Popular Subspace Methods Research Articles

Riemannian Optimal Identification Method for Linear Systems With Symmetric Positive-Definite Matrix

This article develops identification methods for linear continuous-time symmetric systems, such as electrical network systems, multiagent network systems, and temperature dynamics in buildings. To this end, we formulate three system identification problems for the corresponding discrete-time systems. The first is a least-squares problem in which we wish to minimize the sum of squared errors between the true and model outputs on the product manifold of the manifold of symmetric positive-definite matrices and two Euclidean spaces. In the second problem, to reduce the search dimensions, the product manifold is replaced with the quotient set under a specified group action by the orthogonal group. In the third problem, the manifold of symmetric positive-definite matrices in the first problem is replaced by the manifold of matrices with only positive diagonal elements. In particular, we examine the quotient geometry in the second problem. We propose Riemannian conjugate gradient methods for the three problems, and select initial points using a popular subspace method. The effectiveness of our proposed methods is demonstrated through numerical simulations and comparisons with the Gauss–Newton method, which is one of the most popular approach for solving least-squares problems.

Closed-loop subspace identification algorithm based on correlation function estimates

A novel subspace identification method based on correlation function which estimates a state-space system dynamics of unknown plant operating in closed-loop experimental condition is proposed in this paper. It is shown that the cross-correlation function of the output and external input signals are equal to the cross-correlation function of the input and external signals filtered through the system dynamics since noise signal has no correlation with the external input. The proposed algorithm is developed to obtain unbiased estimates of system matrices based on time-shifted invariance of the correlation function estimates. Later the algorithm is compared to other popular subspace methods in the simulation study and the results show the effectiveness of our method in the presence of colored noise and low signal-to-noise ratios.

An adaptive approximation image reconstruction method for single sample problem in face recognition using FLDA

Fisher linear discriminant analysis (FLDA) algorithm is a popular subspace method for face recognition, which requires that the number of training samples for each object is not less than two. In this paper, an adaptive approximation image reconstruction method based on economy singular value decomposition (ESVD) algorithm is proposed for the single sample problem in face recognition. By using ESVD the single training sample is decomposed to a set of basis images. Then an adaptive approximation image reconstruction method is proposed to reconstruct an approximation image by using several significant basis images. The single training image and its approximation image for each object form a new training set, which can make the FLDA be applied to the single sample problem in face recognition. The major contribution of the proposed work is that the number of significant basis images for the reconstruction of an approximation image is evaluated by using a reverse thinking approach based on experimental analysis. The performance of the proposed method is verified on the Yale, FERET, ORL, UMIST and AR face databases. The experimental results indicate that the proposed method is efficient and outperforms some existing methods which are proposed to overcome the single sample problem.

A Decorrelation-Based Nonnegative Matrix Factorization Algorithm for Face Recognition

Nonnegative Matrix Factorization (NMF) is among the most popular subspace methods, widely used in a variety of image processing problems. However, this approach is very time-consuming in face recognition due to the extreme high dimensionality of the original matrix. To remedy this limitation, this paper presents a Decorrelation-based NMF (DNMF) method. The proposed algorithm first takes into account the dimension reduction of the original matrix by preprocessing of decorrelation in spatial domain, and then uses nearest neighbor classifier on the reduced subspace. The developed algorithm has been applied for the ORL standard face image database. Experimental results demonstrate the validity of this method.

Subclass discriminant Nonnegative Matrix Factorization for facial image analysis

Nonnegative Matrix Factorization (NMF) is among the most popular subspace methods, widely used in a variety of image processing problems. Recently, a discriminant NMF method that incorporates Linear Discriminant Analysis inspired criteria has been proposed, which achieves an efficient decomposition of the provided data to its discriminant parts, thus enhancing classification performance. However, this approach possesses certain limitations, since it assumes that the underlying data distribution is unimodal, which is often unrealistic. To remedy this limitation, we regard that data inside each class have a multimodal distribution, thus forming clusters and use criteria inspired by Clustering based Discriminant Analysis. The proposed method incorporates appropriate discriminant constraints in the NMF decomposition cost function in order to address the problem of finding discriminant projections that enhance class separability in the reduced dimensional projection space, while taking into account subclass information. The developed algorithm has been applied for both facial expression and face recognition on three popular databases. Experimental results verified that it successfully identified discriminant facial parts, thus enhancing recognition performance.

Interest filter vs. interest operator: Face recognition using Fisher linear discriminant based on interest filter representation

This paper introduces a novel Fisher discriminant classifier based on the interest filter representation for face recognition. Our interest Fisher classifier (IFC), which is robust to illumination and facial expression variability, applies the Fisher linear discriminant (FLD) to an augmented interest feature vector derived from interest filter representation of face images. The novelty of this paper comes from our proposed interest filter: the interest operator can reveal the local activity of the images but suffer from some drawbacks and we improve the capability of the interest operator and propose a multi-orientation and multi-scale interest filter. In particular, we carry out comparative studies of different similarity measures applied to various classifiers. We also perform comparative experimental studies of various face recognition schemes, including our novel IFC method, the Eigenfaces and the Fisherfaces methods, the combination of interest operator and the Eigenfaces method, the combination of interest operator and the Fisherfaces method, the Eigenfaces on the augmented interest feature vectors and other popular subspace methods. The feasibility of the new IFC method has been successfully tested on two data sets from the FERET and AR databases. The novel IFC method achieves the highest accuracy on face recognition on both two datasets.

Eigenfeature Regularization and Extraction in Face Recognition

This work proposes a subspace approach that regularizes and extracts eigenfeatures from the face image. Eigenspace of the within-class scatter matrix is decomposed into three subspaces: a reliable subspace spanned mainly by the facial variation, an unstable subspace due to noise and finite number of training samples and a null subspace. Eigenfeatures are regularized differently in these three subspaces based on an eigenspectrum model to alleviate problems of instability, over-fitting or poor generalization. This also enables the discriminant evaluation performed in the whole space. Feature extraction or dimensionality reduction occurs only at the final stage after the discriminant assessment. These efforts facilitate a discriminative and stable low-dimensional feature representation of the face image. Experiments comparing the proposed approach with some other popular subspace methods on the FERET, ORL, AR and GT databases show that our method consistently outperforms others.

Hybrid nonlinear moments subspace processing for wireless communication systems using antenna arrays

It is shown that hybrid nonlinear (HKL) moments matrices can be used to identify a multichannel FIR system. The method outperforms the popular subspace method based on second-order statistics in low SNR and/or correlated noise, and it is fundamentally equivalent in terms of computational complexity. The method is applied to the channel identification problem in a cellular base-station receiver employing antenna arrays.

Subspace methods for blind identification of multichannel FIR filters using space-time contraction of cumulants

We show that the popular subspace method for identification of multichannel systems can be implemented using particular contractions of higher-order cumulants, in the case of independent, identically distributed (i.i.d.) inputs. The algorithm appears to outperform the traditional correlation-based subspace algorithm in low signal-to-noise-ratio (SNR) and/or correlated noise.