Generalized Local Discriminant Embedding for Face Recognition

Extracting discriminative features and reducing the dimensionality of data are two main objectives of manifold learning. Among different techniques, nonlinear manifold learning methods have been proposed in order to extract features from data which are not linearly distributed. Kernel trick is one of the famous nonlinear techniques which helps to project the data without an explicit mapping which can be used in combination with different linear techniques (e.g., Linear discriminant analysis and local discriminant embedding (LDE)). In this paper, we propose a Two Subspace-based Kernel Local Discriminant Embedding (TSKLDE) method which extract features from both non-null and null space of the within-class locality preserving scatter matrix of LDE in the kernel space. We evaluated the proposed algorithm using three publicly available face databases. The obtained results demonstrate that the use of both features in TSKLDE leads to more noise tolerant features compared to other kernel methods and to higher discriminant ability than many existing manifold learning techniques.

Hyperspectral image (HSI) has shown promising results in many fields because of its high spectral resolution. However, redundancy and noise in spectral dimension seriously affect the classification of HSI. For this reason, many popular dimensionality reduction (DR) methods are proposed to solve the problem. The local discriminant embedding (LDE) as an effective non-linear method for DR can be more discriminative by constructing two neighborhood graphs. However, HSI is very easy influenced by noise, and the LDE algorithm based on K nearest neighborhood is highly susceptible to interference from extreme point, which may lead to inaccurate graph construction and poor performance of classification. To overcome the problem and retain the advantages of LDE, a modified local discriminant embedding (MLDE) is firstly applied on HSI by constructing neighborhood graphs on a new spectral feature space instead of the original space. We use variance to characterize the pixels similarity of the same class and use covariance to characterize the separation of different classes of pixels. The combination of variance and covariance makes pixels in the same class to be closer and makes greater separation of pixels from different classes, which enhances classification performance of HSI. The way of representing data by using variance and covariance can attenuate the effects of noise. The Log-Euclidean metric is used to capture the similarity between spectral vectors, which can provide a more accurate similarity evaluation than euclidean distance. The experimental results of two hyperspectral datasets demonstrate the effectiveness of our proposed MLDE method.

This paper proposes a new manifold learning-based scheme for multi-fault detection and classification, which utilizes local and nonlocal embedding method to build a statistic index for fault detection and subsequently develops a joint global and local discriminant embedding (GLDE) approach to discover the discriminant features of multiple faults for fault classification. The proposed GLDE approach can capture the global and local/nonlocal structure information of complicated data and obtain the concise discriminant information for classification. Compared with the conventional Fisher discriminant analysis method, GLDE has a strong discriminant power and provides better monitoring results for complex multi-fault Tennessee Eastman process.

Linear discriminant analysis (LDA) is a classical method for discriminative dimensionality reduction. The original LDA may degrade in its performance for non-Gaussian data, and may be unable to extract sufficient features to satisfactorily explain the data when the number of classes is small. Two prominent extensions to address these problems are subclass discriminant analysis (SDA) and mixture subclass discriminant analysis (MSDA). They divide every class into subclasses and re-define the within-class and between-class scatter matrices on the basis of subclass. In this paper we study the issue of how to obtain subclasses more effectively in order to achieve higher class separation. We observe that there is significant overlap between models of the subclasses, which we hypothesise is undesirable. In order to reduce their overlap we propose an extension of LDA, separability oriented subclass discriminant analysis (SSDA), which employs hierarchical clustering to divide a class into subclasses using a separability oriented criterion, before applying LDA optimisation using re-defined scatter matrices. Extensive experiments have shown that SSDA has better performance than LDA, SDA and MSDA in most cases. Additional experiments have further shown that SSDA can project data into LDA space that has higher class separation than LDA, SDA and MSDA in most cases.

Improved PCA + LDA Applies to Gastric Cancer Image Classification Process

We present a subspace learning method, called local discriminant embedding with tensor representation (LDET), that addresses simultaneously the generalization and data representation problems in subspace learning. LDET learns multiple interrelated subspaces for obtaining a lower-dimensional embedding by incorporating both class label information and neighborhood information. By encoding each object as a second- or higher-order tensor, LDET can capture higher-order structures in the data without requiring a large sample size. Extensive empirical studies have been performed to compare LDET with a second- or third-order tensor representation and the original LDE on their face recognition performance. Not only does LDET have a lower computational complexity than LDE, but LDET is also superior to LDE in terms of its recognition accuracy.

We propose a novel set of features extracted using Hybrid Discriminant Analysis (HDA) for use in a facial expression recognition task. HDA is formulated by combining the optimization problems which are solved in Linear Discriminant Analysis (LDA) and Principal Component Analysis (PCA) methods. By tuning weighting parameters, new sets of discriminant directions are obtained. Using these directions for feature extraction, we show that we can obtain excellent recognition rates of 95.9% on a database of 6 expressions plus neutral which is much better than that obtained using PCA or LDA. The performance of HDA is comparable to that of Gabor wavelet based methods. However, the computation time required to form a HDA feature vector is significantly lower than the time required to form a Gabor feature vector making this method very attractive for real-time applications.

Linear discriminant analysis (LDA) is a classical statistical machine-learning method, which aims to find a linear data transformation increasing class discrimination in an optimal discriminant subspace. Traditional LDA sets assumptions related to the Gaussian class distributions and single-label data annotations. In this article, we propose a new variant of LDA to be used in multilabel classification tasks for dimensionality reduction on original data to enhance the subsequent performance of any multilabel classifier. A probabilistic class saliency estimation approach is introduced for computing saliency-based weights for all instances. We use the weights to redefine the between-class and within-class scatter matrices needed for calculating the projection matrix. We formulate six different variants of the proposed saliency-based multilabel LDA (SMLDA) based on different prior information on the importance of each instance for their class(es) extracted from labels and features. Our experiments show that the proposed SMLDA leads to performance improvements in various multilabel classification problems compared to several competing dimensionality reduction methods.

Matrix exponential based semi-supervised discriminant embedding for image classification

Structure–activity relationship study of oxindole-based inhibitors of cyclin-dependent kinases based on least-squares support vector machines

Serum samples were studied using Raman spectroscopy and analyzed through the multivariate statistical methods of principal component analysis (PCA) and linear discriminant analysis (LDA). The blood samples were obtained from 11 patients who were clinically diagnosed with breast cancer and 12 healthy volunteer controls. The PCA allowed us to define the wavelength differences between the spectral bands of the control and patient groups. However, since the differences in the involved molecules were in their tertiary or quaternary structure, it was not possible to determine what molecule caused the observed differences in the spectra. The ratio of the corresponding band intensities were analyzed by calculating the p values and it was found that only seven of these band ratios were significant and corresponded to proteins, phospholipids, and polysaccharides. These specific bands might be helpful during screening for breast cancer using Raman Spectroscopy of serum samples. It is also shown that serum samples from patients with breast cancer and from the control group can be discriminated when the LDA is applied to their Raman spectra.

This paper aims to understand how the discriminative information of neuronal population activity evolves and accumulates over time. We present two classes of approaches namely the probability-based and response-based approaches to predict the perceptual reports of a trained macaque monkey on a single-trial basis by integrating neural signals from multiple electrodes across time. We extend the probability-based integration originally using only the quadratic discriminant analysis (QDA) by considering also the linear discriminant analysis (LDA) and logistic regression methods. Furthermore, we introduce the response-based integration for the QDA, LDA and logistic regression methods. Experimental examples demonstrate the effectiveness of these approaches for determining the perceptual state of a brain under study by integrating its localized spatiotemporal neuronal activity.

Linear Discriminant Analysis (LDA) is a popular statistical method for both feature extraction and dimensionality reduction in face recognition. The major drawback of LDA is the so-called small sample size (3S) problem. This problem always occurs when the total number of training samples is smaller than the dimension of feature space. Under this situation, the within-class scatter matrix Sw becomes singular and LDA approach cannot be implemented directly. To overcome the 3S problem, this paper proposes a novel wavelet-face based subspace LDA algorithm. Wavelet-face feature extraction and dimensionality reduction are based on two-level D4-filter wavelet transform and discarding the null space of total class scatter matrix St. It is shown that our obtained projection matrix satisfies the uncorrelated constraint conditions. Hence in the sense of statistical uncorrelation, this projection matrix is optimal. The proposed method for face recognition has been evaluated with two public available databases, namely ORL and FERET databases. Comparing with existing LDA-based methods to solve the 3S problem, our method gives the best performance.

In this study, we investigated the combined effects of MoS2 QDs' catalytic properties and the colorimetric responses of organic reagents to create a sniffing device based on the sensor array concept of the mammalian olfactory system. The aim was to differentiate the volatile organic compounds (VOCs) present in cigarette smoke. The designed optical nose device was utilized for the classification of various cigarette VOCs. Unsupervised Principal Component Analysis (PCA) and supervised Linear Discriminant Analysis (LDA) methods were employed for data analysis. The LDA analysis showed promising results, with 100% accuracy in both training and cross-validation. To validate the sensor's performance, we assessed its ability to discriminate between five cigarette brands, achieving 100% accuracy in the training set and 82% in the cross-validation set. Additionally, we focused on studying four popular Iranian cigarette brands (Bahman Kootah, Omega, Montana Gold, and Williams), including fraudulent samples. Impressively, the developed sensor array achieved a perfect 100% accuracy in distinguishing these brands and detecting fraud. We further analyzed a total of 126 cigarette samples, including both original and fraudulent ones, using LDA with a matrix size of (126 × 27). The resulting LDA model demonstrated an accuracy of 98%. Our proposed analytical procedure is characterized by its efficiency, affordability, user-friendliness, and reliability. The selectivity exhibited by the developed sensor array positions it as a valuable tool for differentiating between original and counterfeit cigarettes, thus aiding in border control efforts worldwide.

A new face recognition method is proposed in this paper. The proposed method is based on fuzzy regularized linear discriminant analysis (FR-LDA) and combines the regularized linear discriminant analysis (R-LDA) and the fuzzy set theory. R-LDA is based on a new regularized Fisher's discriminant criterion, which is particularly robust against the small sample size problem compared to the traditional one used in LDA. In the proposed method, we calculate the membership degree matrix by Fuzzy K-nearest neighbor (FKNN) and then incorporate the membership degree into the definition of the between-class and within-class scatter matrices and get the fuzzy between-class and within-class scatter matrices. Experimental results obtained on the FERET database demonstrate that the proposed method improves the classification rate performance.