Incremental linear discriminant analysis for face recognition.

Dimensionality reduction methods have been successfully employed for face recognition. Among the various dimensionality reduction algorithms, linear (Fisher) discriminant analysis (LDA) is one of the popular supervised dimensionality reduction methods, and many LDA-based face recognition algorithms/systems have been reported in the last decade. However, the LDA-based face recognition systems suffer from the scalability problem. To overcome this limitation, an incremental approach is a natural solution. The main difficulty in developing the incremental LDA (ILDA) is to handle the inverse of the within-class scatter matrix. In this paper, based on the generalized singular value decomposition LDA (LDA/GSVD), we develop a new ILDA algorithm called GSVD-ILDA. Different from the existing techniques in which the new projection matrix is found in a restricted subspace, the proposed GSVD-ILDA determines the projection matrix in full space. Extensive experiments are performed to compare the proposed GSVD-ILDA with the LDA/GSVD as well as the existing ILDA methods using the face recognition technology face database and the Carneggie Mellon University Pose, Illumination, and Expression face database. Experimental results show that the proposed GSVD-ILDA algorithm gives the same performance as the LDA/GSVD with much smaller computational complexity. The experimental results also show that the proposed GSVD-ILDA gives better classification performance than the other recently proposed ILDA algorithms.     

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.     

基于Fisher判别分析的增量式非负矩阵分解算法

增量式非负矩阵分解算法是基于子空间降维技术的无监督增量学习方法.文中将Fisher判别分析思想引入增量式非负矩阵分解中,提出基于Fisher判别分析的增量式非负矩阵分解算法.首先,利用初始样本训练的先验信息,通过索引矩阵对新增系数矩阵进行初始化赋值.然后,将增量式非负矩阵分解算法的目标函数改进为批量式的增量学习算法,在此基础上施加类间散度最大和类内散度最小的约束.最后,采用乘性迭代的方法计算分解后的因子矩阵.在ORL、Yale B和PIE等3个不同规模人脸数据库上的实验验证文中算法的有效性.     

OPTIMOL: Automatic Online Picture Collection via Incremental Model Learning

The explosion of the Internet provides us with a tremendous resource of images shared online. It also confronts vision researchers the problem of finding effective methods to navigate the vast amount of visual information. Semantic image understanding plays a vital role towards solving this problem. One important task in image understanding is object recognition, in particular, generic object categorization. Critical to this problem are the issues of learning and dataset. Abundant data helps to train a robust recognition system, while a good object classifier can help to collect a large amount of images. This paper presents a novel object recognition algorithm that performs automatic dataset collecting and incremental model learning simultaneously. The goal of this work is to use the tremendous resources of the web to learn robust object category models for detecting and searching for objects in real-world cluttered scenes. Humans contiguously update the knowledge of objects when new examples are observed. Our framework emulates this human learning process by iteratively accumulating model knowledge and image examples. We adapt a non-parametric latent topic model and propose an incremental learning framework. Our algorithm is capable of automatically collecting much larger object category datasets for 22 randomly selected classes from the Caltech 101 dataset. Furthermore, our system offers not only more images in each object category but also a robust object category model and meaningful image annotation. Our experiments show that OPTIMOL is capable of collecting image datasets that are superior to the well known manually collected object datasets Caltech 101 and LabelMe.     

A two-stage linear discriminant analysis via QR-decomposition

Linear discriminant analysis (LDA) is a well-known method for feature extraction and dimension reduction. It has been used widely in many applications involving high-dimensional data, such as image and text classification. An intrinsic limitation of classical LDA is the so-called singularity problems; that is, it fails when all scatter matrices are singular. Many LDA extensions were proposed in the past to overcome the singularity problems. Among these extensions, PCA+LDA, a two-stage method, received relatively more attention. In PCA+LDA, the LDA stage is preceded by an intermediate dimension reduction stage using principal component analysis (PCA). Most previous LDA extensions are computationally expensive, and not scalable, due to the use of singular value decomposition or generalized singular value decomposition. In this paper, we propose a two-stage LDA method, namely LDA/QR, which aims to overcome the singularity problems of classical LDA, while achieving efficiency and scalability simultaneously. The key difference between LDA/QR and PCA+LDA lies in the first stage, where LDA/QR applies QR decomposition to a small matrix involving the class centroids, while PCA+LDA applies PCA to the total scatter matrix involving all training data points. We further justify the proposed algorithm by showing the relationship among LDA/QR and previous LDA methods. Extensive experiments on face images and text documents are presented to show the effectiveness of the proposed algorithm.     

一种改进的线性判别分析算法在人脸识别中的应用

线性判别分析算法是一种经典的特征提取方法,但其仅在大样本情况下适用。本文针对传统线性判别分析算法面临的小样本问题和秩限制问题,提出了一种改进的线性判别分析算法ILDA。该方法在矩阵指数的基础上,重新定义了类内离散度矩阵和类间离散度矩阵,有效地同时提取类内离散度矩阵零空间和非零空间中的信息。若干人脸数据库上的比较实验表明了ILDA在人脸识别方面的有效性。     

LDA merging and splitting with applications to multiagent cooperative learning and system alteration

To adapt linear discriminant analysis (LDA) to real-world applications, there is a pressing need to equip it with an incremental learning ability to integrate knowledge presented by one-pass data streams, a functionality to join multiple LDA models to make the knowledge sharing between independent learning agents more efficient, and a forgetting functionality to avoid reconstruction of the overall discriminant eigenspace caused by some irregular changes. To this end, we introduce two adaptive LDA learning methods: LDA merging and LDA splitting. These provide the benefits of ability of online learning with one-pass data streams, retained class separability identical to the batch learning method, high efficiency for knowledge sharing due to condensed knowledge representation by the eigenspace model, and more preferable time and storage costs than traditional approaches under common application conditions. These properties are validated by experiments on a benchmark face image data set. By a case study on the application of the proposed method to multiagent cooperative learning and system alternation of a face recognition system, we further clarified the adaptability of the proposed methods to complex dynamic learning tasks.     

一种两阶段判别分析方法

为了解决LDA 对复杂分布数据的表达问题,本文提出了一种新的非参数形式的散度矩阵构造方法。该方法 能更好的刻画分类边界信息,并保留更多对分类有用的信息。同时针对小样本问题中非参数结构形式的类内散度矩阵可能奇 异,提出了一种两阶段鉴别分析方法对准则函数进行了最优化求解。该方法通过奇异值分解把人脸图像投影到混合散度矩阵 的主元空间,使类内散度矩阵在投影空间中是非奇异的,通过CS 分解,从理论上分析了同时对角化散度矩阵的求解,并证明了 得到的投影矩阵满足正交约束条件。在ORL,Yale 和YaleB 人脸库上测试的结果显示,改进的算法在性能上优于PCA+LDA, ULDA 和OLDA 等子空间方法。     

SVM-based feature extraction for face recognition

The primary goal of linear discriminant analysis (LDA) in face feature extraction is to find an effective subspace for identity discrimination. The introduction of kernel trick has extended the LDA to nonlinear decision hypersurface. However, there remained inherent limitations for the nonlinear LDA to deal with physical applications under complex environmental factors. These limitations include the use of a common covariance function among each class, and the limited dimensionality inherent to the definition of the between-class scatter. Since these problems are inherently caused by the definition of the Fisher's criterion itself, they may not be solvable under the conventional LDA framework. This paper proposes to adopt a margin-based between-class scatter and a regularization process to resolve the issue. Essentially, we redesign the between-class scatter matrix based on the SVM margins to facilitate an effective and reliable feature extraction. This is followed by a regularization of the within-class scatter matrix. Extensive empirical experiments are performed to compare the proposed method with several other variants of the LDA method using the FERET, AR, and CMU-PIE databases.     

An optimal symmetrical null space criterion of Fisher discriminant for feature extraction and recognition

Linear discriminant analysis (LDA) is one of the most effective feature extraction methods in statistical pattern recognition, which extracts the discriminant features by maximizing the so-called Fisher’s criterion that is defined as the ratio of between-class scatter matrix to within-class scatter matrix. However, classification of high-dimensional statistical data is usually not amenable to standard pattern recognition techniques because of an underlying small sample size (SSS) problem. A popular approach to the SSS problem is the removal of non-informative features via subspace-based decomposition techniques. Motivated by this viewpoint, many elaborate subspace decomposition methods including Fisherface, direct LDA (D-LDA), complete PCA plus LDA (C-LDA), random discriminant analysis (RDA) and multilinear discriminant analysis (MDA), etc., have been developed, especially in the context of face recognition. Nevertheless, how to search a set of complete optimal subspaces for discriminant analysis is still a hot topic of research in area of LDA. In this paper, we propose a novel discriminant criterion, called optimal symmetrical null space (OSNS) criterion that can be used to compute the Fisher’s maximal discriminant criterion combined with the minimal one. Meanwhile, by the reformed criterion, the complete symmetrical subspaces based on the within-class and between-class scatter matrices are constructed, respectively. Different from the traditional subspace learning criterion that derives only one principal subspace, in our approach two null subspaces and their orthogonal complements were all obtained through the optimization of OSNS criterion. Therefore, the algorithm based on OSNS has the potential to outperform the traditional LDA algorithms, especially in the cases of small sample size. Experimental results conducted on the ORL, FERET, XM2VTS and NUST603 face image databases demonstrate the effectiveness of the proposed method.     

IDR/QR: an incremental dimension reduction algorithm via QR decomposition

Dimension reduction is a critical data preprocessing step for many database and data mining applications, such as efficient storage and retrieval of high-dimensional data. In the literature, a well-known dimension reduction algorithm is linear discriminant analysis (LDA). The common aspect of previously proposed LDA-based algorithms is the use of singular value decomposition (SVD). Due to the difficulty of designing an incremental solution for the eigenvalue problem on the product of scatter matrices in LDA, there has been little work on designing incremental LDA algorithms that can efficiently incorporate new data items as they become available. In this paper, we propose an LDA-based incremental dimension reduction algorithm, called IDR/QR, which applies QR decomposition rather than SVD. Unlike other LDA-based algorithms, this algorithm does not require the whole data matrix in main memory. This is desirable for large data sets. More importantly, with the insertion of new data items, the IDR/QR algorithm can constrain the computational cost by applying efficient QR-updating techniques. Finally, we evaluate the effectiveness of the IDR/QR algorithm in terms of classification error rate on the reduced dimensional space. Our experiments on several real-world data sets reveal that the classification error rate achieved by the IDR/QR algorithm is very close to the best possible one achieved by other LDA-based algorithms. However, the IDR/QR algorithm has much less computational cost, especially when new data items are inserted dynamically.     

改进的基于Gabor-LDA的人脸识别方法

鉴于Gabor特征对光照、表情等变化比较鲁棒,并已在人脸识别领域取得成功应用,提出了一种改进的Gabor-LDA算法.首先对人脸图像进行多方向、多尺度Gabor小渡滤波,然后对得到的特征向量使用改进的主成分分析方法(PCA)变换降维,采用自适应加权原理重建类内散布矩阵和类间散布矩阵,从而改进了最佳鉴别分析(LDA)判别函数,有效地解决了训练样本类均值与类中心的偏离问题.对Yale人脸库的数值试验表明,该算法比传统算法有更好的性能.     

一种半监督判别邻域嵌入算法

邻域保持嵌入（Neighborhood Preserving Embedding,NPE）,作为局部线性嵌入（Locally Linear Embedding,LLE）的线性化版本,由于在映射前后保持了数据的局部几何结构并得到了原始数据的子空间描述,在模式识别领域具有较强的应用价值。但作为非监督处理算法,在具体的模式分类中有一定局限性,提出一种NPE的改进算法——半监督判别邻域嵌入（SSDNE）算法,引入标记后样本点的类别信息,并在正则项中引入样本的流形结构,最大化标记样本点的类间信息和类内信息。既增加了算法的辨别能力又减少了监督算法中对样本点进行全标记的工作量。在ORL和YaleB人脸库上的实验结果表明,改进的算法较PCA、LDA、LPP以及原保持近邻判别嵌入算法的识别性能有了较明显的改善。     

Cancer classification by gradient LDA technique using microarray gene expression data

Cancer classification is one of the major applications of the microarray technology. When standard machine learning techniques are applied for cancer classification, they face the small sample size (SSS) problem of gene expression data. The SSS problem is inherited from large dimensionality of the feature space (due to large number of genes) compared to the small number of samples available. In order to overcome the SSS problem, the dimensionality of the feature space is reduced either through feature selection or through feature extraction. Linear discriminant analysis (LDA) is a well-known technique for feature extraction-based dimensionality reduction. However, this technique cannot be applied for cancer classification because of the singularity of the within-class scatter matrix due to the SSS problem. In this paper, we use Gradient LDA technique which avoids the singularity problem associated with the within-class scatter matrix and shown its usefulness for cancer classification. The technique is applied on three gene expression datasets; namely, acute leukemia, small round blue-cell tumour (SRBCT) and lung adenocarcinoma. This technique achieves lower misclassification error as compared to several other previous techniques.     

Incremental Tensor Subspace Learning and Its Applications to Foreground Segmentation and Tracking

Appearance modeling is very important for background modeling and object tracking. Subspace learning-based algorithms have been used to model the appearances of objects or scenes. Current vector subspace-based algorithms cannot effectively represent spatial correlations between pixel values. Current tensor subspace-based algorithms construct an offline representation of image ensembles, and current online tensor subspace learning algorithms cannot be applied to background modeling and object tracking. In this paper, we propose an online tensor subspace learning algorithm which models appearance changes by incrementally learning a tensor subspace representation through adaptively updating the sample mean and an eigenbasis for each unfolding matrix of the tensor. The proposed incremental tensor subspace learning algorithm is applied to foreground segmentation and object tracking for grayscale and color image sequences. The new background models capture the intrinsic spatiotemporal characteristics of scenes. The new tracking algorithm captures the appearance characteristics of an object during tracking and uses a particle filter to estimate the optimal object state. Experimental evaluations against state-of-the-art algorithms demonstrate the promise and effectiveness of the proposed incremental tensor subspace learning algorithm, and its applications to foreground segmentation and object tracking.     

基于对称线性判别分析算法的人脸识别

小样本问题的存在使得类内离散度矩阵为奇异阵,因此求解线性判别分析(LDA)算法的广义特征方程存在病态奇异问题。为解决此问题,在已有算法的基础上,引入镜像图像来扩大样本容量,并采用零空间的方法求得Fisher准则函数的最优解。通过在ORL和Yale标准人脸库上的实验结果表明,人脸识别效果优于传统LDA方法、独立成分分析(ICA)方法以及二维对称主成分分析(2DSPCA)方法。     

Convolutional neural network feature maps selection based on LDA

Convolutional neural network (CNN), as widely applied to vision and speech, has developed lager and lager network size in last few years. In this paper, we propose a CNN feature maps selection method which can simplify CNN structure on the premise of stabilize the classifier performance. Our approach aims to cut the feature map number of the last subsampling layer and achieves shortest runtime on the basis of Linear Discriminant Analysis (LDA). We rebuild feature maps selection formula based on the between-class scatter matrix and within-class scatter matrix, because LDA can lead to information loss in the dimension-reduction process. Our experiments measure on two standard datasets and a dataset made by ourselves. According to the separability value of each feature map, we suggest the least number of feature maps which can keep the classifier performance. Furthermore, we prove that separability value is an effective indicator for reference to select feature maps.     

面对类别不平衡的增量在线序列极限学习机

针对在线序列极限学习机对于类别不平衡数据的学习效率低、分类准确率差的问题,提出了面对类别不平衡的增量在线序列极限学习机(IOS-ELM)。该算法根据类别不平衡比例调整平衡因子,利用分块矩阵的广义逆矩阵对隐含层节点数进行寻优,提高了模型对类别不平衡数据的在线处理能力,最后通过14个二类和多类不平衡数据集对该算法有效性和可行性进行验证。实验结果表明:该算法与同类其他算法相比具有更好的泛化性和准确率,适用于类别不平衡场景下的在线学习。     

Globally maximizing, locally minimizing: unsupervised discriminant projection with applications to face and palm biometrics

This paper develops an unsupervised discriminant projection (UDP) technique for dimensionality reduction of high-dimensional data in small sample size cases. UDP can be seen as a linear approximation of a multimanifolds-based learning framework which takes into account both the local and nonlocal quantities. UDP characterizes the local scatter as well as the nonlocal scatter, seeking to find a projection that simultaneously maximizes the nonlocal scatter and minimizes the local scatter. This characteristic makes UDP more intuitive and more powerful than the most up-to-date method, locality preserving projection (LPP), which considers only the local scatter for clustering or classification tasks. The proposed method is applied to face and palm biometrics and is examined using the Yale, FERET, and AR face image databases and the PolyU palmprint database. The experimental results show that UDP consistently outperforms LPP and PCA and outperforms LDA when the training sample size per class is small. This demonstrates that UDP is a good choice for real-world biometrics applications     

Kernel machine-based rank-lifting regularized discriminant analysis method for face recognition

To address two problems, namely nonlinear problem and singularity problem, of linear discriminant analysis (LDA) approach in face recognition, this paper proposes a novel kernel machine-based rank-lifting regularized discriminant analysis (KRLRDA) method. A rank-lifting theorem is first proven using linear algebraic theory. Combining the rank-lifting strategy with three-to-one regularization technique, the complete regularized methodology is developed on the within-class scatter matrix. The proposed regularized scheme not only adjusts the projection directions but tunes their corresponding weights as well. Moreover, it is shown that the final regularized within-class scatter matrix approaches to the original one as the regularized parameter tends to zero. Two public available databases, namely FERET and CMU PIE face databases, are selected for evaluations. Compared with some existing kernel-based LDA methods, the proposed KRLRDA approach gives superior performance.