Locality Preserving Discriminant Analysis Research Articles

Learning in multimodal and mixmodal data: locality preserving discriminant analysis with kernel and sparse representation techniques

We consider the problem of feature extraction for “multimodal” and “mixmodal” data. A new supervised learning method called locality preserving discriminant analysis (LPDA) is presented, which aims to maximize the weighted between-class distances and minimize the locality-preserved within-class distances. By introducing a specific affinity matrix for each class, LPDA can better preserve the local geometric structure of the samples within it, and thus efficiently derive nonlinear characters of the data structure. Meanwhile, by using the defined between-class weight matrix, LPDA also preserves the interrelation information of data from different classes. This facilitates the separation of between-class data. We further extend LPDA to kernel-LPDA and sparse-LPDA by taking advantage of theories of kernel technique and sparse representation. Experiments for data classification, handwriting and face recognition are carried out to verify the feasibility and effectiveness of the proposed approaches.

Single Sample Face Recognition using LGBP and Locality Preserving Discriminant Analysis

On single sample condition, current face recognition algorithm yields serious performance drop or even fail to work, therefore a face recognition algorithm based on LGBP and locality preserving discriminant analysis (LPDA) was proposed. Image enhancement and geometric transformation were firstly introduced to single sample face image for face reconstruction, making reconstruct image and original counterpart as a new training sample set. The feature of LGBP was then adopted for face image feature extraction. Afterwards LPDA was used for feature dimension reduction. Classification was finally accomplished by Euclidean distanceNearest Neighbour Classifier. The validity of this algorithm was testified by ORL database, Yale database and FERET database.

Fault diagnosis by Locality Preserving Discriminant Analysis and its kernel variation

Linear Discriminant Analysis (LDA) and its nonlinear kernel variation Generalized Discriminant Analysis (GDA) are the most popular supervised dimensionality reduction methods for fault diagnosis. However, we argue that they probably provide suboptimal results for fault diagnosis due to the Fisher's criterion they use. This paper proposes a new supervised dimensionality reduction method named Locality Preserving Discriminant Analysis (LPDA) and its kernel variation Kernel LPDA (KLPDA) for fault diagnosis. (K)LPDA maximizes a new criterion such that local discriminant structure and local geometric structure in data are optimally preserved simultaneously in each dimension of the reduced space. The criterion directly targets at minimizing local overlapping between different classes. Extensive simulations on the Tennessee Eastman (TE) benchmark simulation process and a waste water treatment plant (WWTP) clearly demonstrate the superiority of our methods in terms of misclassification rate and making use of extra training data.

Dynamic fault diagnosis using extended matrix and tensor locality preserving discriminant analysis

It is well acknowledged that utilizing dynamic information can improve accuracy in fault diagnosis for dynamic processes. Conventional methods encode dynamic information by constructing an extended vector comprising current process data as well as past process data. Then the classic Linear Discriminant Analysis (LDA) is usually applied to extended vectors to reduce dimensionality and obtain a discriminative subspace where overlapping among different fault classes is minimized. However, using extended vectors aggravates the “curse of dimensionality” problem and loses structure information in variables. Besides, LDA probably provides suboptimal results when there are more than two candidate fault classes. This paper proposes using extended matrices to encoding dynamic information and using a novel dimensionality reduction method named Tensor Locality Preserving Discriminant Analysis (TLPDA) to perform dimensionality reduction on extend matrices directly. TLPDA is based on local structure in data and overcomes the main drawbacks of LDA. A new dynamic fault diagnosis scheme is developed based on extended matrices and TLPDA. Extensive simulations on the Tennessee Eastman (TE) benchmark simulation process clearly demonstrate the superiority of our methods in terms of misclassification rate and making use of extra training data.

Locality-Preserving Discriminant Analysis in Kernel-Induced Feature Spaces for Hyperspectral Image Classification

Linear discriminant analysis (LDA) has been widely applied for hyperspectral image (HSI) analysis as a popular method for feature extraction and dimensionality reduction. Linear methods such as LDA work well for unimodal Gaussian class-conditional distributions. However, when data samples between classes are nonlinearly separated in the input space, linear methods such as LDA are expected to fail. The kernel discriminant analysis (KDA) attempts to address this issue by mapping data in the input space onto a subspace such that Fisher's ratio in an intermediate (higher-dimensional) kernel-induced space is maximized. In recent studies with HSI data, KDA has been shown to outperform LDA, particularly when the data distributions are non-Gaussian and multimodal, such as when pixels represent target classes severely mixed with background classes. In this letter, a modified KDA algorithm, i.e., kernel local Fisher discriminant analysis (KLFDA), is studied for HSI analysis. Unlike KDA, KLFDA imposes an additional constraint on the mapping-it ensures that neighboring points in the input space stay close-by in the projected subspace and vice versa. Classification experiments with a challenging HSI task demonstrate that this approach outperforms current state-of-the-art HSI-classification methods.

Kernel Self-optimized Locality Preserving Discriminant Analysis for feature extraction and recognition

We propose Kernel Self-optimized Locality Preserving Discriminant Analysis (KSLPDA) for feature extraction and recognition. The procedure of KSLPDA is divided into two stages, i.e., one is to solve the optimal expansion of the data-dependent kernel with the proposed kernel self-optimization method, and the second is to seek the optimal projection matrix for dimensionality reduction. Since the optimal parameters of data-dependent kernel are achieved automatically through solving the constraint optimization equation, based on maximum margin criterion and Fisher criterion in the empirical feature space, KSLPDA works well on feature extraction for classification. The comparative experiments show that KSLPDA outperforms PCA, LDA, LPP, supervised LPP and kernel supervised LPP.