Comments on "globally maximizing, locally minimizing: unsupervised discriminant projection with application to face and palm biometrics"

In (Yang et al., 2007), UDP is proposed to address the limitation of LPP for the clustering and classification tasks. In this communication, we show that the basic ideas of UDP and LPP are identical. In particular, UDP is just a simplified version of LPP on the assumption that the local density is uniform.     

核无监督鉴别投影及人脸识别

提出一种基于核方法的无监督鉴别投影,在较好地描述人脸图像的同时,对图像进行有效地分类.对核局部保留投影(KLPP)和无监督鉴别投影技术(UDP)进行了相应的研究,将两者互相结合.该方法同时考虑到样本的局部特性和非局部特性,有效地利用了对分类有用的重要信息;此外,将核方法和流形学习方法结合起来,有效地描述人脸图像的非线性变化,对于人脸识别问题有较好的效果.在Yale库上的实验表明,该方法的识别率明显高于UDP和PCA,且有较好的分类效果.     

Orthogonal local spline discriminant projection with application to face recognition

In this paper, an efficient feature extraction algorithm called orthogonal local spline discriminant projection (O-LSDP) is proposed for face recognition. Derived from local spline embedding (LSE), O-LSDP not only inherits the advantages of LSE which uses local tangent space as a representation of the local geometry so as to preserve the local structure, but also makes full use of class information and orthogonal subspace to improve discriminant power. Extensive experiments on several standard face databases demonstrate the effectiveness of the proposed method.     

最小距离鉴别投影及其在人脸识别中的应用

针对人脸识别问题,提出了最小距离鉴别投影算法,其与经典的线性鉴别分析不同,它是一种流形学习降维算法。该算法首先定义样本的类内相似度与类间相似度:前者能够度量样本与类内中心的距离关系,后者不仅能够反映样本与类间中心的距离关系而且能够反映样本类间距与类内距的大小关系;然后将高维数据映射到低维特征空间,使得样本到类内中心距离最小同时到类间中心距离最大。最后,在ORL、FERET及AR人脸库上的实验结果表明所提算法识别性能要优于其他算法。     

Semi-supervised locally discriminant projection for classification and recognition

Semi-supervised dimensional reduction methods play an important role in pattern recognition, which are likely to be more suitable for plant leaf and palmprint classification, since labeling plant leaf and palmprint often requires expensive human labor, whereas unlabeled plant leaf and palmprint is far easier to obtain at very low cost. In this paper, we attempt to utilize the unlabeled data to aid plant leaf and palmprint classification task with the limited number of the labeled plant leaf or palmprint data, and propose a semi-supervised locally discriminant projection (SSLDP) algorithm for plant leaf and palmprint classification. By making use of both labeled and unlabeled data in learning a transformation for dimensionality reduction, the proposed method can overcome the small-sample-size (SSS) problem under the situation where labeled data are scant. In SSLDP, the labeled data points, combined with the unlabeled data ones, are used to construct the within-class and between-class weight matrices incorporating the neighborhood information of the data set. The experiments on plant leaf and palmprint databases demonstrate that SSLDP is effective and feasible for plant leaf and palmprint classification.     

Incremental two-dimensional linear discriminant analysis with applications to face recognition

Two dimensional linear discriminant analysis (2DLDA) has been verified as an effective method to solve the small sample size (SSS) problem in linear discriminant analysis (LDA). However, most of the existing 2DLDA techniques do not support incremental subspace analysis for updating the discriminant eigenspace. Incremental learning has proven to enable efficient training if large amounts of training data have to be processed or if not all data are available in advance as, for example, in on-line situations. Instead of having to re-training across the entire training data whenever a new sample is added, this paper proposed an incremental two-dimensional linear discriminant analysis (I2DLDA) algorithm with closed-form solution to extract facial features of the appearance image on-line. The proposed I2DLDA inherits the advantages of the 2DLDA and the Incremental LDA (ILDA) and overcomes the number of the classes or chunk size limitation in the ILDA because the size of the between-class scatter matrix and the size of the within-class scatter matrix in the I2DLDA are much smaller than the ones in the ILDA. The results on experiments using the ORL and XM2VTS databases show that the I2DLDA is computationally more efficient than the batch 2DLDA and can achieve better recognition results than the ILDA.     

SRC最佳鉴别投影及其在人脸识别中的应用

根据稀疏表示分类器的分类准则,提出了一种稀疏表示分类器最佳判别的投影方法。该方法优化两个目标,一是数据集的类间和类内稀疏重构误差,二是数据集中区分度。优化结果使样本投影到低维空间中,确保SRC具有更好的分类性能。在AR和Yale数据库上进行人脸识别实验,并与几种流行的方法进行了比较,结果表明所提出的方法具有良好的有效性和鲁棒性。     

Feature extraction based on fuzzy class mean embedding (FCME) with its application to face and palm biometrics

In the local discriminant embedding (LDE) framework, the neighbor and class of data points were used to construct the graph embedding for classification problems. From a high-dimensional to a low-dimensional subspace, data points of the same class maintain their intrinsic neighbor relations, whereas neighboring data points of different classes no longer stick to one another. However, face images are always affected by variations in illumination conditions and different facial expressions in the real world. So, distant data points are not deemphasized efficiently by LDE and it may degrade the performance of classification. In order to solve above problems, in this paper, we investigate the fuzzy set theory and class mean of LDE, called fuzzy class mean embedding (FCME), using the fuzzy k-nearest neighbor (FKNN) and the class sample average to enhance its discriminant power in their mapping into a low dimensional space. In the proposed method, a membership degree matrix is firstly calculated using FKNN, then the membership degree and class mean are incorporated into the definition of the Laplacian scatter matrix. The optimal projections of FCME can be obtained by solving a generalized eigenfunction. Experimental results on the Wine dataset, ORL, Yale, AR, FERET face database and PolyU palmprint database show the effectiveness of the proposed method.     

Multimodal soft biometrics: combining ear and face biometrics for age and gender classification

Multimedia Tools and Applications - In this paper, we present a multimodal, multitask deep convolutional neural network framework for age and gender classification. In the developed framework, we...     

Non-parametric unsupervised learning with applications to image classification

A non-parametric, unsupervised learning technique is described. The technique makes use of a relation matrix to classify binary pattern vectors presented in random sequence. As each vector is classified, the elements of the matrix are adjusted in such a way as to reinforce the latest class assignment. A preliminary analysis shows that this process produces decision surfaces of a reasonable form. Extensive experiments with both simulated and real-world data confirm that the method performs very well in many circumstances.     

Median Fisher Discriminator: a robust feature extraction method with applications to biometrics

In existing Linear Discriminant Analysis (LDA) models, the class population mean is always estimated by the class sample average. In small sample size problems, such as face and palm recognition, however, the class sample average does not suffice to provide an accurate estimate of the class population mean based on a few of the given samples, particularly when there are outliers in the training set. To overcome this weakness, the class median vector is used to estimate the class population mean in LDA modeling. The class median vector has two advantages over the class sample average: (1) the class median (image) vector preserves useful details in the sample images, and (2) the class median vector is robust to outliers that exist in the training sample set. In addition, a weighting mechanism is adopted to refine the characterization of the within-class scatter so as to further improve the robustness of the proposed model. The proposed Median Fisher Discriminator (MFD) method was evaluated using the Yale and the AR face image databases and the PolyU (Polytechnic University) palmprint database. The experimental results demonstrated the robustness and effectiveness of the proposed method.     

Locality preserving and global discriminant projection with prior information

Existing supervised and semi-supervised dimensionality reduction methods utilize training data only with class labels being associated to the data samples for classification. In this paper, we present a new algorithm called locality preserving and global discriminant projection with prior information (LPGDP) for dimensionality reduction and classification, by considering both the manifold structure and the prior information, where the prior information includes not only the class label but also the misclassification of marginal samples. In the LPGDP algorithm, the overlap among the class-specific manifolds is discriminated by a global class graph, and a locality preserving criterion is employed to obtain the projections that best preserve the within-class local structures. The feasibility of the LPGDP algorithm has been evaluated in face recognition, object categorization and handwritten Chinese character recognition experiments. Experiment results show the superior performance of data modeling and classification to other techniques, such as linear discriminant analysis, locality preserving projection, discriminant locality preserving projection and marginal Fisher analysis.     

From projection pursuit and CART to adaptive discriminant analysis?

While many efforts have been put into the development of nonlinear approximation theory and its applications to signal and image compression, encoding and denoising, there seems to be very few theoretical developments of adaptive discriminant representations in the area of feature extraction, selection and signal classification. In this paper, we try to advocate the idea that such developments and efforts are worthwhile, based on the theoretical study of a data-driven discriminant analysis method on a simple-yet instructive-example. We consider the problem of classifying a signal drawn from a mixture of two classes, using its projections onto low-dimensional subspaces. Unlike the linear discriminant analysis (LDA) strategy, which selects subspaces that do not depend on the observed signal, we consider an adaptive sequential selection of projections, in the spirit of nonlinear approximation and classification and regression trees (CART): at each step, the subspace is enlarged in a direction that maximizes the mutual information with the unknown class. We derive explicit characterizations of this adaptive discriminant analysis (ADA) strategy in two situations. When the two classes are Gaussian with the same covariance matrix but different means, the adaptive subspaces are actually nonadaptive and can be computed with an algorithm similar to orthonormal matching pursuit. When the classes are centered Gaussians with different covariances, the adaptive subspaces are spanned by eigen-vectors of an operator given by the covariance matrices (just as could be predicted by regular LDA), however we prove that the order of observation of the components along these eigen-vectors actually depends on the observed signal. Numerical experiments on synthetic data illustrate how data-dependent features can be used to outperform LDA on a classification task, and we discuss how our results could be applied in practice.     

Structural hidden Markov models for biometrics: Fusion of face and fingerprint

The goal of this paper is threefold: (i) propose a novel face and fingerprint feature modeling using the structural hidden Markov models (SHMMs) paradigm, (ii) explore the use of some feature extraction techniques such as ridgelet transform, discrete wavelet transform with various classifiers for biometric identification, and (iii) determine the best method for classifier combination. The experimental results reported in both fingerprint and face recognition reveal that the SHMMs concept is promising since it has outperformed several state-of-the-arts classifiers when combined with the discrete wavelet transform. Besides, this study has shown that the ridgelet transform without principal components analysis (PCA) dimension reduction fits better with the support vector machines (SVMs) classifier than it does with the SHMMs in the fingerprint recognition task. Finally, these results also reveal a small improvement of the bimodal biometric system over unimodal systems; which suggest that a most effective fusion scheme is necessary.     

Kernel-based improved discriminant analysis and its application to face recognition

Kernel discriminant analysis (KDA) is a widely used tool in feature extraction community. However, for high-dimensional multi-class tasks such as face recognition, traditional KDA algorithms have the limitation that the Fisher criterion is nonoptimal with respect to classification rate. Moreover, they suffer from the small sample size problem. This paper presents a variant of KDA called kernel-based improved discriminant analysis (KIDA), which can effectively deal with the above two problems. In the proposed framework, origin samples are projected firstly into a feature space by an implicit nonlinear mapping. After reconstructing between-class scatter matrix in the feature space by weighted schemes, the kernel method is used to obtain a modified Fisher criterion directly related to classification error. Finally, simultaneous diagonalization technique is employed to find lower-dimensional nonlinear features with significant discriminant power. Experiments on face recognition task show that the proposed method is superior to the traditional KDA and LDA.     

PCAPooL: unsupervised feature learning for face recognition using PCA,LBP, and pyramid pooling

Pattern Analysis and Applications - Human face is a widely used biometric modality for verification and revealing the identity of a person. In spite of a great deal of research on face recognition,...     

A novel Bayesian logistic discriminant model: An application to face recognition

The linear discriminant analysis (LDA) is a linear classifier which has proven to be powerful and competitive compared to the main state-of-the-art classifiers. However, the LDA algorithm assumes the sample vectors of each class are generated from underlying multivariate normal distributions of common covariance matrix with different means (i.e., homoscedastic data). This assumption has restricted the use of LDA considerably. Over the years, authors have defined several extensions to the basic formulation of LDA. One such method is the heteroscedastic LDA (HLDA) which is proposed to address the heteroscedasticity problem. Another method is the nonparametric DA (NDA) where the normality assumption is relaxed. In this paper, we propose a novel Bayesian logistic discriminant (BLD) model which can address both normality and heteroscedasticity problems. The normality assumption is relaxed by approximating the underlying distribution of each class with a mixture of Gaussians. Hence, the proposed BLD provides more flexibility and better classification performances than the LDA, HLDA and NDA. A subclass and multinomial versions of the BLD are proposed. The posterior distribution of the BLD model is elegantly approximated by a tractable Gaussian form using variational transformation and Jensen's inequality, allowing a straightforward computation of the weights. An extensive comparison of the BLD to the LDA, support vector machine (SVM), HLDA, NDA and subclass discriminant analysis (SDA), performed on artificial and real data sets, has shown the advantages and superiority of our proposed method. In particular, the experiments on face recognition have clearly shown a significant improvement of the proposed BLD over the LDA.     

Sparsity preserving projections with applications to face recognition

Dimensionality reduction methods (DRs) have commonly been used as a principled way to understand the high-dimensional data such as face images. In this paper, we propose a new unsupervised DR method called sparsity preserving projections (SPP). Unlike many existing techniques such as local preserving projection (LPP) and neighborhood preserving embedding (NPE), where local neighborhood information is preserved during the DR procedure, SPP aims to preserve the sparse reconstructive relationship of the data, which is achieved by minimizing a L1 regularization-related objective function. The obtained projections are invariant to rotations, rescalings and translations of the data, and more importantly, they contain natural discriminating information even if no class labels are provided. Moreover, SPP chooses its neighborhood automatically and hence can be more conveniently used in practice compared to LPP and NPE. The feasibility and effectiveness of the proposed method is verified on three popular face databases (Yale, AR and Extended Yale B) with promising results.     

A blur-robust descriptor with applications to face recognition

Understanding the effect of blur is an important problem in unconstrained visual analysis. We address this problem in the context of image-based recognition by a fusion of image-formation models and differential geometric tools. First, we discuss the space spanned by blurred versions of an image and then, under certain assumptions, provide a differential geometric analysis of that space. More specifically, we create a subspace resulting from convolution of an image with a complete set of orthonormal basis functions of a prespecified maximum size (that can represent an arbitrary blur kernel within that size), and show that the corresponding subspaces created from a clean image and its blurred versions are equal under the ideal case of zero noise and some assumptions on the properties of blur kernels. We then study the practical utility of this subspace representation for the problem of direct recognition of blurred faces by viewing the subspaces as points on the Grassmann manifold and present methods to perform recognition for cases where the blur is both homogenous and spatially varying. We empirically analyze the effect of noise, as well as the presence of other facial variations between the gallery and probe images, and provide comparisons with existing approaches on standard data sets.