resolution contain at least 5% area estimation error for most land cover types. Proportion layers, which contain precise information on land cover percentage, are suggested for use when coarser resolution land cover data are required.展开更多
In this paper, we study, mathematically speaking, the problem-the number of admissible preference orderings for the transitivity of simple majority vote(SMV) derived from Arrow’s Impossibility Theorem. In our researc...In this paper, we study, mathematically speaking, the problem-the number of admissible preference orderings for the transitivity of simple majority vote(SMV) derived from Arrow’s Impossibility Theorem. In our research, we find, by computer enumerating, that some results given by Craven are not correct. By defining a set of constraints, we give the recurrence formula of the local maximal number of admissible preference orderings and some other useful results.展开更多
文摘Parkinson's disease(PD)is a neurodegenerative disorder characterized by motor and non-motor symptoms that significantly impact an individual's quality of life.Voice changes have shown promise as early indicators of PD,making voice analysis a valuable tool for early detection and intervention.This study aims to assess and detect the severity of PD through voice analysis using the mobile device voice recordings dataset.The dataset consisted of recordings from PD patients at different stages of the disease and healthy control subjects.A novel approach was employed,incorporating a voice activity detection algorithm for speech segmentation and the wavelet scattering transform for feature extraction.A Bayesian optimization technique is used to fine-tune the hyperparameters of seven commonly used classifiers and optimize the performance of machine learning classifiers for PD severity detection.AdaBoost and K-nearest neighbor consistently demonstrated superior performance across various evaluation metrics among the classifiers.Furthermore,a weighted majority voting(WMV)technique is implemented,leveraging the predictions of multiple models to achieve a near-perfect accuracy of 98.62%,improving classification accuracy.The results highlight the promising potential of voice analysis in PD diagnosis and monitoring.Integrating advanced signal processing techniques and machine learning models provides reliable and accessible tools for PD assessment,facilitating early intervention and improving patient outcomes.This study contributes to the field by demonstrating the effectiveness of the proposed methodology and the significant role of WMV in enhancing classification accuracy for PD severity detection.
基金supported by the National Natural Science Foundation of China(6177340561751312)the Major Scientific and Technological Innovation Projects of Shandong Province(2019JZZY020123)。
文摘Extreme learning machine(ELM)has been proved to be an effective pattern classification and regression learning mechanism by researchers.However,its good performance is based on a large number of hidden layer nodes.With the increase of the nodes in the hidden layers,the computation cost is greatly increased.In this paper,we propose a novel algorithm,named constrained voting extreme learning machine(CV-ELM).Compared with the traditional ELM,the CV-ELM determines the input weight and bias based on the differences of between-class samples.At the same time,to improve the accuracy of the proposed method,the voting selection is introduced.The proposed method is evaluated on public benchmark datasets.The experimental results show that the proposed algorithm is superior to the original ELM algorithm.Further,we apply the CV-ELM to the classification of superheat degree(SD)state in the aluminum electrolysis industry,and the recognition accuracy rate reaches87.4%,and the experimental results demonstrate that the proposed method is more robust than the existing state-of-the-art identification methods.
文摘After the celebrations marking the birth of Africa’s newest nation,much work lies ahead for South Sudan by Alphonce Shiundu IN Nairobi,shirtless men,with white body powder sprinkled on their black chests and shoulders,jumped up and down singing and shouting.Not to be left behind,tall dark women in extravagant bright-colored clothes also ululated as they vigorously shook their shoulders in a beautiful,rhythmical dance.
文摘This paper focuses on improving decision tree induction algorithms when a kind of tie appears during the rule generation procedure for specific training datasets. The tie occurs when there are equal proportions of the target class outcome in the leaf node's records that leads to a situation where majority voting cannot be applied. To solve the above mentioned exception, we propose to base the prediction of the result on the naive Bayes (NB) estimate, k-nearest neighbour (k-NN) and association rule mining (ARM). The other features used for splitting the parent nodes are also taken into consideration.
文摘The Hand Gestures Recognition(HGR)System can be employed to facilitate communication between humans and computers instead of using special input and output devices.These devices may complicate communication with computers especially for people with disabilities.Hand gestures can be defined as a natural human-to-human communication method,which also can be used in human-computer interaction.Many researchers developed various techniques and methods that aimed to understand and recognize specific hand gestures by employing one or two machine learning algorithms with a reasonable accuracy.Thiswork aims to develop a powerful hand gesture recognition model with a 100%recognition rate.We proposed an ensemble classification model that combines the most powerful machine learning classifiers to obtain diversity and improve accuracy.The majority voting method was used to aggregate accuracies produced by each classifier and get the final classification result.Our model was trained using a self-constructed dataset containing 1600 images of ten different hand gestures.The employing of canny’s edge detector and histogram of oriented gradient method was a great combination with the ensemble classifier and the recognition rate.The experimental results had shown the robustness of our proposed model.Logistic Regression and Support Vector Machine have achieved 100%accuracy.The developed model was validated using two public datasets,and the findings have proved that our model outperformed other compared studies.
基金This work is supported by Foundation of Beijing Key Laboratory of Internet Culture and Digital Dissemination Research No.ICDDXN004Foundation of Beijing Advanced Innovation Center for Materials Genome Engineering.
文摘In order to effectively solve the problem of copyright protection of materials genome engineering data,this paper proposes a method for copyright protection of materials genome engineering data based on zero-watermarking technology.First,the important attribute values are selected from the materials genome engineering database;then,use the method of remainder to group the selected attribute values and extract eigenvalues;then,the eigenvalues sequence is obtained by the majority election method;finally,XOR the sequence with the actual copyright information to obtain the watermarking information and store it in the third-party authentication center.When a copyright dispute requires copyright authentication for the database to be detected.First,the zero-watermarking construction algorithm is used to obtain an eigenvalues sequence;then,this sequence is XORed with the watermarking information stored in the third-party authentication center to obtain copyright information to-be-detected.Finally,the ownership is determined by calculating the similarity between copyright information to-be-detected and copyright information that has practical significance.The experimental result shows that the zero-watermarking method proposed in this paper can effectively resist various common attacks,and can well achieve the copyright protection of material genome engineering database.
文摘Pulmonary diseases are common throughout the world,especially in developing countries.These diseases include chronic obstructive pulmonary diseases,pneumonia,asthma,tuberculosis,fibrosis,and recently COVID-19.In general,pulmonary diseases have a similar footprint on chest radiographs which makes them difficult to discriminate even for expert radiologists.In recent years,many image processing techniques and artificial intelligence models have been developed to quickly and accurately diagnose lung diseases.In this paper,the performance of four popular pretrained models(namely VGG16,DenseNet201,DarkNet19,and XceptionNet)in distinguishing between different pulmonary diseases was analyzed.To the best of our knowledge,this is the first published study to ever attempt to distinguish all four cases normal,pneumonia,COVID-19 and lung opacity from ChestX-Ray(CXR)images.All models were trained using Chest-X-Ray(CXR)images,and statistically tested using 5-fold cross validation.Using individual models,XceptionNet outperformed all other models with a 94.775%accuracy and Area Under the Curve(AUC)of Receiver Operating Characteristic(ROC)of 99.84%.On the other hand,DarkNet19 represents a good compromise between accuracy,fast convergence,resource utilization,and near real time detection(0.33 s).Using a collection of models,the 97.79%accuracy achieved by Ensemble Features was the highest among all surveyed methods,but it takes the longest time to predict an image(5.68 s).An efficient effective decision support system can be developed using one of those approaches to assist radiologists in the field make the right assessment in terms of accuracy and prediction time,such a dependable system can be used in rural areas and various healthcare sectors.
基金This study is supported in part by the University of Aizu’s Competitive Research Fund(2020-P-24)。
文摘This study proposes a convolutional neural network(CNN)-based identity recognition scheme using electrocardiogram(ECG)at different water temperatures(WTs)during bathing,aiming to explore the impact of ECG length on the recognition rate.ECG data was collected using non-contact electrodes at five different WTs during bathing.Ten young student subjects(seven men and three women)participated in data collection.Three ECG recordings were collected at each preset bathtub WT for each subject.Each recording is 18 min long,with a sampling rate of 200 Hz.In total,150 ECG recordings and 150 WT recordings were collected.The R peaks were detected based on the processed ECG(baseline wandering eliminated,50-Hz hum removed,ECG smoothing and ECG normalization)and the QRS complex waves were segmented.These segmented waves were then transformed into binary images,which served as the datasets.For each subject,the training,validation,and test data were taken from the first,second,and third ECG recordings,respectively.The number of training and validation images was 84297 and 83734,respectively.In the test stage,the preliminary classification results were obtained using the trained CNN model,and the finer classification results were determined using the majority vote method based on the preliminary results.The validation rate was 98.71%.The recognition rates were 95.00%and 98.00%when the number of test heartbeats was 7 and 17,respectively,for each subject.
文摘Results of the 2005 PRPA Survey indicated that the majority of PR professional respondents are interested in going through an accreditation process for better public recognition.
基金Supported by the National Natural Science Foundation of China (No.61105057)the Ph.D Foundation of Jiangsu University of Science and Technology (Nos.35301002 and 35211104)
文摘There have been many skewed cancer gene expression datasets in the post-genomic era. Extraction of differential expression genes or construction of decision rules using these skewed datasets by traditional algorithms will seriously underestimate the performance of the minority class, leading to inaccurate diagnosis in clinical trails. This paper presents a skewed gene selection algorithm that introduces a weighted metric into the gene selection procedure. The extracted genes are paired as decision rules to distinguish both classes, with these decision rules then integrated into an ensemble learning framework by majority voting to recognize test examples; thus avoiding tedious data normalization and classifier construction. The mining and integrating of a few reliable decision rules gave higher or at least comparable classification performance than many traditional class imbalance learning algorithms on four benchmark imbalanced cancer gene expression datasets.
基金The project is supported by the National Natural Science Foundation of China[grant number 71572109].
文摘This paper studies the traveling location prediction problem for detecting whether mobile users will leave their living area and where they will go.We investigate the hidden connections between users’behaviors in different locations and online social interactions.We combine dynamic Bayesian networks with a majority voting model which is based on social interaction information to estimate the users’behaviors and predict the locations.By analyzing Instagram media records,spanning a period of 3 months,we explore rarely visited locations,which are often ignored as noise in previous research.In comparison,our model,using Instagram data with two existing location prediction models,shows that(1)our location prediction is more accurate and robust in both the general location and the location outside the living area;(2)social relations are instrumental in the location prediction as social interaction information can increase the accuracy of the prediction.
基金supported by the National High-tech R&D Program of China(Grant No.2009AA12200101)the National Natural Science Foundation of China(Grant No.41301445)+1 种基金an Open Fund from the State Key Laboratory of Remote Sensing Science(Grant No.OFSLRSS201202)a research grant from Tsinghua University(Grant No.2012Z02287)
文摘Recent developments of 30 m global land characterization datasets (e.g., land cover, vegetation continues field) represent the finest spatial resolution inputs for global scale studies. Here, we present results from further improvement to land cover map- ping and impact analysis of spatial resolution on area estimation for different land cover types. We proposed a set of methods to aggregate two existing 30 m resolution circa 2010 global land cover maps, namely FROM-GLC (Finer Resolution Observa- tion and Monitoring-Global Land Cover) and FROM-GLC-seg (Segmentation), with two coarser resolution global maps on development, i.e., Nighttime Light Impervious Surface Area (NL-ISA) and MODIS urban extent (MODIS-urban), to produce an improved 30 m global land cover map-FROM-GLC-agg (Aggregation). It was pos-processed using additional coarse res- olution datasets (i.e., MCD12Q1, GlobCover2009, MOD44W etc.) to reduce land cover type confusion. Around 98.9% pixels remain 30 m resolution after some post-processing to this dataset. Based on this map, majority aggregation and proportion ag- gregation approaches were employed to create a multi-resolution hierarchy (i.e., 250 m, 500 m, 1 km, 5 km, 10 km, 25 km, 50 km, 100 km) of land cover maps to meet requirements for different resolutions from different applications. Through accuracy assessment, we found that the best overall accuracies for the post-processed base map (at 30 m) and the three maps subse- quently aggregated at 250 m, 500 m, 1 km resolutions are 69.50%, 76.65%, 74.65%, and 73.47%, respectively. Our analysis of area-estimation biases for different land cover types at different resolutions suggests that maps at coarser than 5 km resolution contain at least 5% area estimation error for most land cover types. Proportion layers, which contain precise information on land cover percentage, are suggested for use when coarser resolution land cover data are required.
基金This project is supported by Doctoral Fundation of National Educational Committee.
文摘In this paper, we study, mathematically speaking, the problem-the number of admissible preference orderings for the transitivity of simple majority vote(SMV) derived from Arrow’s Impossibility Theorem. In our research, we find, by computer enumerating, that some results given by Craven are not correct. By defining a set of constraints, we give the recurrence formula of the local maximal number of admissible preference orderings and some other useful results.