Fault diagnosis and monitoring are very important for complex chemical process. There are numerous methods that have been studied in this field, in which the effective visualization method is still challenging. In ord...Fault diagnosis and monitoring are very important for complex chemical process. There are numerous methods that have been studied in this field, in which the effective visualization method is still challenging. In order to get a better visualization effect, a novel fault diagnosis method which combines self-organizing map (SOM) with Fisher discriminant analysis (FDA) is proposed. FDA can reduce the dimension of the data in terms of maximizing the separability of the classes. After feature extraction by FDA, SOM can distinguish the different states on the output map clearly and it can also be employed to monitor abnormal states. Tennessee Eastman (TE) process is employed to illustrate the fault diagnosis and monitoring performance of the proposed method. The result shows that the SOM integrated with FDA method is efficient and capable for real-time monitoring and fault diagnosis in complex chemical process.展开更多
A Fisher discriminant analysis (FDA) model for the prediction of classification of rockburst in deep-buried long tunnel was established based on the Fisher discriminant theory and the actual characteristics of the pro...A Fisher discriminant analysis (FDA) model for the prediction of classification of rockburst in deep-buried long tunnel was established based on the Fisher discriminant theory and the actual characteristics of the project.First, the major factors of rockburst,such as the maximum tangential stress of the cavern wall σ_θ, uniaxial compressive strength σ_c, uniaxial tensile strength σ_t, and the elastic energy index of rock W_(et), were taken into account in the analysis.Three factors, Stress coefficient σ_θlσ_c, rock brittleness coefficient σ_c/σ_t, and elastic energy index W_(et), were defined as the criterion indices for rockburst prediction in the proposed model.After training and testing of 12 sets of measured data, the discriminant functions of FDA were solved, and the ratio of misdiscrimination is zero.Moreover, the proposed model was used to predict rockbursts of Qinling tunnel along Xi'an-Ankang railway.The results show that three forecast results are identical with the actual situation.Therefore, the prediction accuracy of the FDA model is acceptable.展开更多
In gene prediction, the Fisher discriminant analysis (FDA) is used to separate protein coding region (exon) from non-coding regions (intron). Usually, the positive data set and the negative data set are of the same si...In gene prediction, the Fisher discriminant analysis (FDA) is used to separate protein coding region (exon) from non-coding regions (intron). Usually, the positive data set and the negative data set are of the same size if the number of the data is big enough. But for some situations the data are not sufficient or not equal, the threshold used in FDA may have important influence on prediction results. This paper presents a study on the selection of the threshold. The eigen value of each exon/intron sequence is computed using the Z-curve method with 69 variables. The experiments results suggest that the size and the standard deviation of the data sets and the threshold are the three key elements to be taken into consideration to improve the prediction results.展开更多
A new on-line batch process monitoring and diagnosing approach based on Fisher discriminant analysis (FDA) was proposed. This method does not need to predict the future observations of variables, so it is more sensiti...A new on-line batch process monitoring and diagnosing approach based on Fisher discriminant analysis (FDA) was proposed. This method does not need to predict the future observations of variables, so it is more sensitive to fault detection and stronger implement for monitoring. In order to improve the monitoring performance, the variables trajectories of batch process are separated into several blocks. The key to the proposed approach for on-line monitoring is to calculate the distance of block data that project to low-dimension Fisher space between new batch and reference batch. Comparing the distance with the predefine threshold, it can be considered whether the batch process is normal or abnormal. Fault diagnosis is performed based on the weights in fault direction calculated by FDA. The proposed method was applied to the simulation model of fed-batch penicillin fermentation and the results were compared with those obtained using MPCA. The simulation results clearly show that the on-line monitoring method based on FDA is more efficient than the MPCA.展开更多
A new method based on kernel Fisher discriminant analysis (KFDA) is proposed for target detection of hyperspectral images. The KFDA combines kernel mapping derived from support vector machine and the classical linear ...A new method based on kernel Fisher discriminant analysis (KFDA) is proposed for target detection of hyperspectral images. The KFDA combines kernel mapping derived from support vector machine and the classical linear Fisher discriminant analysis (LFDA), and it possesses good ability to process nonlinear data such as hyperspectral images. According to the Fisher rule that the ratio of the between-class and within-class scatters is maximized, the KFDA is used to obtain a set of optimal discriminant basis vectors in high dimensional feature space. All pixels in the hyperspectral images are projected onto the discriminant basis vectors and the target detection is performed according to the projection result. The numerical experiments are performed on hyperspectral data with 126 bands collected by Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). The experimental results show the effectiveness of the proposed detection method and prove that this method has good ability to overcome small sample size and spectral variability in the hyperspectral target detection.展开更多
Marginal Fisher analysis （MFA） not only aims to maintain the original relations of neighboring data points of the same class but also wants to keep away neighboring data points of the different classes.MFA can effec...Marginal Fisher analysis （MFA） not only aims to maintain the original relations of neighboring data points of the same class but also wants to keep away neighboring data points of the different classes.MFA can effectively overcome the limitation of linear discriminant analysis （LDA） due to data distribution assumption and available projection directions.However,MFA confronts the undersampled problems.Generalized marginal Fisher analysis （GMFA） based on a new optimization criterion is presented,which is applicable to the undersampled problems.The solutions to the proposed criterion for GMFA are derived,which can be characterized in a closed form.Among the solutions,two specific algorithms,namely,normal MFA （NMFA） and orthogonal MFA （OMFA）,are studied,and the methods to implement NMFA and OMFA are proposed.A comparative study on the undersampled problem of face recognition is conducted to evaluate NMFA and OMFA in terms of classification accuracy,which demonstrates the effectiveness of the proposed algorithms.展开更多
Today, mammography is the best method for early detection of breast cancer. Radiologists failed to detect evident cancerous signs in approximately 20% of false negative mammograms. False negatives have been identified...Today, mammography is the best method for early detection of breast cancer. Radiologists failed to detect evident cancerous signs in approximately 20% of false negative mammograms. False negatives have been identified as the inability of the radiologist to detect the abnormalities due to several reasons such as poor image quality, image noise, or eye fatigue. This paper presents a framework for a computer aided detection system that integrates Principal Component Analysis (PCA), Fisher Linear Discriminant (FLD), and Nearest Neighbor Classifier (KNN) algorithms for the detection of abnormalities in mammograms. Using normal and abnormal mammograms from the MIAS database, the integrated algorithm achieved 93.06% classification accuracy. Also in this paper, we present an analysis of the integrated algorithm’s parameters and suggest selection criteria.展开更多
This paper proposes the discriminant analysis on land grading after analyzing the common methods and discussing the Fisher’s discriminant in detail. Actually this method deduces the dimension from multi to single, th...This paper proposes the discriminant analysis on land grading after analyzing the common methods and discussing the Fisher’s discriminant in detail. Actually this method deduces the dimension from multi to single, thus it makes the feature vectors in n \|dimension change to a scalar, and use this scalar to classify samples. This paper illustrates the result by giving an example of the residential land grading by the discriminant analysis.展开更多
This paper presents a novel bootstrap based method for Receiver Operating Characteristic (ROC) analysis of Fisher classifier. By defining Fisher classifier’s output as a statistic, the bootstrap technique is used to ...This paper presents a novel bootstrap based method for Receiver Operating Characteristic (ROC) analysis of Fisher classifier. By defining Fisher classifier’s output as a statistic, the bootstrap technique is used to obtain the sampling distributions of the outputs for the positive class and the negative class respectively. As a result, the ROC curve is a plot of all the (False Positive Rate (FPR), True Positive Rate (TPR)) pairs by varying the decision threshold over the whole range of the boot- strap sampling distributions. The advantage of this method is, the bootstrap based ROC curves are much stable than those of the holdout or cross-validation, indicating a more stable ROC analysis of Fisher classifier. Experiments on five data sets publicly available demonstrate the effectiveness of the proposed method.展开更多
Foley-Sammon linear discriminant analysis (FSLDA) and uncorrelated linear discriminant analysis (ULDA) are two well-known kinds of linear discriminant analysis. Both ULDA and FSLDA search the kth discriminant vector i...Foley-Sammon linear discriminant analysis (FSLDA) and uncorrelated linear discriminant analysis (ULDA) are two well-known kinds of linear discriminant analysis. Both ULDA and FSLDA search the kth discriminant vector in an n-k+1 dimensional subspace, while they are subject to their respective constraints. Evidenced by strict demonstration, it is clear that in essence ULDA vectors are the covariance-orthogonal vectors of the corresponding eigen-equation. So, the algorithms for the covariance-orthogonal vectors are equivalent to the original algorithm of ULDA, which is time-consuming. Also, it is first revealed that the Fisher criterion value of each FSLDA vector must be not less than that of the corresponding ULDA vector by theory analysis. For a discriminant vector, the larger its Fisher criterion value is, the more powerful in discriminability it is. So, for FSLDA vectors, corresponding to larger Fisher criterion values is an advantage. On the other hand, in general any two feature components extracted by FSLDA vectors are statistically correlated with each other, which may make the discriminant vectors set at a disadvantageous position. In contrast to FSLDA vectors, any two feature components extracted by ULDA vectors are statistically uncorrelated with each other. Two experiments on CENPARMI handwritten numeral database and ORL database are performed. The experimental results are consistent with the theory analysis on Fisher criterion values of ULDA vectors and FSLDA vectors. The experiments also show that the equivalent algorithm of ULDA, presented in this paper, is much more efficient than the original algorithm of ULDA, as the theory analysis expects. Moreover, it appears that if there is high statistical correlation between feature components extracted by FSLDA vectors, FSLDA will not perform well, in spite of larger Fisher criterion value owned by every FSLDA vector. However, when the average correlation coefficient of feature components extracted by FSLDA vectors is at a low level, the performance of FSLDA are comparable with ULDA.展开更多
基金Supported by the National Basic Research Program of China （2013CB733600）, the National Natural Science Foundation of China （21176073）, the Doctoral Fund of Ministry of Education of China （20090074110005）, the Program for New Century Excellent Talents in University （NCET-09-0346）, Shu Guang Project （09SG29） and the Fundamental Research Funds for the Central Universities.
文摘Fault diagnosis and monitoring are very important for complex chemical process. There are numerous methods that have been studied in this field, in which the effective visualization method is still challenging. In order to get a better visualization effect, a novel fault diagnosis method which combines self-organizing map (SOM) with Fisher discriminant analysis (FDA) is proposed. FDA can reduce the dimension of the data in terms of maximizing the separability of the classes. After feature extraction by FDA, SOM can distinguish the different states on the output map clearly and it can also be employed to monitor abnormal states. Tennessee Eastman (TE) process is employed to illustrate the fault diagnosis and monitoring performance of the proposed method. The result shows that the SOM integrated with FDA method is efficient and capable for real-time monitoring and fault diagnosis in complex chemical process.
基金Supported by the National 11th Five-Year Science and Technology Supporting Plan of China(2006BAB02A02)Central South University Innovation funded projects (2009ssxt230, 2009ssxt234)
文摘A Fisher discriminant analysis (FDA) model for the prediction of classification of rockburst in deep-buried long tunnel was established based on the Fisher discriminant theory and the actual characteristics of the project.First, the major factors of rockburst,such as the maximum tangential stress of the cavern wall σ_θ, uniaxial compressive strength σ_c, uniaxial tensile strength σ_t, and the elastic energy index of rock W_(et), were taken into account in the analysis.Three factors, Stress coefficient σ_θlσ_c, rock brittleness coefficient σ_c/σ_t, and elastic energy index W_(et), were defined as the criterion indices for rockburst prediction in the proposed model.After training and testing of 12 sets of measured data, the discriminant functions of FDA were solved, and the ratio of misdiscrimination is zero.Moreover, the proposed model was used to predict rockbursts of Qinling tunnel along Xi'an-Ankang railway.The results show that three forecast results are identical with the actual situation.Therefore, the prediction accuracy of the FDA model is acceptable.
文摘In gene prediction, the Fisher discriminant analysis (FDA) is used to separate protein coding region (exon) from non-coding regions (intron). Usually, the positive data set and the negative data set are of the same size if the number of the data is big enough. But for some situations the data are not sufficient or not equal, the threshold used in FDA may have important influence on prediction results. This paper presents a study on the selection of the threshold. The eigen value of each exon/intron sequence is computed using the Z-curve method with 69 variables. The experiments results suggest that the size and the standard deviation of the data sets and the threshold are the three key elements to be taken into consideration to improve the prediction results.
文摘A new on-line batch process monitoring and diagnosing approach based on Fisher discriminant analysis (FDA) was proposed. This method does not need to predict the future observations of variables, so it is more sensitive to fault detection and stronger implement for monitoring. In order to improve the monitoring performance, the variables trajectories of batch process are separated into several blocks. The key to the proposed approach for on-line monitoring is to calculate the distance of block data that project to low-dimension Fisher space between new batch and reference batch. Comparing the distance with the predefine threshold, it can be considered whether the batch process is normal or abnormal. Fault diagnosis is performed based on the weights in fault direction calculated by FDA. The proposed method was applied to the simulation model of fed-batch penicillin fermentation and the results were compared with those obtained using MPCA. The simulation results clearly show that the on-line monitoring method based on FDA is more efficient than the MPCA.
基金Foundation of China(Grant No.60272073 and No.60402025),Development Program for Outstanding Young Teachers in Harbin Institute of Technology and China Postdoctoral Science Foundation.
文摘A new method based on kernel Fisher discriminant analysis (KFDA) is proposed for target detection of hyperspectral images. The KFDA combines kernel mapping derived from support vector machine and the classical linear Fisher discriminant analysis (LFDA), and it possesses good ability to process nonlinear data such as hyperspectral images. According to the Fisher rule that the ratio of the between-class and within-class scatters is maximized, the KFDA is used to obtain a set of optimal discriminant basis vectors in high dimensional feature space. All pixels in the hyperspectral images are projected onto the discriminant basis vectors and the target detection is performed according to the projection result. The numerical experiments are performed on hyperspectral data with 126 bands collected by Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). The experimental results show the effectiveness of the proposed detection method and prove that this method has good ability to overcome small sample size and spectral variability in the hyperspectral target detection.
基金supported by Science Foundation of the Fujian Province of China (No. 2010J05099)
文摘Marginal Fisher analysis （MFA） not only aims to maintain the original relations of neighboring data points of the same class but also wants to keep away neighboring data points of the different classes.MFA can effectively overcome the limitation of linear discriminant analysis （LDA） due to data distribution assumption and available projection directions.However,MFA confronts the undersampled problems.Generalized marginal Fisher analysis （GMFA） based on a new optimization criterion is presented,which is applicable to the undersampled problems.The solutions to the proposed criterion for GMFA are derived,which can be characterized in a closed form.Among the solutions,two specific algorithms,namely,normal MFA （NMFA） and orthogonal MFA （OMFA）,are studied,and the methods to implement NMFA and OMFA are proposed.A comparative study on the undersampled problem of face recognition is conducted to evaluate NMFA and OMFA in terms of classification accuracy,which demonstrates the effectiveness of the proposed algorithms.
文摘Today, mammography is the best method for early detection of breast cancer. Radiologists failed to detect evident cancerous signs in approximately 20% of false negative mammograms. False negatives have been identified as the inability of the radiologist to detect the abnormalities due to several reasons such as poor image quality, image noise, or eye fatigue. This paper presents a framework for a computer aided detection system that integrates Principal Component Analysis (PCA), Fisher Linear Discriminant (FLD), and Nearest Neighbor Classifier (KNN) algorithms for the detection of abnormalities in mammograms. Using normal and abnormal mammograms from the MIAS database, the integrated algorithm achieved 93.06% classification accuracy. Also in this paper, we present an analysis of the integrated algorithm’s parameters and suggest selection criteria.
文摘This paper proposes the discriminant analysis on land grading after analyzing the common methods and discussing the Fisher’s discriminant in detail. Actually this method deduces the dimension from multi to single, thus it makes the feature vectors in n \|dimension change to a scalar, and use this scalar to classify samples. This paper illustrates the result by giving an example of the residential land grading by the discriminant analysis.
基金the Natural Science Foundation of Zhejiang Province of China (No. Y104540)the Foundation of the Key Laboratory of Advanced Information Science and Network Technology of Beijing, China (No.TDXX0509).
文摘This paper presents a novel bootstrap based method for Receiver Operating Characteristic (ROC) analysis of Fisher classifier. By defining Fisher classifier’s output as a statistic, the bootstrap technique is used to obtain the sampling distributions of the outputs for the positive class and the negative class respectively. As a result, the ROC curve is a plot of all the (False Positive Rate (FPR), True Positive Rate (TPR)) pairs by varying the decision threshold over the whole range of the boot- strap sampling distributions. The advantage of this method is, the bootstrap based ROC curves are much stable than those of the holdout or cross-validation, indicating a more stable ROC analysis of Fisher classifier. Experiments on five data sets publicly available demonstrate the effectiveness of the proposed method.
基金The National Natural Science Foundation of China (Grant No.60472060 ,60473039 and 60472061)
文摘Foley-Sammon linear discriminant analysis (FSLDA) and uncorrelated linear discriminant analysis (ULDA) are two well-known kinds of linear discriminant analysis. Both ULDA and FSLDA search the kth discriminant vector in an n-k+1 dimensional subspace, while they are subject to their respective constraints. Evidenced by strict demonstration, it is clear that in essence ULDA vectors are the covariance-orthogonal vectors of the corresponding eigen-equation. So, the algorithms for the covariance-orthogonal vectors are equivalent to the original algorithm of ULDA, which is time-consuming. Also, it is first revealed that the Fisher criterion value of each FSLDA vector must be not less than that of the corresponding ULDA vector by theory analysis. For a discriminant vector, the larger its Fisher criterion value is, the more powerful in discriminability it is. So, for FSLDA vectors, corresponding to larger Fisher criterion values is an advantage. On the other hand, in general any two feature components extracted by FSLDA vectors are statistically correlated with each other, which may make the discriminant vectors set at a disadvantageous position. In contrast to FSLDA vectors, any two feature components extracted by ULDA vectors are statistically uncorrelated with each other. Two experiments on CENPARMI handwritten numeral database and ORL database are performed. The experimental results are consistent with the theory analysis on Fisher criterion values of ULDA vectors and FSLDA vectors. The experiments also show that the equivalent algorithm of ULDA, presented in this paper, is much more efficient than the original algorithm of ULDA, as the theory analysis expects. Moreover, it appears that if there is high statistical correlation between feature components extracted by FSLDA vectors, FSLDA will not perform well, in spite of larger Fisher criterion value owned by every FSLDA vector. However, when the average correlation coefficient of feature components extracted by FSLDA vectors is at a low level, the performance of FSLDA are comparable with ULDA.
