An Optimization Criterion for Generalized Marginal Fisher Analysis on Undersampled Problems

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.

Predicting pillar stability for underground mine using Fisher discriminant analysis and SVM methods

The purpose of this study is to apply some statistical and soft computing methods such as Fisher discriminant analysis （FDA） and support vector machines （SVMs） methodology to the determination of pillar stability for underground mines selected from various coal and stone mines by using some index and mechanical properties, including the width, the height, the ratio of the pillar width to its height, the uniaxial compressive strength of the rock and pillar stress. The study includes four main stages： sampling, testing, modeling and assessment of the model performances. During the modeling stage, two pillar stability prediction models were investigated with FDA and SVMs methodology based on the statistical learning theory. After using 40 sets of measured data in various mines in the world for training and testing, the model was applied to other 6 data for validating the trained proposed models. The prediction results of SVMs were compared with those of FDA as well as the measured field values. The general performance of models developed in this study is close; however, the SVMs exhibit the best performance considering the performance index with the correct classification rate Prs by re-substitution method and Pcv by cross validation method. The results show that the SVMs approach has the potential to be a reliable and practical tool for determination of pillar stability for underground mines.

Fault Diagnosis in Chemical Process Based on Self-organizing Map Integrated with Fisher Discriminant Analysis

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.

Fault Diagnosis for Batch Processes by Improved Multi-model Fisher Discriminant Analysis

Since there are not enough fault data in historical data sets, it is very difficult to diagnose faults for batch processes. In addition, a complete batch trajectory can be obtained till the end of its operation. In order to overcome the need for estimated or filled up future unmeasured values in the online fault diagnosis, sufficiently utilize the finite information of faults, and enhance the diagnostic performance, an improved multi-model Fisher discriminant analysis is represented. The trait of the proposed method is that the training data sets are made of the current measured information and the past major discriminant information, and not only the current information or the whole batch data. An industrial typical multi-stage streptomycin fermentation process is used to test the performance of fault diagnosis of the proposed method.

Fisher discriminant analysis model and its application for prediction of classification of rockburst in deep-buried long tunnel

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 σθ, uniaxial compressive strength σc, uniaxial tensile strength or, and the elastic energy index of rock Wet, were taken into account in the analysis. Three factors, Stress coefficient σθ/σc, rock brittleness coefficient σc/σt, and elastic energy index Wet, 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 misdiscrimina- tion 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.

Cobalt crust recognition based on kernel Fisher discriminant analysis and genetic algorithm in reverberation environment

Recognition of substrates in cobalt crust mining areas can improve mining efficiency.Aiming at the problem of unsatisfactory performance of using single feature to recognize the seabed material of the cobalt crust mining area,a method based on multiple-feature sets is proposed.Features of the target echoes are extracted by linear prediction method and wavelet analysis methods,and the linear prediction coefficient and linear prediction cepstrum coefficient are also extracted.Meanwhile,the characteristic matrices of modulus maxima,sub-band energy and multi-resolution singular spectrum entropy are obtained,respectively.The resulting features are subsequently compressed by kernel Fisher discriminant analysis(KFDA),the output features are selected using genetic algorithm(GA)to obtain optimal feature subsets,and recognition results of classifier are chosen as genetic fitness function.The advantages of this method are that it can describe the signal features more comprehensively and select the favorable features and remove the redundant features to the greatest extent.The experimental results show the better performance of the proposed method in comparison with only using KFDA or GA.

Kernel-based fisher discriminant analysis for hyperspectral target detection

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）, Tbe 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.

On-line Batch Process Monitoring and Diagnosing Based on Fisher Discriminant Analysis

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 resuits 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.

BOOTSTRAP TECHNIQUE FOR ROC ANALYSIS: A STABLE EVALUATION OF FISHER CLASSIFIER PERFORMANCE

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.

Monitoring and Fault Diagnosis for Batch Process Based on Feature Extract in Fisher Subspace

Multivariate statistical process control methods have been widely used in biochemical industries. Batch process is usually monitored by the method of multi-way principal component analysis (MPCA). In this article, a new batch process monitoring and fault diagnosis method based on feature extract in Fisher subspace is proposed. The feature vector and the feature direction are extracted by projecting the high-dimension process data onto the low-dimension Fisher space. The similarity of feature vector between the current and the reference batch is calcu- lated for on-line process monitoring and the contribution plot of weights in feature direction is calculated for fault diagnosis. The approach overcomes the need for estimating or filling in the unknown portion of the process vari- ables trajectories from the current time to the end of the batch. Simulation results on the benchmark model of peni- cillin fermentation process can demonstrate that in comparison to the MPCA method, the proposed method is more accurate and efficient for process monitoring and fault diagnosis.

Texture Analysis and Characteristic Identification About Plaque Tissues of IVUS

Intravascular ultrasound can provide clear real-time cross-sectional images,including lumen and plaque.In practice,to identify the plaques tissues in different pathological changes is very important.However,the grayscale differences of them are not so apparent.In this paper a new textural characteristic space vector was formed by the combination of Co-occurrence Matrix and fraction methods.The vector was projected to the new characteristic space after multiplied by a projective matrix which can best classify those plaques according to the Fisher linear discriminant.Then the classification was completed in the new vector space.Experimental results found that the veracity of this classification could reach up to 88%,which would be an accessorial tool for doctors to identify each plaque.

DISCRIMINATIVE ANALYSIS OF FUNCTIONAL NEAR-INFRARED SPECTROSCOPY SIGNALS FOR DEVELOPMENT OF NEUROIMAGING BIOMARKERS OF ELDERLY DEPRESSION

Functional near-infrared spectroscopy(fNIRS)is a neuroimaging technology which is suitable for psychiatric patients.Several fNIRS studies have found abnormal brain activations during cognitive tasks in elderly depression.In this paper,we proposed a discriminative model of multivariate pattern classification based on fNIRS signals to distinguish elderly depressed patients from healthy controls.This model used the brain activation patterns during a verbal fluency task as features of classification.Then Pseudo-Fisher Linear Discriminant Analysis was performed on the feature space to generate discriminative model.Using leave-one-out(LOO)cross-validation,our results showed a correct classification rate of 88%.The discriminative model showed its ability to identify people with elderly depression and suggested that fNIRS may be an efficient clinical tool for diagnosis of depression.This study may provide the first step for the development of neuroimaging biomarkers based on fNIRS in psychiatric disorders.

Classification of mine blasts and microseismic events using starting-up features in seismograms

To find discriminating features in seismograms for the classification of mine seismic events,signal databases of blasts and microseismic events were established based on manual identification.Criteria including the repetition of waveforms,tail decreasing,dominant frequency and occurrence time of day were considered in the establishment of the databases.Signals from databases of different types were drawn into a unified coordinate system.It is noticed that the starting-up angles of the two types tend to be concentrated into two different intervals.However,it is difficult to calculate the starting-up angle directly due to the inaccuracy of the P-wave arrival＇s picking.The slope value of the starting-up trend line,which was obtained by linear regression,was proposed to substitute the angle.Two slope values associated with the coordinates of the first peak and the maximum peak were extracted as the characteristic parameters.A statistical model with correct discrimination rate of greater than 97.1% was established by applying the Fisher discriminant analysis.

A Novel Systematic Method of Quality Monitoring and Prediction Based on FDA and Kernel Regression

A novel systematic quality monitoring and prediction method based on Fisher discriminant analysis (FDA) and kernel regression is proposed. The FDA method is first used for quality monitoring. If the process is un-der normal condition, then kernel regression is further used for quality prediction and estimation. If faults have oc-curred, the contribution plot in the fault feature direction is used for fault diagnosis. The proposed method can ef-fectively detect the fault and has better ability to predict the response variables than principle component regression (PCR) and partial least squares (PLS). Application results to the industrial fluid catalytic cracking unit (FCCU) show the effectiveness of the proposed method.

Using endocarp-remains of seeds of wild apricot Prunus armeniaca to identify rodent seed predators

Some rodent-dispersed seeds have a hard seed-coat(e.g.woody endocarp).Specific scrapes or dental marks on the hard seed-coat left by rodents when they eat these seeds can be used to identify seed predators.In this study we measured the morphological traits of endocarp-remains of seeds of wild apricot Prunus armeniaca used by Chinese white-bellied rats Niviventor confucianus and Korean field mice Apodemus peninsulae.We established their Fisher's linear discriminant functions to separate endocarp-remains between the two predators.A total of 90.0% of the endocarp-remains left by Korean field mice and 88.0% of those left by Chinese white-bellied rats were correctly classified.The overall percentage of correct classification was 89.0%.One hundred and sixty endocarp-remains of unknown what species predated them were classified using the functions.The method may allow more reliable quantitative studies of the effects of Chinese white-bellied rats and Korean field mice on seed consumption and dispersal of wild apricot and this study might be used for reference in other studies of seed predators identification on hard seeds.

New Method for Multivariate Statistical Process Monitoring

A new method using discriminant analysis and control charts is proposed for monitoring multivariate process operations more reliably.Fisher discriminant analysis （FDA） is used to derive a feature discriminant direction （FDD） between each normal and fault operations,and each FDD thus decided constructs the feature space of each fault operation.Individuals control charts （XmR charts） are used to monitor multivariate processes using the process data projected onto feature spaces.Upper control limit （UCL） and lower control limit （LCL） on each feature space from normal process operation are calculated for XmR charts,and are used to distinguish fault from normal.A variation trend on an XmR chart reveals the type of relevant fault operation.Applications to Tennessee Eastman simulation processes show that this proposed method can result in better monitoring performance than principal component analysis （PCA）-based methods and can better identify step type faults on XmR charts.

A novel multimode process monitoring method integrating LCGMM with modified LFDA

Complex processes often work with multiple operation regions, it is critical to develop effective monitoring approaches to ensure the safety of chemical processes. In this work, a discriminant local consistency Gaussian mixture model(DLCGMM) for multimode process monitoring is proposed for multimode process monitoring by integrating LCGMM with modified local Fisher discriminant analysis(MLFDA). Different from Fisher discriminant analysis(FDA) that aims to discover the global optimal discriminant directions, MLFDA is capable of uncovering multimodality and local structure of the data by exploiting the posterior probabilities of observations within clusters calculated from the results of LCGMM. This may enable MLFDA to capture more meaningful discriminant information hidden in the high-dimensional multimode observations comparing to FDA. Contrary to most existing multimode process monitoring approaches, DLCGMM performs LCGMM and MFLDA iteratively, and the optimal subspaces with multi-Gaussianity and the optimal discriminant projection vectors are simultaneously achieved in the framework of supervised and unsupervised learning. Furthermore, monitoring statistics are established on each cluster that represents a specific operation condition and two global Bayesian inference-based fault monitoring indexes are established by combining with all the monitoring results of all clusters. The efficiency and effectiveness of the proposed method are evaluated through UCI datasets, a simulated multimode model and the Tennessee Eastman benchmark process.

GSM-MRF based classification approach for real-time moving object detection

Statistical and contextual information are typically used to detect moving regions in image sequences for a fixed camera.In this paper,we propose a fast and stable linear discriminant approach based on Gaussian Single Model(GSM)and Markov Random Field(MRF).The performance of GSM is analyzed first,and then two main improvements corresponding to the drawbacks of GSM are proposed:the latest filtered data based update scheme of the background model and the linear classification judgment rule based on spatial-temporal feature specified by MRF.Experimental results show that the proposed method runs more rapidly and accurately when compared with other methods.

Probabilistic Fisher discriminant analysis based on Gaussian mixture model for estimating shale oil sweet spots

The delineation of shale oil sweet spots is a crucial step in the exploration of shale oil reservoirs.A single attribute such as total organic carbon(TOC)is conventionally used to evaluate the sweet spots of shale oil.This study proposes a probabilistic Fisher discriminant approach for estimating shale oil sweet spots,in which the probabilistic method and Gaussian mixture model are incorporated.Statistical features of shale oil facies are obtained based on the well log interpretation of the samples.Several key parameters of shale oil are projected to data sets with low dimensions in each shale oil facies.Furthermore,the posterior distribution of different shale oil facies is built based on the classification of each shale oil facies.Various key physical parameters of shale oil facies are inversed by the Bayesian method,and important elastic properties are extracted from the elastic impedance inversion(EVA-DSVD method).The method proposed in this paper has been successfully used to delineate the sweet spots of shale oil reservoirs with multiple attributes from the real pre-stack seismic data sets and is validated by the well log data.

Target detection and recognition in SAR imagery based on KFDA

Current research on target detection and recognition from synthetic aperture radar （SAR） images is usually carried out separately. It is difficult to verify the ability of a target recognition algorithm for adapting to changes in the environment. To realize the whole process of SAR automatic target recognition （ATR）, es- pecially for the detection and recognition of vehicles, an algorithm based on kernel fisher discdminant analysis （KFDA） is proposed. First, in order to make a better description of the difference be- tween the background and the target, KFDA is extended to the detection part. Image samples are obtained with a dual-window approach and features of the inner and outer window samples are extracted by using KFDA. The difference between the features of inner and outer window samples is compared with a threshold to determine whether a vehicle exists. Second, for the target area, we propose an improved KFDA-IMED （image Euclidean distance） combined with a support vector machine （SVM） to recognize the vehicles. Experimental results validate the performance of our method. On the detection task, our proposed method obtains not only a high detection rate but also a low false alarm rate without using any prior information. For the recognition task, our method overcomes the SAR image aspect angle sensitivity, reduces the requirements for image preprocessing and improves the recogni- tion rate.