Kernel Fisher Discriminant Analysis Research Articles

Flow regime classification using various dimensionality reduction methods and AutoML

Accurate identification of flow regimes is paramount in several industries, especially in chemical and hydrocarbon sectors. This paper describes a comprehensive data-driven workflow for flow regime identification. The workflow encompasses: i) the collection of dynamic pressure signals using an experimentally verified numerical two-phase flow model for three different flow regimes: stratified, slug and annular flow, ii) feature extraction from pressure signals using Discrete Wavelet Transformation (DWT), iii) Evaluation and testing of 12 different Dimensionality Reduction (DR) techniques, iv) the application of an AutoML framework for automated Machine Learning classifier selection among K-Nearest Neighbors, Artificial Neural Networks, Support Vector Machines, Gradient Boosting, Random Forest, and Logistic Regression, with hyper-parameter tuning. Kernel Fisher Discriminant Analysis (KFDA) is the best DR technique, exhibiting superior goodness of clustering, while KNN proved to be the top classifier with an accuracy of 92.5 % and excellent repeatability. The combination of DWT, KFDA and KNN was used to produce a virtual flow regime map. The proposed workflow represents a significant step forward in automating flow regime identification and enhancing the interpretability of ML classifiers, allowing its application to opaque pipes fitted with pressure sensors for achieving flow assurance and automatic monitoring of two-phase flow in various process industries.

Two-phase flow regime identification using multi-method feature extraction and explainable kernel Fisher discriminant analysis

Purpose Identifying the flow regime is a prerequisite for accurately modeling two-phase flow. This paper aims to introduce a comprehensive data-driven workflow for flow regime identification. Design/methodology/approach A numerical two-phase flow model was validated against experimental data and was used to generate dynamic pressure signals for three different flow regimes. First, four distinct methods were used for feature extraction: discrete wavelet transform (DWT), empirical mode decomposition, power spectral density and the time series analysis method. Kernel Fisher discriminant analysis (KFDA) was used to simultaneously perform dimensionality reduction and machine learning (ML) classification for each set of features. Finally, the Shapley additive explanations (SHAP) method was applied to make the workflow explainable. Findings The results highlighted that the DWT + KFDA method exhibited the highest testing and training accuracy at 95.2% and 88.8%, respectively. Results also include a virtual flow regime map to facilitate the visualization of features in two dimension. Finally, SHAP analysis showed that minimum and maximum values extracted at the fourth and second signal decomposition levels of DWT are the best flow-distinguishing features. Practical implications This workflow can be applied to opaque pipes fitted with pressure sensors to achieve flow assurance and automatic monitoring of two-phase flow occurring in many process industries. Originality/value This paper presents a novel flow regime identification method by fusing dynamic pressure measurements with ML techniques. The authors’ novel DWT + KFDA method demonstrates superior performance for flow regime identification with explainability.

Dynamic Feature Extraction-Based Quadratic Discriminant Analysis for Industrial Process Fault Classification and Diagnosis.

This paper introduces a novel method for enhancing fault classification and diagnosis in dynamic nonlinear processes. The method focuses on dynamic feature extraction within multivariate time series data and utilizes dynamic reconstruction errors to augment the feature set. A fault classification procedure is then developed, using the weighted maximum scatter difference (WMSD) dimensionality reduction criterion and quadratic discriminant analysis (QDA) classifier. This method addresses the challenge of high-dimensional, sample-limited fault classification, offering early diagnosis capabilities for online samples with smaller amplitudes than the training set. Validation is conducted using a cold rolling mill simulation model, with performance compared to classical methods like linear discriminant analysis (LDA) and kernel Fisher discriminant analysis (KFD). The results demonstrate the superiority of the proposed method for reliable industrial process monitoring and fault diagnosis.

A Multi-Layer Classifier Model XR-KS of Human Activity Recognition for the Problem of Similar Human Activity

Sensor-based human activity recognition is now well developed, but there are still many challenges, such as insufficient accuracy in the identification of similar activities. To overcome this issue, we collect data during similar human activities using three-axis acceleration and gyroscope sensors. We developed a model capable of classifying similar activities of human behavior, and the effectiveness and generalization capabilities of this model are evaluated. Based on the standardization and normalization of data, we consider the inherent similarities of human activity behaviors by introducing the multi-layer classifier model. The first layer of the proposed model is a random forest model based on the XGBoost feature selection algorithm. In the second layer of this model, similar human activities are extracted by applying the kernel Fisher discriminant analysis (KFDA) with feature mapping. Then, the support vector machine (SVM) model is applied to classify similar human activities. Our model is experimentally evaluated, and it is also applied to four benchmark datasets: UCI DSA, UCI HAR, WISDM, and IM-WSHA. The experimental results demonstrate that the proposed approach achieves recognition accuracies of 97.69%, 97.92%, 98.12%, and 90.6%, indicating excellent recognition performance. Additionally, we performed K-fold cross-validation on the random forest model and utilized ROC curves for the SVM classifier to assess the model’s generalization ability. The results indicate that our multi-layer classifier model exhibits robust generalization capabilities.

Identification of reservoir types in deep carbonates based on mixed-kernel machine learning using geophysical logging data

Identification of reservoir types in deep carbonates has always been a great challenge due to complex logging responses caused by the heterogeneous scale and distribution of storage spaces. Traditional cross-plot analysis and empirical formula methods for identifying reservoir types using geophysical logging data have high uncertainty and low efficiency, which cannot accurately reflect the nonlinear relationship between reservoir types and logging data. Recently, the kernel Fisher discriminant analysis (KFD), a kernel-based machine learning technique, attracts attention in many fields because of its strong nonlinear processing ability. However, the overall performance of KFD model may be limited as a single kernel function cannot simultaneously extrapolate and interpolate well, especially for highly complex data cases. To address this issue, in this study, a mixed kernel Fisher discriminant analysis (MKFD) model was established and applied to identify reservoir types of the deep Sinian carbonates in central Sichuan Basin, China. The MKFD model was trained and tested with 453 datasets from 7 coring wells, utilizing GR, CAL, DEN, AC, CNL and RT logs as input variables. The particle swarm optimization (PSO) was adopted for hyper-parameter optimization of MKFD model. To evaluate the model performance, prediction results of MKFD were compared with those of basic-kernel based KFD, RF and SVM models. Subsequently, the built MKFD model was applied in a blind well test, and a variable importance analysis was conducted. The comparison and blind test results demonstrated that MKFD outperformed traditional KFD, RF and SVM in the identification of reservoir types, which provided higher accuracy and stronger generalization. The MKFD can therefore be a reliable method for identifying reservoir types of deep carbonates.

ISL-GKFDA: An incomplete supervision manifold learning framework based on propagation graph of data

To improve manifold classification results using unlabeled data with high dimensional redundancy, we propose an incomplete supervision manifold learning framework. In this framework, Euclidean distance and Euclidean neighborhood are replaced by manifold distance and manifold neighborhood respectively. The pseudo label of unlabeled data is generated by constructing label propagation network in manifold neighborhood. By adding the local manifold neighborhood structure into KFDA (Kernel Fisherś Discriminant Analysis) as regularization term, the local manifold structure is stressed. Subsequently, we propose the ISL-GKFDA (Incomplete Supervision Learning (ISL) with propagation Graph of data in Kernel Fisher Discriminant Analysis) algorithm. We validate ISL-GKFDA by comparing it with FDA (Fisher's Discrimination Analysis), KFDA (Kernel FDA), ISL-FDA (ISL version FDA), ISL-KFDA (ISL version KFDA), SSDA (semi-supervised discriminant analysis based on manifold distance), and KSSDA (Kernel SSDA). In typical manifold datasets, ISL-GKFDA can more accurately capture the boundaries of binary classification; and visually in handwritten digital dataset, ISL-GKFDA can separate three data types more clearly. Finally, we use the UCI database and compare multiple algorithms. When measured by accuracy, the proposed ISL-GKFDA reaches a maximum in at least three datasets of five when labeling ratio is 5%, 15% and 30%, respectively. When measured by F1, ISL-GKFDA reaches the maximum in all datasets.

Validation of the test for finding word retrieval deficits (WoFi) in detecting Alzheimer's disease in a naturalistic clinical setting

BackgroundDetecting impaired naming capacity contributes to the detection of mild (MildND) and major (MajorND) neurocognitive disorder due to Alzheimer’s disease (AD). The Test for Finding Word retrieval deficits (WoFi) is a new, 50-item, auditory stimuli-based instrument.ObjectiveThe study aimed to adapt WoFi to the Greek language, to develop a short version of WoFi (WoFi-brief), to compare the item frequency and the utility of both instruments with the naming subtest of the widely used Addenbrooke’s cognitive examination III (ACEIIINaming) in detecting MildND and MajorND due to AD.MethodsThis cross-sectional, validation study included 99 individuals without neurocognitive disorder, as well as 114 and 49 patients with MildND and MajorND due to AD, respectively. The analyses included categorical principal components analysis using Cramer’s V, assessment of the frequency of test items based on corpora of television subtitles, comparison analyses, Kernel Fisher discriminant analysis models, proportional odds logistic regression (POLR) models and stratified repeated random subsampling used to recursive partitioning to training and validation set (70/30 ratio).ResultsWoFi and WoFi-brief, which consists of 16 items, have comparable item frequency and utility and outperform ACEIIINaming. According to the results of the discriminant analysis, the misclassification error was 30.9%, 33.6% and 42.4% for WoFi, WoFi-brief and ACEIIINaming, respectively. In the validation regression model including WoFi the mean misclassification error was 33%, while in those including WoFi-brief and ACEIIINaming it was 31% and 34%, respectively.ConclusionsWoFi and WoFi-brief are more effective in detecting MildND and MajorND due to AD than ACEIIINaming.

RobustDespeckling: Robust speckle noise reduction method using multi-scale and kernel fisher discriminant analysis

In medical ultrasound imaging, speckle noise is an important property since it usually involves worsening the image resolution along with contrast, thus reducing the diagnostic significance of the imaging modality. The "RobustDespeckling" method, which has been proposed in this study to reduce speckle noise, involves extracting the noise-only signal from the image signal through applying the bidimesional empirical mode decomposition (BEMD) method and wavelet transform (WT) in the encapsulated way. Then, wavelet coefficients are thresholded to filter the noisy coefficients by an optimal threshold parameter that is estimated from kernel fisher discriminant analysis (KFDA). Finally, BEMD and WT processes are employed to obtain a de-noised image. The investigation is conducted by way of upsampling and downsampling operations of ultrasound images to analyze the efficiency of different de-noising techniques including the proposed “RobustDespeckling” method. The visual observation and statistical analysis signify that the “RobustDespeckling” method is robust in minimizing the speckle noise of ultrasound images over existing de-noising techniques. Consequently, the method is more competent to preserve the clarity of the edge without losing the significant image detail.

Seismic response analysis and distribution prediction of source rocks in a survey of the South China Sea

Identification and prediction of high-quality source rocks is the key to obtaining new resources in the exploration area of Cenozoic basins in offshore China. We research the seismic response and distribution of hydrocarbon source rocks using seismic data, well curves, lithologic interpretation, and geochemical analysis. The target is the source rock development zone of the W Formation in a survey of the South China Sea. The results show that the seismic response of thick layer source rocks differ from surrounding rocks in the seismic profile (strong reflections with opposite polarity at the top and bottom and messy or chaotic reflections inside). Seismic reflections of interlayer source rocks have the characteristics of low frequency and continuous strong amplitude. The dominant frequency and maximum amplitude decrease as the number of mudstone layers increases. Through seismic petrophysical analysis, we have obtained three sensitive parameters of source rock in this survey: clay content, P-wave impedance, and elastic impedance. Different classification methods can realize the classification and prediction of hydrocarbon source rocks, among which the Kernel Fisher discriminant analysis method is the best. The prediction results are consistent with the geological background, geochemical information, and well curves.

Time and Space Complexity Reduction of KFDA-based LTE Modulation Classification

Background: Kernel Fisher discriminant analysis (KFDA) is a nonlinear discrimination technique for improving automatic modulation classification (AMC) accuracy. Our study showed that the higher-order cumulants (HOCs) of the Long-term evolution (LTE) modulation types are nonlinearly separable, so the KFDA technique is a good solution for its modulation classification problem. Still, research papers showed that the KFDA suffers from high time and space computational complexity. Some studies concentrated on reducing the KFDA time complexity while preserving the AMC performance accuracy by finding faster calculation techniques, but unfortunately, they couldn't reduce the space complexity. Objective: This study aims to reduce the time and space computational complexity of the KFDA algorithm while preserving the AMC performance accuracy. Methods: Two new time and space complexity reduction algorithms have been proposed. The first algorithm is the most discriminative dataset points (MDDP) algorithm, while the second is the k-nearest neighbors-based clustering (KNN-C) algorithm Results: The simulation results show that these algorithms could reduce the time and space complexities, but their complexity reduction is a function of signal-to-noise ratio (SNR) values. On the other hand, the KNN-C-based KFDA algorithm has less complexity than the MDDP-based KFDA algorithm Conclusion: The time and space computation complexity of the KFDA could be effectively reduced using MDDP and KNN-C algorithms; as a result, its calculation became much faster and had less storage size.

Skill-level classification and performance evaluation for endoscopic sleeve gastroplasty.

We previously developed grading metrics for quantitative performance measurement for simulated endoscopic sleeve gastroplasty (ESG) to create a scalar reference to classify subjects into experts and novices. In this work, we used synthetic data generation and expanded our skill level analysis using machine learning techniques. We used the synthetic data generation algorithm SMOTE to expand and balance our dataset of seven actual simulated ESG procedures using synthetic data. We performed optimization to seek optimum metrics to classify experts and novices by identifying the most critical and distinctive sub-tasks. We used support vector machine (SVM), AdaBoost, K-nearest neighbors (KNN) Kernel Fisher discriminant analysis (KFDA), random forest, and decision tree classifiers to classify surgeons as experts or novices after grading. Furthermore, we used an optimization model to create weights for each task and separate the clusters by maximizing the distance between the expert and novice scores. We split our dataset into a training set of 15 samples and a testing dataset of five samples. We put this dataset through six classifiers, SVM, KFDA, AdaBoost, KNN, random forest, and decision tree, resulting in 0.94, 0.94, 1.00, 1.00, 1.00, and 1.00 accuracy, respectively, for training and 1.00 accuracy for the testing results for SVM and AdaBoost. Our optimization model maximized the distance between the expert and novice groups from 2 to 53.72. This paper shows that feature reduction, in combination with classification algorithms such as SVM and KNN, can be used in tandem to classify endoscopists as experts or novices based on their results recorded using our grading metrics. Furthermore, this work introduces a non-linear constraint optimization to separate the two clusters and find the most important tasks using weights.

On ALIF-WT-GDA-based Terahertz spectral method for identification of transgenic cotton seeds

Terahertz (THz) time-domain spectroscopy can interact with organic molecules to produce “resonance” absorption, and it is suitable for qualitative and quantitative analysis on the basis of spectral absorption mechanism. However, there are some problems with it, such as un-obviousness signal peaks and positions, signal oscillations and low recognition accuracy. Therefore, this paper has proposed a method named ALIF-WT-GDA-based THz spectrum for identifying transgenic cotton seeds, which can strengthen and accurately identify features of the THz spectral data. First, this paper has put forward a pretreatment method of THz spectral data based on Adaptive Local Iterative Filtering (ALIF) and Wavelet Transform (WT). Specifically speaking, ALIF is used to decompose THz time-domain spectral signals and extract useful mode components for signal reconstruction in order to improve the signal-to-noise ratio (SNR). Also, WT is employed to perform smoothing filtering of THz signals, which makes THz absorbance curves much smoother and absorption peak positions much more obvious. Then, thanks to the advantages of kernel methods, Generalized Discriminant Analysis (GDA) method of Kernel Fisher Discriminant Analysis (KFDA) is used for dimension reduction and clustering analysis. Finally, the proposed ALIF-WT-GDA method is adopted for pretreatment and clustering of the THz spectral data from four different types of transgenic cotton seeds, with its identification accuracy of 98.33%. The above result has proved that the proposed ALIF-WT-GDA method is effective.

Elastic impedance inversion incorporating fusion initial model and kernel Fisher discriminant analysis approach

Seismic inversion is a significant technique for estimating petroleum reservoir parameters. The low frequency component of the initial model represents the geological background information, which plays an important role in the seismic inversion. It is challenging to precisely depict the actual geological model in seismic inversion because of the inherent velocity-depth ambiguity. Therefore, the initial model which is closer to genuine geological backdrop is essential. We propose a workflow which estimates a fusion initial model based on data fusion algorithms. It is well known that seismic facies analysis can provide more low-frequency information about the geological background. For example, the boundaries of sedimentary bodies can be represented by seismic facies classification data. We utilize a combination of the seismic facies classification data and well curves interpolation initial models to accurately invert the special geological body with the support of a feature-level fusion algorithm. Then, a practical pre-stack seismic inversion method is implemented, and a field data example further demonstrates its applicability and steadiness in seismic inversion.

Bearing Fault Diagnosis Based on Randomized Fisher Discriminant Analysis.

In this paper, a novel randomized Fisher discriminant analysis (RFDA) based bearing fault diagnosis method is proposed. First, several representative time-domain features are extracted from the raw vibration signals. Second, linear Fisher discriminant analysis (FDA) is extended to nonlinear FDA named RFDA by introducing the random feature map to deal with the non-linearity issue. Specifically, the extracted time-domain features data are mapped onto a high-dimensional space using the random feature map function rather than kernel functions. Third, the time-domain features are fed into the built RFDA model to extract the discriminant features for diagnosis. Moreover, a Bayesian inference is employed to identify the class of the collected vibration signals to diagnose the bearing status. The proposed method uses random Fourier features to approximate the kernel matrix in the kernel Fisher discriminant analysis. Through employing randomized Fisher discriminant analysis, the nonlinearity issue is dealt with, and the computational burden is remarkably reduced compared to the kernel Fisher discriminant analysis (KFDA). To illustrate the superior performance of the proposed RFDA-based bearing fault diagnosis method, comparative experiments are conducted on two widely used datasets, the Case Western Reserve University (CWRU) bearing dataset and the Paderborn University (PU) bearing dataset. For the CWRU dataset, the computation time of RFDA is much shorter than KFDA, while the accuracy rate reaches the same level of KFDA. For the PU dataset, the accuracy rate of RFDA is slightly higher than KFDA, and the computation time is only 44.14% of KFDA.

Research on Face Recognition Algorithm Based on Image Processing.

While network technology is convenient for our daily life, the problems that are exposed are also endless. The most important thing for everyone is information security. In order to improve the security level of network information and identify and detect faces, the method used in this paper has improved compared with the traditional AdaBoost method and skin color method. AdaBoost detection is performed on the image, which reduces the probability of false detection. The experiment compares the experimental results of the AdaBoost method, the skin color method and the skin color + AdaBoost method. All operations in the KPCA and KFDA algorithms are performed by the inner product kernel function defined in the original space, and no specific non-linear mapping function is involved.The full name of KPCA is kernel principal component analysis. The full name of KFDA is kernel Fisher discriminant analysis. Combining the zero-space method kernel discriminant analysis method improves the ability of discriminant analysis to extract non-linear features. Through the secondary extraction of PCA features, a better recognition result than the PCA method is obtained. This paper also proposes a zero-space based Fisher discriminant analysis method. Experiments show that the zero-space-based method makes full use of the useful discriminant information in the zero space of the intraclass dispersion matrix, which improves the accuracy of face recognition to some extent.If you choose the polynomial kernel function, when d = 0.8, KPCA has a higher recognition ability. When d = 2, the recognition rate of KFDA and zero space-based KFDA is the largest. For polynomial functions, in general, d = 2.

Lithofacies identification in carbonate reservoirs by multiple kernel Fisher discriminant analysis using conventional well logs: A case study in A oilfield, Zagros Basin, Iraq

Lithofacies identification in carbonate reservoirs using conventional well logs is a typically complex nonlinear problem due to influences of multiple factors, such as fluids and fractures. Kernel Fisher discriminant analysis (KFD) is a useful nonlinear single-kernelled method to classify lithofacies. However, the prediction capacity of a single kernel is limited to some extent, especially for complicated lithofacies identification problems. To alleviate this issue, a multiple kernel Fisher discriminant analysis (MKFD) method, an improved KFD, is introduced in this work. MKFD utilizes multi-scaled kernel functions to realize the optimal nonlinear mapping instead of a single kernel used by KFD, which can extract more efficient nonlinear lithologic features. It first increases dimension of input data to obtain more nonlinear features and then reduces dimension to extract effective information from these features for lithofacies identification. To examine the effectiveness of MKFD for lithofacies identification in carbonate reservoirs, a conventional log dataset labelled by rock cores from carbonate reservoirs of Asmari Formation in Paleogene Oligocene-Neogene Miocene in A Oilfield, Zagros Basin, Iraq is used. Both statistical (confusion matrix) and geological evaluations (blind well test) indicate that MKFD outperforms KFD and the prediction results of MKFD are more consistent with rock cores. It has been demonstrated that MKFD can provide an accurate and effective means for lithofacies identification in carbonate reservoirs.

Fault Diagnosis of Power Plant Condenser With the Optimized Deep Forest Algorithm

As an important component of power plant operation, condenser fault diagnosis plays a vital role in the safe and stable unit performance. However, the precision of most existing diagnostic methods is not high enough for condenser fault diagnosis. It is considerably difficult to diagnose a condenser fault even under various complicated conditions. In this study, a novel classification hybrid model (PCA-DF) combining the Principal Component Analysis (PCA) method with the Deep Forest (DF) model is proposed based on the motivation of improving the diagnosis accuracy of condenser fault. The algorithm of this hybrid model takes the dimension reduction result of the PCA method as the input to the DF model. The multigrained scanning structure and the dimension reduction method are considered to create a good effect. The experimental results verify the feasibility and effectiveness of this method on the historical fault sample data of the condenser. The focus on the work presented of this paper is to optimize the DF model based on PCA and study the fault diagnosis effect of the hybrid model. Results show that (1) the prediction accuracy for the condenser fault diagnosis can be improved by increasing the sample size with the PCA-DF method. (2) The accuracy of the results obtained by proposing the improved hybrid models is 1%-8% higher than the accuracy of the results obtained by directly introducing the DF model. The modified hybrid models still have advantages over the DF model for a small sample. (3) With an increase in the proportion of training sets, the accuracy of the modified hybrid models is improved correspondingly from 88.18% to 99.23%. (4) Compared with the backpropagation neural network, convolutional neural network, relevance vector machine and kernel Fisher discriminant analysis models, the PCA-DF model has higher accuracy. In this study, the proposed models can eliminate the influence of autocorrelation between data, and condenser fault diagnosis based on modified models has the fastest convergence speed and best accuracy. Furthermore, the proposed novel models can be extended to more complex fault diagnosis in other fields.

Physics-based data-driven interpretation and prediction of rolling contact fatigue damage on high-speed train wheels

Rolling contact fatigue (RCF) of high-speed train wheels is detrimental to reliability and entails huge maintenance costs. Accurate prediction of RCF damage is important for train operators, however, physics-based methods are not suitable for practical applications. Based on accumulated RCF data, this paper develops a physics-based data-driven method for the interpretation and prediction of RCF damage risk. First, based on RCF mechanism, it is found that many relevant parameters can be used for RCF prediction. Then, eight predictors are extracted from RCF-related data through dimensionality reduction methods, including linear discriminant analysis and kernel Fisher discriminant analysis. It shows that greater wheel out-of-roundness or smaller wheel diameters leads to higher RCF risks; previously defective wheels are more likely to reencounter RCF damage; the RCF risk varies in different seasons; the effect of wear on RCF damage is significantly nonlinear. Afterwards, a predictive model is established based on logistic regression. Validation results yield an average accuracy of 75% and also demonstrate its easy interpretability, fast computational speed and stable performance. Further, test result shows an accuracy of 85% to distinguish high-risk wheelsets prior to RCF inspections. The proposed method can be applied to the risk-based maintenance of high-speed train wheels.

An Object Recognition Approach for Synthetic Aperture Radar Images

In this paper, an object recognition approach for synthetic aperture radar (SAR) images is addressed, which is based on the enhanced kernel sparse representation of monogenic signal. It consists of two main modules. In the first module, to capture the spatial and spectral properties of a target at the same time, a multi-scale monogenic feature extraction scheme is proposed. In the second module, an enhanced kernel sparse representation-based classifier (KSRC) is designed. Different from the traditional KSRC, in the enhanced KSRC, we first integrate the kernel principal component analysis (KPCA) as well as the kernel fisher discriminant analysis (KFDA) to generate an augmented pseudo-transformation matrix. Then, a new discriminative feature mapping approach is presented by exploiting the augmented pseudo-transformation matrix so that the dimensionality of the kernel feature space can be effectively reduced. At last, the l1 -norm minimization is utilized to calculate the sparse coefficients for a test sample, and thus the inference can be reached in terms of the total reconstruction error. Experimental results on the public moving and stationary target acquisition and recognition dataset (MSTAR) demonstrate that the proposed method achieves high recognition accuracy for SAR automatic target recognition.

Measures of Scatter and Fisher Discriminant Analysis for Uncertain Data

Uncertain data objects are objects that can be characterized by either a probability density function (PDF) or with multiple points. Because of existing levels of uncertainty for uncertain data objects, the scatter of this type of objects might be very different than the scatter of certain data objects. Measures of scatter for uncertain objects have not been defined before. In this paper, we define covariance matrix, within scatter matrix, and between scatter matrix as the measures of scatter for uncertain data objects. Also, in this paper, we extend the idea of Fisher linear discriminant analysis for uncertain objects (UFLDA). We also develop kernel Fisher discriminant analysis for uncertain objects (UKFDA). The developed uncertain kernel Fisher discriminants are for two cases: 1) when the uncertain objects are given with PDF and 2) when the uncertain objects are given with multiple points. We compare the performance of our developed uncertain Fisher discriminants (UFLDA and UKFDA) with a few other methods in classification of uncertain data objects through several examples on both simulated and real-world data. We will show in the experiments that our developed uncertain Fisher discriminants outperform other methods in classifying uncertain data objects.