Fuzzy Linear Discriminant Analysis Research Articles

Qualitative Analysis of Lambda-Cyhalothrin on Chinese Cabbage Using Mid-Infrared Spectroscopy Combined with Fuzzy Feature Extraction Algorithms

Excess pesticide residues on cabbage are harmful to humans. In this study, we propose an innovative strategy for a quick and nondestructive qualitative test of lambda-cyhalothrin residues on Chinese cabbage. Spectral profiles of Chinese cabbage leaf samples with different concentrations of surface residues of lambda-cyhalothrin were collected with an Agilent Cary 630 FTIR Spectrometer. Standard normal variate (SNV), multiplicative scatter correlation (MSC), and principle component analysis (PCA) were utilized to preprocess the spectra. Then, fuzzy Foley-Sammon transformation (FFST), fuzzy linear discriminant analysis (FLDA), and fuzzy uncorrelated discriminant transformation (FUDT) were employed to extract features from the spectra data. Finally, k-nearest neighbor (kNN) was applied to classify samples according to the concentration of lambda-cyhalothrin residue. The highest identification accuracy rates of FFST, FLDA, and FUDT were 100%, 97.22%, and 100%, respectively. FUDT performed the best considering the combination of accuracy rate and required computing time. We believe that mid-infrared spectroscopy combined with fuzzy uncorrelated discriminant analysis is an effective method to accurately and quickly conduct qualitative analyses of lambda-cyhalothrin residues on Chinese cabbages. This method may have applications in other crops and other pesticide residues.

Fuzzy characterization and classification of bacteria species detected at single-cell level by surface-enhanced Raman scattering

Advanced chemometric methods, such as fuzzy c-means, a semi-supervised clustering method, and fuzzy linear discriminant analysis (FLDA), a new robust supervised classification method in combination with principal component analysis (PCA), namely PCA-FLDA, have been successfully applied for characterization and classification of bacterial species detected at single-cell level by surface-enhanced Raman scattering (SERS) spectroscopy. SERS spectra of three species (S. aureus, E. faecalis and P. aeruginosa) were recorded in an original fashion, using in situ laser induced silver spot as metallic substrate. The detection process of bacteria was isolated inside a hermetically sealed in-house built microfluidic device, connected to a syringe pump for injecting the analytes and a portable Raman spectrometer as detection tool. The obtained results (fuzzy partitions) and spectra of the prototypes (robust fuzzy spectra mean corresponding to each fuzzy partition) clearly demonstrated the efficiency and information power of the advanced fuzzy methods in bacteria characterization and classification based on SERS spectra, and allowed a rationale assigning to a specific group. Also, this powerful detection and classification methodology generates the premises for future investigations of Raman and other spectroscopic data obtained for various samples.

A novel fuzzy linear discriminant analysis for face recognition

A novel fuzzy linear discriminant analysis for face recognition

Performance Comparison of Fuzzy ARTMAP and LDA in Qualitative Classification of Iranian Rosa damascena Essential Oils by an Electronic Nose.

Quality control of essential oils is an important topic in industrial processing of medicinal and aromatic plants. In this paper, the performance of Fuzzy Adaptive Resonant Theory Map (ARTMAP) and linear discriminant analysis (LDA) algorithms are compared in the specific task of quality classification of Rosa damascene essential oil samples (one of the most famous and valuable essential oils in the world) using an electronic nose (EN) system based on seven metal oxide semiconductor (MOS) sensors. First, with the aid of a GC-MS analysis, samples of Rosa damascene essential oils were classified into three different categories (low, middle, and high quality, classes C1, C2, and C3, respectively) based on the total percent of the most crucial qualitative compounds. An ad-hoc electronic nose (EN) system was implemented to sense the samples and acquire signals. Forty-nine features were extracted from the EN sensor matrix (seven parameters to describe each sensor curve response). The extracted features were ordered in relevance by the intra/inter variance criterion (Vr), also known as the Fisher discriminant. A leave-one-out cross validation technique was implemented for estimating the classification accuracy reached by both algorithms. Success rates were calculated using 10, 20, 30, and the entire selected features from the response of the sensor array. The results revealed a maximum classification accuracy of 99% when applying the Fuzzy ARTMAP algorithm and 82% for LDA, using the first 10 features in both cases. Further classification results explained that sub-optimal performance is likely to occur when all the response features are applied. It was found that an electronic nose system employing a Fuzzy ARTMAP classifier could become an accurate, easy, and inexpensive alternative tool for qualitative control in the production of Rosa damascene essential oil.

Classification of Apple Varieties Using Near Infrared Reflectance Spectroscopy and Fuzzy Discriminant C‐Means Clustering Model

AbstractThis research proposed a novel fuzzy clustering model, called fuzzy discriminant c‐means (FDCM) clustering, to classify apple varieties couple with near infrared spectroscopy. FDCM can not only partition samples but also extract discriminant information from them by introducing fuzzy linear discriminant analysis (FLDA) into fuzzy c‐means (FCM) clustering. The 200 apple samples of four apple varieties were made experiments to collect the near infrared reflectance (NIR) spectra. Principal component analysis (PCA) was used to reduce the high dimensionality of NIR spectra data. FDCM and FCM were performed as classifiers to cluster the data, respectively. The clustering accuracy of FDCM achieved 97% which was higher than FCM, possibilistic c‐means and Gustafson–Kessel (GK) clustering. Furthermore, soluble solids content and total acidity of apples were measured, and the quantitative results showed that different types of apples contain different content of the nutritional composition. This makes it feasible for classification of apple varieties via NIR technology. The clustering results obtained in experiments showed that NIR spectroscopy combined with PCA and FDCM clustering could successfully discriminate apple varieties.Practical ApplicationsPostharvest processing of apple is very important for the agricultural industry. For this purpose, the proposed fuzzy discriminant c‐means clustering model coupled with near infrared spectroscopy can be used to select higher quality of apples for grading and sorting machines.

Extended semi-supervised fuzzy learning method for nonlinear outliers via pattern discovery

This article presents an extended Parameterized Fuzzy Semi-supervised learning (PFSL) method, in which the key innovation is the capability of separating a sample set into two independent subsets: outlier sample subset and regular sample subset. In our proposed PFSL, we first develop an improved parameterized Fuzzy Linear Discriminant Analysis (F-LDA) algorithm to classify regular samples, in which the distribution information of each sample in terms of fuzzy membership degree is incorporated with the redefined within-class and between-class scatter matrices. To achieve good parameter estimation for this improved F-LDA, we advocate the use of Hopfield Neural Networks (HNN) due to its efficiency. Second, a new semi-supervised Fuzzy C-Means (S-FCM) algorithm is designed using pre-computed cluster number and cluster centers in the supervised pattern discovery stage. It is applied to classify the remaining outlier samples and generate the final classification result. Third, since Kernel Fisher Discriminant (KFD) is an efficient way to extract nonlinear discriminant features, a kernel version of the proposed PFSL (K-PFSL) is discussed. Extensive experiments on the ORL, NUST603, FERET and Yale face datasets show the effectiveness and the superiority of the proposed algorithm.

Fuzzy Linear Discriminant Analysis-guided maximum entropy fuzzy clustering algorithm

Linear Discriminant Analysis (LDA) is a classical statistical approach for supervised feature extraction and dimensionality reduction, hard c-means (HCM) is a classical unsupervised learning algorithm for clustering. Based on the analysis of the relationship between LDA and HCM, Linear Discriminant Analysis-guided adaptive subspace hard c-means clustering algorithm (LDA–HCM) had been proposed. LDA–HCM combines LDA and HCM into a coherent framework and can adaptively reduce the dimension of data while performing data clustering simultaneously. Seeing that LDA–HCM is still a hard clustering algorithm, we consider the fuzzy extension version of LDA–HCM in this paper. To this end, firstly, we propose a new optimization criterion of Fuzzy Linear Discriminant Analysis (FLDA) by extending the value of membership function in classical LDA from binary 0 or 1 into closed interval [0, 1]. In the meantime, we present an efficient algorithm for the proposed FLDA. Secondly, we show the close relationship between FLDA and Maximum Entropy Fuzzy Clustering Algorithm (MEFCA): they both are maximizing fuzzy between-class scatter and minimizing within-class scatter simultaneously. Finally, based on the above analysis, combining FLDA and MEFCA into a joint framework, we propose fuzzy Linear Discriminant Analysis-guided maximum entropy fuzzy clustering algorithm (FLDA–MEFCA). LDA–MEFCA is a natural and effective fuzzy extension of LDA–HCM. Due to the introduction of soft decision strategy, FLDA–MEFCA can yield fuzzy partition of data set and is more flexible than LDA–HCM. We also give the convergence proof of FLDA–MEFCA. Extensive experiments on a collection of benchmark data sets are presented to show the effectiveness of the proposed algorithm.

Modified Fuzzy Linear Discriminant Analysis for Threshold Selection

Otsu’s thresholding method is a popular and efficient method for image segmentation. However, its performance is greatly affected by noise and the population size of object and background. In this paper, a novel thresholding method is proposed based on modified fuzzy linear discriminant analysis (MFLDA). MFLDA is an extension of linear discriminant analysis to fuzzy domain, where the between-class variance is modified as the distance between the centers of background and object. The optimal threshold is selected such that the MFLDA criterion is maximized. Some images are used to test the performance of the proposed thresholding method and results reveal that the proposed method is less affected by noise, the population size of objects and background, and better segmentation results are obtained than Otsu’s method and other classical thresholding methods.

Random walk-based fuzzy linear discriminant analysis for dimensionality reduction

Dealing with high-dimensional data has always been a major problem with the research of pattern recognition and machine learning, and linear discriminant analysis (LDA) is one of the most popular methods for dimensionality reduction. However, it suffers from the problem of being too sensitive to outliers. Hence to solve this problem, fuzzy membership can be introduced to enhance the performance of algorithms by reducing the effects of outliers. In this paper, we analyze the existing fuzzy strategies and propose a new effective one based on Markov random walks. The new fuzzy strategy can maintain high consistency of local and global discriminative information and preserve statistical properties of dataset. In addition, based on the proposed fuzzy strategy, we then derive an efficient fuzzy LDA algorithm by incorporating the fuzzy membership into learning. Theoretical analysis and extensive simulations show the effectiveness of our algorithm. The presented results demonstrate that our proposed algorithm can achieve significantly improved results compared with other existing algorithms.

Classification of apoptosis proteins by discriminant analysis

Objective: Prediction of the locations of apoptosis proteins which are divided into four locations as cytoplasmic proteins, plasma membrane-bound proteins, mitochondrial inner-outer proteins and other proteins; that have different biological function in each location. Methods: In this paper, we have encoded protein sequences as amino acid composition, thereby protein sequences are expressed via high dimensional structure, and consequently this case causes computational complexity. Principal component analysis has been used to reduce the dimension of apoptosis protein sequences. After this preprocessing step, apoptosis proteins are classified by linear discriminant analysis and fuzzy linear discriminant analysis. Results: The overall prediction accuracies for linear discriminant analysis and fuzzy linear discriminant analysis are obtained as 16.3% and 80.2%, respectively. Apoptosis proteins assigned as testing data set represent overlapping data structure, therefore linear discriminant analysis yields unsuccessful result. Since fuzzy logic is appropriate for classification and clustering of overlapping data, fuzzy linear discriminant analysis, the integration of fuzzy logic and linear discriminant analysis, gives satisfying prediction accuracy rates. Conclusion: It can be argued that the association of fuzzy approach with other classical methods can yield higher and more robust prediction accuracy rates for the classification problems of apoptosis proteins.

Face Recognition based on Fuzzy Linear Discriminant Analysis

Recently, linear discriminant analysis (LDA) was proposed to manifold learning and pattern classification. LDA, a supervised method, aims to find the optimal set of projection vectors that maximize the determinant of the between-class scatter matrix and at the same time minimise the determinant of the within-class scatter matrix. But, since the dimension of vectors is high and the number of observations is small,usually tens or hundreds of samples, an intrinsic limitation of traditional LDA is that it fails to work when the within-class scatter matrix becomes singular, which is known as the small sample size (SSS) problems. In the real-world applications, the performances of face recognition are always affected by variations in illumination conditions and different facial expressions. In this study, the fuzzy linear discriminant analysis (FLDA) algorithm is proposed, in which the fuzzy k-nearest neighbor (FKNN) is implemented to reduce these outer effects to obtain the correct local distribution information to persuit good performance. In the proposed method, a membership degree matrix is firstly calculated using FKNN, then the membership degree is incorporated into the definition of the Laplacian scatter matrix to obtain the fuzzy Laplacian scatter matrix. The optimal projections of FLDA can be obtained by solving a generalised eigenfunction. Experimental results on ORL face databases show the effectiveness of the proposed method.

Illumination Invariant Face Recognition Using Fuzzy LDA and FFNN

The most significant practical challenge for face recognition is perhaps variability in lighting intensity. In this paper, we developed a face recognition which is insensitive to large variation in illumination. Normalization step including two steps, first we used Histogram truncation as a pre-processing step and then we implemented Homomorphic filter. The main idea is that, achieving illumination invariance causes to simplify feature extraction module and increases recognition rate. Then we utilized Fuzzy Linear Discriminant Analysis (FLDA) in feature extraction stage which showed a good discriminating ability compared to other methods while classification is performed using Feedforward Neural Network (FFNN). The experiments were performed on the ORL (Olivetti Research Laboratory) face image database and the results show the present method outweighs other techniques applied on the same database and reported in literature.

A genetically modified fuzzy linear discriminant analysis for face recognition

This paper addresses the face recognition problem through a modification of the Fuzzy Fisherface classification method. In conventional methods, the relationship of each face to a class is assumed to be crisp. The Fuzzy Fisherface method introduces a gradual level of assignment of each face pattern to a class, using a membership grading based upon the K-Nearest Neighbor (KNN) algorithm. This method was further modified by incorporating the membership grade of each face pattern into the calculation of the between-class and within-class scatter matrices, termed as Complete Fuzzy LDA (CFLDA). The present work aims at improving the assignment of class membership by improving the parameters of the membership functions. A genetic algorithm is employed to optimize these parameters by searching the parameter space. Furthermore, the genetic algorithm is used to find the optimal number of nearest neighbors to be considered during the training phase. The experiments were performed on the Olivetti Research Laboratory (ORL) face image database and the results show consistent improvement in the recognition rate when compared to the results from other techniques applied on the same database and reported in literature.

Orthogonal Fuzzy Neighborhood Discriminant Analysis for Multifunction Myoelectric Hand Control

Developing accurate and powerful electromyogram (EMG) driven prostheses controllers that can provide the amputees with effective control on their artificial limbs, has been the focus of a great deal of research in the past few years. One of the major challenges in such research is extracting an informative subset of features that can best discriminate between the different forearm movements. In this paper, a new dimensionality reduction method, referred to as orthogonal fuzzy neighborhood discriminant analysis (OFNDA), is proposed as a response to such a challenge. Unlike existing attempts in fuzzy linear discriminant analysis, the objective of the proposed OFNDA is to minimize the distance between samples that belong to the same class and maximize the distance between the centers of different classes, while taking into account the contribution of the samples to the different classes. The proposed OFNDA is validated on EMG datasets collected from seven subjects performing a range of 5 to 10 classes of forearm movements. Practical results indicate the significance of OFNDA in comparison to many other feature projection methods (including locality preserving and uncorrelated variants of discriminant analysis) with accuracies ranging from 97.66% to 87.84% for 5 to 10 classes of movements, respectively, using only two EMG electrodes.

Fuzzy linear and nonlinear discriminant analysis algorithms for face recognition

This paper presents two novels algorithms based on fuzzy logic and discriminant analysis for face recognition. The first one is a fuzzy extension of a linear discriminant analysis algorithm namely LDA/QR and the second one is a fuzzy extension of kernel scatter-difference based discriminant analysis (KSDA) algorithm. They can deal with small sample size and nonlinear problems which degrade the performance of face recognition system. Experimental results on the ORL and the extended Yale B face databases show that the two proposed approaches, using fuzzy logic, achieves a better performance in face recognition compared with their original versions.

A complete fuzzy discriminant analysis approach for face recognition

In this paper, some studies have been made on the essence of fuzzy linear discriminant analysis (F-LDA) algorithm and fuzzy support vector machine (FSVM) classifier, respectively. As a kernel-based learning machine, FSVM is represented with the fuzzy membership function while realizing the same classification results with that of the conventional pair-wise classification. It outperforms other learning machines especially when unclassifiable regions still remain in those conventional classifiers. However, a serious drawback of FSVM is that the computation requirement increases rapidly with the increase of the number of classes and training sample size. To address this problem, an improved FSVM method that combines the advantages of FSVM and decision tree, called DT-FSVM, is proposed firstly. Furthermore, in the process of feature extraction, a reformative F-LDA algorithm based on the fuzzy k-nearest neighbors (FKNN) is implemented to achieve the distribution information of each original sample represented with fuzzy membership grade, which is incorporated into the redefinition of the scatter matrices. In particular, considering the fact that the outlier samples in the patterns may have some adverse influence on the classification result, we developed a novel F-LDA algorithm using a relaxed normalized condition in the definition of fuzzy membership function. Thus, the classification limitation from the outlier samples is effectively alleviated. Finally, by making full use of the fuzzy set theory, a complete F-LDA (CF-LDA) framework is developed by combining the reformative F-LDA (RF-LDA) feature extraction method and DT-FSVM classifier. This hybrid fuzzy algorithm is applied to the face recognition problem, extensive experimental studies conducted on the ORL and NUST603 face images databases demonstrate the effectiveness of the proposed algorithm.

걸음걸이 인식을 통한 감시용 로봇에서의 개인 확인

The surveillance robot has been an important component in the field of service robot industry. In the surveillance robot technology, one of the most important technology is to identify a person. In this paper, we propose a gait recognition method based on contourlet and fuzzy LDA (Linear Discriminant Analysis) for surveillance robots. After decomposing a gait image into directional subband images by contourlet, features are obtained in each subband by the fuzzy LDA. The final gait recognition is performed by a fusion technique that effectively combines similarities calculated respectively in each local subband. To show the effectiveness of the proposed algorithm, various experiments are performed for CBNU and NLPR DB datasets. From these, we obtained better classification rates in comparison with the result produced by previous methods.

Exploring the structure of supervised data by Discriminant Isometric Mapping

In this paper, we investigated nonlinear dimensionality reduction (NLDR) for supervised learning and introduced a novel algorithm named supervised isometric mapping (SIsomap) which was based on a combination of two well-known methods: isomap and fuzzy linear discriminant analysis (LDA).

SVM 결정법칙에 의한 얼굴 및 서명기반 다중생체인식 시스템

본 논문에서는 SVM에 기반을 둔 결정법칙에 의해 얼굴인식과 서명인식시스템으로 구성된 다중생체인식시스템을 제안하고자 한다. 이를 위해 퍼지 선형판별기법(Fuzzy Linear Discriminant Analysis : Fnzzy LDA)를 이용한 얼굴인식과 선형판별분석기법과 구간매칭기법을 이용한 서명인식을 구축하였다. 두 개의 단일생체인식시스템을 효과적으로 융합시키기 위해 우선 독립적인 두 개의 생체인식시스템에 의해 산출된 매칭도로부터 등록자(Genuine)와 침입자(Impostor)의 확률 분포 모델을 생성한 후, SVM(Support Vector Machine)에 의해 최종 인증하는 구조로 되어있다. 제안된 방법인 SVM기반 결정법칙을 적용하여 실험한 결과 기존에 결정법칙으로 많이 사용되고 있는 가중치합과 결정트리 방식에 비해 각각 <TEX>$1.654{\%}$</TEX>와 <TEX>$3.3{\%}$</TEX>의 인식률 향상을 나타내 제안된 방법의 우수성을 나타냈다. In this paper, we propose a multi-modal biometrics system based on face and signature recognition system. Here, the face recognition system is designed by fuzzy LDA, and the signature recognition system is implemented with the LDA and segment matching methods. To effectively aggregate two systems, we obtain statistical distribution models based on matching values for genuine and impostor, respectively. And then, the final verification is Performed by the support vector machine. From the various experiments, we find that the proposed method shows high recognition rates comparing with the conventional methods.

Fuzzy Classification of Ecological Habitats from FIA Data

Abstract Fuzzy c-mean classification (FCM), multi-layer perceptron neural network (MLP), fuzzy ARTMAP, and linear discriminant analysis (LDA) were used to classify Forest Inventory and Analysis (FIA) plots into six ecological habitats in the U.S. Northeast. Among the four classifiers, both FCM and MLP produced “soft” classifications based on fuzzy membership values. In contrast, fuzzy ARTMAP and LDA generated only “hard” classifications in which a plot is assigned to the dominant habitat class, based on binary logic, without considering any coexisting classes. The error matrix and several accuracy indices were calculated to assess the classification accuracy of the methods and to test the differences among the four classifiers. The classification accuracies of FCM and MLP were 98% and 97%, respectively, for overall classification, while fuzzy ARTMAP and LDA had an overall classification accuracy of 92% and 85%, respectively. The χ2 test showed that there was no significant difference between the FCM and MLP methods in classification accuracy. But they were significantly better than both fuzzy ARTMAP and LDA methods at a significant level of α = 0.05. This study showed that the fuzzy classifiers such as FCM and MLP were preferable in the classification of ecological habitats using FIA plots, especially for the classification of ambiguous plots with mixed overstory and understory species compositions. FOR. SCI. 50(1):117–127.