A direct linear discriminant analysis algorithm based on economic singular value decomposition （DLDA/ESVD） is proposed to address the computationally complex problem of the conventional DLDA algorithm, which directl...A direct linear discriminant analysis algorithm based on economic singular value decomposition （DLDA/ESVD） is proposed to address the computationally complex problem of the conventional DLDA algorithm, which directly uses ESVD to reduce dimension and extract eigenvectors corresponding to nonzero eigenvalues. Then a DLDA algorithm based on column pivoting orthogonal triangular （QR） decomposition and ESVD （DLDA/QR-ESVD） is proposed to improve the performance of the DLDA/ESVD algorithm by processing a high-dimensional low rank matrix, which uses column pivoting QR decomposition to reduce dimension and ESVD to extract eigenvectors corresponding to nonzero eigenvalues. The experimental results on ORL, FERET and YALE face databases show that the proposed two algorithms can achieve almost the same performance and outperform the conventional DLDA algorithm in terms of computational complexity and training time. In addition, the experimental results on random data matrices show that the DLDA/QR-ESVD algorithm achieves better performance than the DLDA/ESVD algorithm by processing high-dimensional low rank matrices.展开更多
Visual process monitoring is important in complex chemical processes.To address the high state separation of industrial data,we propose a new criterion for feature extraction called balanced multiple weighted linear d...Visual process monitoring is important in complex chemical processes.To address the high state separation of industrial data,we propose a new criterion for feature extraction called balanced multiple weighted linear discriminant analysis(BMWLDA).Then,we combine BMWLDA with self-organizing map(SOM)for visual monitoring of industrial operation processes.BMWLDA can extract the discriminative feature vectors from the original industrial data and maximally separate industrial operation states in the space spanned by these discriminative feature vectors.When the discriminative feature vectors are used as the input to SOM,the training result of SOM can differentiate industrial operation states clearly.This function improves the performance of visual monitoring.Continuous stirred tank reactor is used to verify that the class separation performance of BMWLDA is more effective than that of traditional linear discriminant analysis,approximate pairwise accuracy criterion,max–min distance analysis,maximum margin criterion,and local Fisher discriminant analysis.In addition,the method that combines BMWLDA with SOM can effectively perform visual process monitoring in real time.展开更多
A kernel-based discriminant analysis method called kernel direct discriminant analysis is employed, which combines the merit of direct linear discriminant analysis with that of kernel trick. In order to demonstrate it...A kernel-based discriminant analysis method called kernel direct discriminant analysis is employed, which combines the merit of direct linear discriminant analysis with that of kernel trick. In order to demonstrate its better robustness to the complex and nonlinear variations of real face images, such as illumination, facial expression, scale and pose variations, experiments are carried out on the Olivetti Research Laboratory, Yale and self-built face databases. The results indicate that in contrast to kernel principal component analysis and kernel linear discriminant analysis, the method can achieve lower （7%） error rate using only a very small set of features. Furthermore, a new corrected kernel model is proposed to improve the recognition performance. Experimental results confirm its superiority （1% in terms of recognition rate） to other polynomial kernel models.展开更多
An air classifier is used in the recycling process of covered electric wire in the recycling factories, in which the covered electric wires are crushed, sieved, and classified by the air classifier, which generates wa...An air classifier is used in the recycling process of covered electric wire in the recycling factories, in which the covered electric wires are crushed, sieved, and classified by the air classifier, which generates wastes. In these factories, operators manually adjust the air flow rate while checking the wastes discharged from the separator outlet. However, the adjustments are basically done by trial and error, and it is difficult to do them appropriately. In this study, we tried to develop the image processing system that calculates the ratio of copper (Cu) product and polyvinyl chloride (PVC) in the wastes as a substitute for the operator’s eyes. Six colors of PVC (white, gray, green, blue, black, and red) were used in the present work. An image consists of foreground and background. An image’s regions of interest are objects (Cu particles) in its foreground. However, the particles having a color similar to the background color are buried in the background. Using the difference of two color backgrounds, we separated particles and background without dependent of background. The Otsu’ thresholding was employed to choose the threshold to maximize the degree of separation of the particles and background. The ratio of Cu to PVC pixels from mixed image was calculated by linear discriminant analysis. The error of PVC pixels resulted in zero, whereas the error of Cu pixels arose to 4.19%. Comparing the numbers of Cu and PVC pixels within the contour, the minority of the object were corrected to the majority of the object. The error of Cu pixels discriminated as PVC incorrectly became zero percent through this correction.展开更多
An algorithm for unsupervised linear discriminant analysis was presented. Optimal unsupervised discriminant vectors are obtained through maximizing covariance of all samples and minimizing covariance of local k-neares...An algorithm for unsupervised linear discriminant analysis was presented. Optimal unsupervised discriminant vectors are obtained through maximizing covariance of all samples and minimizing covariance of local k-nearest neighbor samples. The experimental results show our algorithm is effective.展开更多
Linear discriminant analysis and kernel vector quantization are integrated into vector quantization based speech recognition system for improving the recognition accuracy of Mandarin digits. These techniques increase ...Linear discriminant analysis and kernel vector quantization are integrated into vector quantization based speech recognition system for improving the recognition accuracy of Mandarin digits. These techniques increase the class separability and optimize the clustering procedure. Speaker-dependent (SD) and speaker-independent (SI) experiments are performed to evaluate the performance of the proposed method. The experiment results show that the proposed method is capable of reaching the word error rate of 3.76% in SD case and 6.60 % in SI case. Such a system can be suitable for being embedded in personal digital assistant(PDA), mobile phone and so on to perform voice controlling such as digit dialing, calculating, etc.展开更多
To achieve efficient a d compact low-dimensional features for speech emotion recognition,a novel featurereduction method using uncertain linear discriminant analysis is proposed.Using the same principles as for conven...To achieve efficient a d compact low-dimensional features for speech emotion recognition,a novel featurereduction method using uncertain linear discriminant analysis is proposed.Using the same principles as for conventional linear discriminant analysis(LDA),uncertainties of the noisy or distorted input data ae employed in order to estimate maximaiy discriminant directions.The effectiveness of the proposed uncertain LDA(ULDA)is demonstrated in the Uyghur speech emotion recognition task.The emotional features of Uyghur speech,especially,the fundamental fequency and formant,a e analyzed in the collected emotional data.Then,ULDA is employed in dimensionality reduction of emotional features and better performance is achieved compared with other dimensionality reduction techniques.The speech emotion recognition of Uyghur is implemented by feeding the low-dimensional data to support vector machine(SVM)based on the proposed ULDA.The experimental results show that when employing a appropriate uncertainty estimation algorithm,uncertain LDA outperforms the conveetional LDA counterpart on Uyghur speech emotion recognition.展开更多
The recognition of pathological voice is considered a difficult task for speech analysis.Moreover,otolaryngologists needed to rely on oral communication with patients to discover traces of voice pathologies like dysph...The recognition of pathological voice is considered a difficult task for speech analysis.Moreover,otolaryngologists needed to rely on oral communication with patients to discover traces of voice pathologies like dysphonia that are caused by voice alteration of vocal folds and their accuracy is between 60%–70%.To enhance detection accuracy and reduce processing speed of dysphonia detection,a novel approach is proposed in this paper.We have leveraged Linear Discriminant Analysis(LDA)to train multiple Machine Learning(ML)models for dysphonia detection.Several ML models are utilized like Support Vector Machine(SVM),Logistic Regression,and K-nearest neighbor(K-NN)to predict the voice pathologies based on features like Mel-Frequency Cepstral Coefficients(MFCC),Fundamental Frequency(F0),Shimmer(%),Jitter(%),and Harmonic to Noise Ratio(HNR).The experiments were performed using Saarbrucken Voice Data-base(SVD)and a privately collected dataset.The K-fold cross-validation approach was incorporated to increase the robustness and stability of the ML models.According to the experimental results,our proposed approach has a 70%increase in processing speed over Principal Component Analysis(PCA)and performs remarkably well with a recognition accuracy of 95.24%on the SVD dataset surpassing the previous best accuracy of 82.37%.In the case of the private dataset,our proposed method achieved an accuracy rate of 93.37%.It can be an effective non-invasive method to detect dysphonia.展开更多
Optimizing the sensor energy is one of the most important concern in Three-Dimensional(3D)Wireless Sensor Networks(WSNs).An improved dynamic hierarchical clustering has been used in previous works that computes optimu...Optimizing the sensor energy is one of the most important concern in Three-Dimensional(3D)Wireless Sensor Networks(WSNs).An improved dynamic hierarchical clustering has been used in previous works that computes optimum clusters count and thus,the total consumption of energy is optimal.However,the computational complexity will be increased due to data dimension,and this leads to increase in delay in network data transmission and reception.For solving the above-mentioned issues,an efficient dimensionality reduction model based on Incremental Linear Discriminant Analysis(ILDA)is proposed for 3D hierarchical clustering WSNs.The major objective of the proposed work is to design an efficient dimensionality reduction and energy efficient clustering algorithm in 3D hierarchical clustering WSNs.This ILDA approach consists of four major steps such as data dimension reduction,distance similarity index introduction,double cluster head technique and node dormancy approach.This protocol differs from normal hierarchical routing protocols in formulating the Cluster Head(CH)selection technique.According to node’s position and residual energy,optimal cluster-head function is generated,and every CH is elected by this formulation.For a 3D spherical structure,under the same network condition,the performance of the proposed ILDA with Improved Dynamic Hierarchical Clustering(IDHC)is compared with Distributed Energy-Efficient Clustering(DEEC),Hybrid Energy Efficient Distributed(HEED)and Stable Election Protocol(SEP)techniques.It is observed that the proposed ILDA based IDHC approach provides better results with respect to Throughput,network residual energy,network lifetime and first node death round.展开更多
We revisit a comparison of two discriminant analysis procedures, namely the linear combination classifier of Chung and Han (2000) and the maximum likelihood estimation substitution classifier for the problem of classi...We revisit a comparison of two discriminant analysis procedures, namely the linear combination classifier of Chung and Han (2000) and the maximum likelihood estimation substitution classifier for the problem of classifying unlabeled multivariate normal observations with equal covariance matrices into one of two classes. Both classes have matching block monotone missing training data. Here, we demonstrate that for intra-class covariance structures with at least small correlation among the variables with missing data and the variables without block missing data, the maximum likelihood estimation substitution classifier outperforms the Chung and Han (2000) classifier regardless of the percent of missing observations. Specifically, we examine the differences in the estimated expected error rates for these classifiers using a Monte Carlo simulation, and we compare the two classifiers using two real data sets with monotone missing data via parametric bootstrap simulations. Our results contradict the conclusions of Chung and Han (2000) that their linear combination classifier is superior to the MLE classifier for block monotone missing multivariate normal data.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
The identification of liquor brands is very important for food safety. Most of the fake liquors are usually made into the products with the same flavor and alcohol content as regular brand, so the identification for t...The identification of liquor brands is very important for food safety. Most of the fake liquors are usually made into the products with the same flavor and alcohol content as regular brand, so the identification for the liquor brands with the same flavor and the same alcohol content is essential. However, it is also difficult because the components of such liquor samples are very similar. Near-infrared (NIR) spectroscopy combined with partial least squares discriminant analysis (PLS-DA) was applied to identification of liquor brands with the same flavor and alcohol content. A total of 160 samples of Luzhou Laojiao liquor and 200 samples of non-Luzhou Laojiao liquor with the same flavor and alcohol content were used for identification. Samples of each type were randomly divided into the modeling and validation sets. The modeling samples were further divided into calibration and prediction sets using the Kennard-Stone algorithm to achieve uniformity and representativeness. In the modeling and validation processes based on PLS-DA method, the recognition rates of samples achieved 99.1% and 98.7%, respectively. The results show high prediction performance for the identification of liquor brands, and were obviously better than those obtained from the principal component linear discriminant analysis method. NIR spectroscopy combined with the PLS-DA method provides a quick and effective means of the discriminant analysis of liquor brands, and is also a promising tool for large-scale inspection of liquor food safety.展开更多
The moving window bis corelation coefficients(MW BiCC)was proposed and employed for the discriminant analysis of transgenic sugarcane leaves and B-thalassemia with visible and near-infrared(Vis NIR)spectroscopy.The we...The moving window bis corelation coefficients(MW BiCC)was proposed and employed for the discriminant analysis of transgenic sugarcane leaves and B-thalassemia with visible and near-infrared(Vis NIR)spectroscopy.The well-performed moving window principal component analysis linear discriminant analysis(MWPCA-LDA)was also conducted for comparison.A total of 306 transgenic(positive)and 150 nont ransgenic(negative)leave samples of sugarcane were collected and divided to calibration,prediction,and validation.The diffuse reflection spectra were corected using Savitzky-Golay(SG)smoothing with first-order derivative(d=1),third-degree polynomial(p=3)and 25 smpothing points(m=25).The selected waveband was 736-1054nm with MW-BiCC,and the positive and negative validation recognition rates(V_REC^(+),VREC^(-))were 100%,98.0%,which achieved the same effect as MWPCA-LDA.Another example,the 93 B-thalassemia(positive)and 148 nonthalassemia(negative)of human hemolytic samples were colloctod.The transmission spectra were corrected using SG smoothing withd=1,p=3 and m=53.Using M W-BiCC,many best wavebands were selected(e.g.,1116-1146,17941848 and 22842342nm).The V_REC^(+)and V_REC^(-)were both 100%,which achieved the same effect as MW-PCA-LDA.Importantly,the BICC only required ca lculating correlation cofficients between the spectrum of prediction sample and the average spectra of two types of calibration samples.Thus,BiCC was very simple in algorithm,and expected to obtain more applications.The results first confirmed the feasibility of distinguishing B-thalassemia and normal control samples by NIR spectroscopy,and provided a promising simple tool for large population thalassemia screening.展开更多
Linear discrimiant analysis (LDA) has been used in face recognition. But it is difficult to handle the high nonlinear problems, such as changes of large viewpoint and illumination. In order to overcome these problems,...Linear discrimiant analysis (LDA) has been used in face recognition. But it is difficult to handle the high nonlinear problems, such as changes of large viewpoint and illumination. In order to overcome these problems, kernel discriminant analysis for face recognition is presented. This approach adopts the kernel functions to replace the dot products of nonlinear mapping in the high dimensional feature space, and then the nonlinear problem can be solved in the input space conveniently without explicit mapping. Two face databases are given.展开更多
基金The National Natural Science Foundation of China (No.61374194)
文摘A direct linear discriminant analysis algorithm based on economic singular value decomposition （DLDA/ESVD） is proposed to address the computationally complex problem of the conventional DLDA algorithm, which directly uses ESVD to reduce dimension and extract eigenvectors corresponding to nonzero eigenvalues. Then a DLDA algorithm based on column pivoting orthogonal triangular （QR） decomposition and ESVD （DLDA/QR-ESVD） is proposed to improve the performance of the DLDA/ESVD algorithm by processing a high-dimensional low rank matrix, which uses column pivoting QR decomposition to reduce dimension and ESVD to extract eigenvectors corresponding to nonzero eigenvalues. The experimental results on ORL, FERET and YALE face databases show that the proposed two algorithms can achieve almost the same performance and outperform the conventional DLDA algorithm in terms of computational complexity and training time. In addition, the experimental results on random data matrices show that the DLDA/QR-ESVD algorithm achieves better performance than the DLDA/ESVD algorithm by processing high-dimensional low rank matrices.
基金support of National Key Research and Development Program of China(2020YFA0908303)National Natural Science Foundation of China(21878081).
文摘Visual process monitoring is important in complex chemical processes.To address the high state separation of industrial data,we propose a new criterion for feature extraction called balanced multiple weighted linear discriminant analysis(BMWLDA).Then,we combine BMWLDA with self-organizing map(SOM)for visual monitoring of industrial operation processes.BMWLDA can extract the discriminative feature vectors from the original industrial data and maximally separate industrial operation states in the space spanned by these discriminative feature vectors.When the discriminative feature vectors are used as the input to SOM,the training result of SOM can differentiate industrial operation states clearly.This function improves the performance of visual monitoring.Continuous stirred tank reactor is used to verify that the class separation performance of BMWLDA is more effective than that of traditional linear discriminant analysis,approximate pairwise accuracy criterion,max–min distance analysis,maximum margin criterion,and local Fisher discriminant analysis.In addition,the method that combines BMWLDA with SOM can effectively perform visual process monitoring in real time.
文摘A kernel-based discriminant analysis method called kernel direct discriminant analysis is employed, which combines the merit of direct linear discriminant analysis with that of kernel trick. In order to demonstrate its better robustness to the complex and nonlinear variations of real face images, such as illumination, facial expression, scale and pose variations, experiments are carried out on the Olivetti Research Laboratory, Yale and self-built face databases. The results indicate that in contrast to kernel principal component analysis and kernel linear discriminant analysis, the method can achieve lower （7%） error rate using only a very small set of features. Furthermore, a new corrected kernel model is proposed to improve the recognition performance. Experimental results confirm its superiority （1% in terms of recognition rate） to other polynomial kernel models.
文摘An air classifier is used in the recycling process of covered electric wire in the recycling factories, in which the covered electric wires are crushed, sieved, and classified by the air classifier, which generates wastes. In these factories, operators manually adjust the air flow rate while checking the wastes discharged from the separator outlet. However, the adjustments are basically done by trial and error, and it is difficult to do them appropriately. In this study, we tried to develop the image processing system that calculates the ratio of copper (Cu) product and polyvinyl chloride (PVC) in the wastes as a substitute for the operator’s eyes. Six colors of PVC (white, gray, green, blue, black, and red) were used in the present work. An image consists of foreground and background. An image’s regions of interest are objects (Cu particles) in its foreground. However, the particles having a color similar to the background color are buried in the background. Using the difference of two color backgrounds, we separated particles and background without dependent of background. The Otsu’ thresholding was employed to choose the threshold to maximize the degree of separation of the particles and background. The ratio of Cu to PVC pixels from mixed image was calculated by linear discriminant analysis. The error of PVC pixels resulted in zero, whereas the error of Cu pixels arose to 4.19%. Comparing the numbers of Cu and PVC pixels within the contour, the minority of the object were corrected to the majority of the object. The error of Cu pixels discriminated as PVC incorrectly became zero percent through this correction.
文摘An algorithm for unsupervised linear discriminant analysis was presented. Optimal unsupervised discriminant vectors are obtained through maximizing covariance of all samples and minimizing covariance of local k-nearest neighbor samples. The experimental results show our algorithm is effective.
文摘Linear discriminant analysis and kernel vector quantization are integrated into vector quantization based speech recognition system for improving the recognition accuracy of Mandarin digits. These techniques increase the class separability and optimize the clustering procedure. Speaker-dependent (SD) and speaker-independent (SI) experiments are performed to evaluate the performance of the proposed method. The experiment results show that the proposed method is capable of reaching the word error rate of 3.76% in SD case and 6.60 % in SI case. Such a system can be suitable for being embedded in personal digital assistant(PDA), mobile phone and so on to perform voice controlling such as digit dialing, calculating, etc.
基金The National Natural Science Foundation of China(No.61673108,61231002)
文摘To achieve efficient a d compact low-dimensional features for speech emotion recognition,a novel featurereduction method using uncertain linear discriminant analysis is proposed.Using the same principles as for conventional linear discriminant analysis(LDA),uncertainties of the noisy or distorted input data ae employed in order to estimate maximaiy discriminant directions.The effectiveness of the proposed uncertain LDA(ULDA)is demonstrated in the Uyghur speech emotion recognition task.The emotional features of Uyghur speech,especially,the fundamental fequency and formant,a e analyzed in the collected emotional data.Then,ULDA is employed in dimensionality reduction of emotional features and better performance is achieved compared with other dimensionality reduction techniques.The speech emotion recognition of Uyghur is implemented by feeding the low-dimensional data to support vector machine(SVM)based on the proposed ULDA.The experimental results show that when employing a appropriate uncertainty estimation algorithm,uncertain LDA outperforms the conveetional LDA counterpart on Uyghur speech emotion recognition.
文摘The recognition of pathological voice is considered a difficult task for speech analysis.Moreover,otolaryngologists needed to rely on oral communication with patients to discover traces of voice pathologies like dysphonia that are caused by voice alteration of vocal folds and their accuracy is between 60%–70%.To enhance detection accuracy and reduce processing speed of dysphonia detection,a novel approach is proposed in this paper.We have leveraged Linear Discriminant Analysis(LDA)to train multiple Machine Learning(ML)models for dysphonia detection.Several ML models are utilized like Support Vector Machine(SVM),Logistic Regression,and K-nearest neighbor(K-NN)to predict the voice pathologies based on features like Mel-Frequency Cepstral Coefficients(MFCC),Fundamental Frequency(F0),Shimmer(%),Jitter(%),and Harmonic to Noise Ratio(HNR).The experiments were performed using Saarbrucken Voice Data-base(SVD)and a privately collected dataset.The K-fold cross-validation approach was incorporated to increase the robustness and stability of the ML models.According to the experimental results,our proposed approach has a 70%increase in processing speed over Principal Component Analysis(PCA)and performs remarkably well with a recognition accuracy of 95.24%on the SVD dataset surpassing the previous best accuracy of 82.37%.In the case of the private dataset,our proposed method achieved an accuracy rate of 93.37%.It can be an effective non-invasive method to detect dysphonia.
文摘Optimizing the sensor energy is one of the most important concern in Three-Dimensional(3D)Wireless Sensor Networks(WSNs).An improved dynamic hierarchical clustering has been used in previous works that computes optimum clusters count and thus,the total consumption of energy is optimal.However,the computational complexity will be increased due to data dimension,and this leads to increase in delay in network data transmission and reception.For solving the above-mentioned issues,an efficient dimensionality reduction model based on Incremental Linear Discriminant Analysis(ILDA)is proposed for 3D hierarchical clustering WSNs.The major objective of the proposed work is to design an efficient dimensionality reduction and energy efficient clustering algorithm in 3D hierarchical clustering WSNs.This ILDA approach consists of four major steps such as data dimension reduction,distance similarity index introduction,double cluster head technique and node dormancy approach.This protocol differs from normal hierarchical routing protocols in formulating the Cluster Head(CH)selection technique.According to node’s position and residual energy,optimal cluster-head function is generated,and every CH is elected by this formulation.For a 3D spherical structure,under the same network condition,the performance of the proposed ILDA with Improved Dynamic Hierarchical Clustering(IDHC)is compared with Distributed Energy-Efficient Clustering(DEEC),Hybrid Energy Efficient Distributed(HEED)and Stable Election Protocol(SEP)techniques.It is observed that the proposed ILDA based IDHC approach provides better results with respect to Throughput,network residual energy,network lifetime and first node death round.
文摘We revisit a comparison of two discriminant analysis procedures, namely the linear combination classifier of Chung and Han (2000) and the maximum likelihood estimation substitution classifier for the problem of classifying unlabeled multivariate normal observations with equal covariance matrices into one of two classes. Both classes have matching block monotone missing training data. Here, we demonstrate that for intra-class covariance structures with at least small correlation among the variables with missing data and the variables without block missing data, the maximum likelihood estimation substitution classifier outperforms the Chung and Han (2000) classifier regardless of the percent of missing observations. Specifically, we examine the differences in the estimated expected error rates for these classifiers using a Monte Carlo simulation, and we compare the two classifiers using two real data sets with monotone missing data via parametric bootstrap simulations. Our results contradict the conclusions of Chung and Han (2000) that their linear combination classifier is superior to the MLE classifier for block monotone missing multivariate normal data.
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.
文摘The identification of liquor brands is very important for food safety. Most of the fake liquors are usually made into the products with the same flavor and alcohol content as regular brand, so the identification for the liquor brands with the same flavor and the same alcohol content is essential. However, it is also difficult because the components of such liquor samples are very similar. Near-infrared (NIR) spectroscopy combined with partial least squares discriminant analysis (PLS-DA) was applied to identification of liquor brands with the same flavor and alcohol content. A total of 160 samples of Luzhou Laojiao liquor and 200 samples of non-Luzhou Laojiao liquor with the same flavor and alcohol content were used for identification. Samples of each type were randomly divided into the modeling and validation sets. The modeling samples were further divided into calibration and prediction sets using the Kennard-Stone algorithm to achieve uniformity and representativeness. In the modeling and validation processes based on PLS-DA method, the recognition rates of samples achieved 99.1% and 98.7%, respectively. The results show high prediction performance for the identification of liquor brands, and were obviously better than those obtained from the principal component linear discriminant analysis method. NIR spectroscopy combined with the PLS-DA method provides a quick and effective means of the discriminant analysis of liquor brands, and is also a promising tool for large-scale inspection of liquor food safety.
基金supported by the Science and Technology Project of Guangdong Province of China(Nos.2014A020213016 and 2014A020212445).
文摘The moving window bis corelation coefficients(MW BiCC)was proposed and employed for the discriminant analysis of transgenic sugarcane leaves and B-thalassemia with visible and near-infrared(Vis NIR)spectroscopy.The well-performed moving window principal component analysis linear discriminant analysis(MWPCA-LDA)was also conducted for comparison.A total of 306 transgenic(positive)and 150 nont ransgenic(negative)leave samples of sugarcane were collected and divided to calibration,prediction,and validation.The diffuse reflection spectra were corected using Savitzky-Golay(SG)smoothing with first-order derivative(d=1),third-degree polynomial(p=3)and 25 smpothing points(m=25).The selected waveband was 736-1054nm with MW-BiCC,and the positive and negative validation recognition rates(V_REC^(+),VREC^(-))were 100%,98.0%,which achieved the same effect as MWPCA-LDA.Another example,the 93 B-thalassemia(positive)and 148 nonthalassemia(negative)of human hemolytic samples were colloctod.The transmission spectra were corrected using SG smoothing withd=1,p=3 and m=53.Using M W-BiCC,many best wavebands were selected(e.g.,1116-1146,17941848 and 22842342nm).The V_REC^(+)and V_REC^(-)were both 100%,which achieved the same effect as MW-PCA-LDA.Importantly,the BICC only required ca lculating correlation cofficients between the spectrum of prediction sample and the average spectra of two types of calibration samples.Thus,BiCC was very simple in algorithm,and expected to obtain more applications.The results first confirmed the feasibility of distinguishing B-thalassemia and normal control samples by NIR spectroscopy,and provided a promising simple tool for large population thalassemia screening.
文摘Linear discrimiant analysis (LDA) has been used in face recognition. But it is difficult to handle the high nonlinear problems, such as changes of large viewpoint and illumination. In order to overcome these problems, kernel discriminant analysis for face recognition is presented. This approach adopts the kernel functions to replace the dot products of nonlinear mapping in the high dimensional feature space, and then the nonlinear problem can be solved in the input space conveniently without explicit mapping. Two face databases are given.
