Linear Subspace Analysis Research Articles

Analytical Study of Face Recognition Methods Using Machine Learning

Many facial recognition algorithms, as well as their adaptations, have previously been devised during the last decades. A number is indicated for standard algorithms. They are divided into two categories: appearance-based and model-based. Three distinct linear subspace analysis strategies for appearance-based processes are presented, along with a brief examination of numerous non-linear manifold analysis approaches for face recognition. Elastic Bunch Graph matching, Active Appearance Model, and 3D Model processes are discussed. A vast variety of publicly available face datasets and performance evaluation ratings are examined. Based on previous recognition outcomes, more study areas are recommended. Face recognition has piqued the interest of academics in biometrics, pattern recognition, and computer vision. Previous research in this field had a basic fault in that it was designed to recognize just single faces, resulting in a long detection time and additional time for annotation. The goal of this study is to create a face recognition system that makes use of a machine learning algorithm and principal component analysis (PCA). The study makes use of linear discriminant analysis, multilayer perceptrons, Naive Bayes, and support vector machines. Furthermore, it obtained 97% and 100% identification accuracy, respectively, using PCA and linear discriminant analysis. The extensive comprehension CNNs are the most frequent form of machine learning algorithm used for facial recognition. CNNs are a sort of artificial neural network that performs exceptionally well at image categorization. Face recognition is a popular topic in artificial intelligence. This program was widely used in our daily life. Several face recognition devices were installed on phones to protect private information and utilized on Facebook to quickly recognize when Facebook users appeared in photographs. Several face recognition algorithms have previously been developed; yet, it remains incredibly difficult in real-world situations. A basic technique for differentiating people is influenced by factors such as partial facial occlusion, illumination, and posture variance.

Ensemble Linear Subspace Analysis of High-Dimensional Data.

Regression models provide prediction frameworks for multivariate mutual information analysis that uses information concepts when choosing covariates (also called features) that are important for analysis and prediction. We consider a high dimensional regression framework where the number of covariates (p) exceed the sample size (n). Recent work in high dimensional regression analysis has embraced an ensemble subspace approach that consists of selecting random subsets of covariates with fewer than p covariates, doing statistical analysis on each subset, and then merging the results from the subsets. We examine conditions under which penalty methods such as Lasso perform better when used in the ensemble approach by computing mean squared prediction errors for simulations and a real data example. Linear models with both random and fixed designs are considered. We examine two versions of penalty methods: one where the tuning parameter is selected by cross-validation; and one where the final predictor is a trimmed average of individual predictors corresponding to the members of a set of fixed tuning parameters. We find that the ensemble approach improves on penalty methods for several important real data and model scenarios. The improvement occurs when covariates are strongly associated with the response, when the complexity of the model is high. In such cases, the trimmed average version of ensemble Lasso is often the best predictor.

A Subspace Method for Fast Locally Injective Harmonic Mapping

AbstractWe present a fast algorithm for low‐distortion locally injective harmonic mappings of genus 0 triangle meshes with and without cone singularities. The algorithm consists of two portions, a linear subspace analysis and construction, and a nonlinear non‐convex optimization for determination of a mapping within the reduced subspace. The subspace is the space of solutions to the Harmonic Global Parametrization (HGP) linear system [BCW17], and only vertex positions near cones are utilized, decoupling the variable count from the mesh density. A key insight shows how to construct the linear subspace at a cost comparable to that of a linear solve, extracting a very small set of elements from the inverse of the matrix without explicitly calculating it. With a variable count on the order of the number of cones, a tangential alternating projection method [HCW17] and a subsequent Newton optimization [CW17] are used to quickly find a low‐distortion locally injective mapping. This mapping determination is typically much faster than the subspace construction. Experiments demonstrating its speed and efficacy are shown, and we find it to be an order of magnitude faster than HGP and other alternatives.

Linear and nonlinear subspace analysis of hand movements during grasping.

This study investigated nonlinear patterns of coordination, or synergies, underlying whole-hand grasping kinematics. Prior research has shed considerable light on roles played by such coordinated degrees-of-freedom (DOF), illuminating how motor control is facilitated by structural and functional specializations in the brain, peripheral nervous system, and musculoskeletal system. However, existing analyses suppose that the patterns of coordination can be captured by means of linear analyses, as linear combinations of nominally independent DOF. In contrast, hand kinematics is itself highly nonlinear in nature. To address this discrepancy, we sought to to determine whether nonlinear synergies might serve to more accurately and efficiently explain human grasping kinematics than is possible with linear analyses. We analyzed motion capture data acquired from the hands of individuals as they grasped an array of common objects, using four of the most widely used linear and nonlinear dimensionality reduction algorithms. We compared the results using a recently developed algorithm-agnostic quality measure, which enabled us to assess the quality of the dimensional reductions that resulted by assessing the extent to which local neighborhood information in the data was preserved. Although qualitative inspection of this data suggested that nonlinear correlations between kinematic variables were present, we found that linear modeling, in the form of Principle Components Analysis, could perform better than any of the nonlinear techniques we applied.

Quantifying the predictive consequences of model error with linear subspace analysis

All computer models are simplified and imperfect simulators of complex natural systems. The discrepancy arising from simplification induces bias in model predictions, which may be amplified by the process of model calibration. This paper presents a new method to identify and quantify the predictive consequences of calibrating a simplified computer model. The method is based on linear theory, and it scales efficiently to the large numbers of parameters and observations characteristic of groundwater and petroleum reservoir models. The method is applied to a range of predictions made with a synthetic integrated surface-water/groundwater model with thousands of parameters. Several different observation processing strategies and parameterization/regularization approaches are examined in detail, including use of the Karhunen-Loeve parameter transformation. Predictive bias arising from model error is shown to be prediction specific and often invisible to the modeler. The amount of calibration-induced bias is influenced by several factors, including how expert knowledge is applied in the design of parameterization schemes, the number of parameters adjusted during calibration, how observations and model-generated counterparts are processed, and the level of fit with observations achieved through calibration. Failure to properly implement any of these factors in a prediction-specific manner may increase the potential for predictive bias in ways that are not visible to the calibration and uncertainty analysis process.

Manifold subspace distance derived from kernel principal angles and its application to machinery structural damage assessment

Damage assessment of machinery structure is beneficial for identifying structural health states and preventing sudden failures. A novel scheme for damage assessment is presented by using manifold subspace distance in this study. Vibration response signals from the machinery structure are collected by accelerometers first, and feature matrices are extracted to characterize the acceleration response comprehensively. Thereafter, a manifold learning method, namely kernel locality preserving projection (KLPP), is performed to obtain manifold subspace from the feature matrix. KLPP is available to mine nonlinear information hidden in the feature matrix, which makes it different from the linear subspace analysis method. This merit enables KLPP to be more effective in exploring the intrinsic model of the feature matrix. Further, kernel principal angles that represent similarity between the manifold subspaces are calculated. Finally, a manifold subspace distance is derived from the kernel principal angles. This distance is an appropriate metric for measuring closeness or similarity between the subspaces embedded on a manifold. The distance between manifold subspaces from normal state and damage state of a machinery structure is defined as a damage index. Effectiveness of the proposed scheme is validated by two case studies with regard to damage assessment for different machinery structures. The results show that the defined damage index is not only sensitive to the occurrence of structural damage but also increases obviously with the increasing damage level. These positive results illustrate that the proposed scheme has promise for future performance and is a valuable method for damage assessment.

Pseudo-Gabor wavelet for face recognition

An efficient face-recognition algorithm is proposed, which not only possesses the advantages of linear subspace analysis approaches—such as low computational complexity—but also has the advantage of a high recognition performance with the wavelet- based algorithms. Based on the linearity of Gabor-wavelet transfor- mation and some basic assumptions on face images, we can extract pseudo-Gabor features from the face images without performing any complex Gabor-wavelet transformations. The computational com- plexity can therefore be reduced while a high recognition performance is still maintained by using the principal component analysis (PCA) method. The proposed algorithm is evaluated based on the Yale data- base, the Caltech database, the ORL database, the AR database, and the Facial Recognition Technology database, and is compared with several different face recognition methods such as PCA, Gabor wavelets plus PCA, kernel PCA, locality preserving projection, and dual-tree complex wavelet transformation plus PCA. Experiments show that consistent and promising results are obtained. © 2013 SPIE and IS&T (DOI: 10.1117/1.JEI.22.2.023029)

A new extension of kernel feature and its application for visual recognition

In this paper, we first conceive a new perception of the kernel feature. The kernel subspace methods can be regarded as two independent steps: an explicit kernel feature extraction step and a linear subspace analysis step on the extracted kernel features. The kernel feature vector of an image is composed of dot products between the image and all the training images using nonlinear dot product kernel. Then, based on this perception, we further extend the kernel feature vector of an image to a kernel feature matrix for visual recognition. This extension takes different representation cues of images into account, respectively, while only global average information is used in the traditional kernel methods. From the view of dot product as similarity, this extension means using multiple similarities to measure two images, which is more accordant to human vision. In order to efficiently deal with the problem of numerical computation, a matrix-based kernel discriminant analysis algorithm is employed to learn discriminating kernel features for visual recognition. Experiments on the FERET face database, the COIL-100 object database, and the Wang's nature image database show the advantage of the proposed method.

Orthogonal neighborhood preserving discriminant analysis for face recognition

In this paper, we propose a new linear subspace analysis algorithm, called orthogonal neighborhood preserving discriminant analysis (ONPDA). Given a set of data points in the ambient space, a weight matrix is firstly built which describes the relationship between the data points. Then optimal between-class scatter matrix and within-class scatter matrix are defined such that the neighborhood structure can be preserved. In order to improve the discriminating power, a new method is presented for orthogonalizing the basis eigenvectors. We evaluate the performance of the proposed algorithm for face recognition with the use of different databases. Consistent and promising results demonstrate the effectiveness of our algorithm.

An Analysis of Linear Subspace Approaches for Computer Vision and Pattern Recognition

Linear subspace analysis (LSA) has become rather ubiquitous in a wide range of problems arising in pattern recognition and computer vision. The essence of these approaches is that certain structures are intrinsically (or approximately) low dimensional: for example, the factorization approach to the problem of structure from motion (SFM) and principal component analysis (PCA) based approach to face recognition. In LSA, the singular value decomposition (SVD) is usually the basic mathematical tool. However, analysis of the performance, in the presence of noise, has been lacking. We present such an analysis here. First, the "denoising capacity" of the SVD is analysed. Specifically, given a rank-r matrix, corrupted by noise--how much noise remains in the rank-r projected version of that corrupted matrix? Second, we study the "learning capacity" of the LSA-based recognition system in a noise-corrupted environment. Specifically, LSA systems that attempt to capture a data class as belonging to a rank-r column space will be affected by noise in both the training samples (measurement noise will mean the learning samples will not produce the "true subspace") and the test sample (which will also have measurement noise on top of the ideal clean sample belonging to the "true subspace"). These results should help one to predict aspects of performance and to design more optimal systems in computer vision, particularly in tasks, such as SFM and face recognition. Our analysis agrees with certain observed phenomenon, and these observations, together with our simulations, verify the correctness of our theory.

Kernel-based nonlinear discriminant analysis for face recognition

Linear subspace analysis methods have been successfully applied to extract features for face recognition. But they are inadequate to represent the complex and nonlinear variations of real face images, such as illumination, facial expression and pose variations, because of their linear properties. In this paper, a nonlinear subspace analysis method, Kernel-based Nonlinear Discriminant Analysis (KNDA), is presented for face recognition, which combines the nonlinear kernel trick with the linear subspace analysis method -- Fisher Linear Discriminant Analysis (FLDA). First, the kernel trick is used to project the input data into an implicit feature space, then FLDA is performed in this feature space. Thus nonlinear discriminant features of the input data are yielded. In addition, in order to reduce the computational complexity, a geometry-based feature vectors selection scheme is adopted. Another similar nonlinear subspace analysis is Kernel-based Principal Component Analysis (KPCA), which combines the kernel trick with linear Principal Component Analysis (PCA). Experiments are performed with the polynomial kernel, and KNDA is compared with KPCA and FLDA. Extensive experimental results show that KNDA can give a higher recognition rate than KPCA and FLDA.