Incremental robust principal component analysis for face recognition using ridge regression

Principal component analysis (PCA) has been proven to be an efficient method in pattern recognition and image analysis. Recently, PCA has been extensively employed for face-recognition algorithms, such as eigenface and fisherface. The encouraging results have been reported and discussed in the literature. Many PCA-based face-recognition systems have also been developed in the last decade. However, existing PCA-based face-recognition systems are hard to scale up because of the computational cost and memory-requirement burden. To overcome this limitation, an incremental approach is usually adopted. Incremental PCA (IPCA) methods have been studied for many years in the machine-learning community. The major limitation of existing IPCA methods is that there is no guarantee on the approximation error. In view of this limitation, this paper proposes a new IPCA method based on the idea of a singular value decomposition (SVD) updating algorithm, namely an SVD updating-based IPCA (SVDU-IPCA) algorithm. In the proposed SVDU-IPCA algorithm, we have mathematically proved that the approximation error is bounded. A complexity analysis on the proposed method is also presented. Another characteristic of the proposed SVDU-IPCA algorithm is that it can be easily extended to a kernel version. The proposed method has been evaluated using available public databases, namely FERET, AR, and Yale B, and applied to existing face-recognition algorithms. Experimental results show that the difference of the average recognition accuracy between the proposed incremental method and the batch-mode method is less than 1%. This implies that the proposed SVDU-IPCA method gives a close approximation to the batch-mode PCA method.

In this paper, we propose a robust incremental principal component analysis (IPCA) for stream data that can handle missing values on an ongoing basis. In the proposed IPCA, a missing value is substituted with the value estimated from a conditional probability density function. The conditional probability density functions are incrementally updated when new data are given. In the experiments, we evaluate the performance for both artificial and real data sets through the comparison with the two conventional approaches to handing missing values. We first investigate the estimation errors of missing values. The experimental results demonstrate that the proposed IPCA gives lower estimation errors compared to the other approaches. Next, we investigate the approximation accuracy of eigenvectors. The results show that the proposed IPCA has relatively good accuracy of eigenvectors not only for major components but also for minor components.

We present a range of new incremental (single-pass streaming) algorithms for incremental principal components analysis (IPCA) and show that they are more effective than exiting ones. IPCA algorithms process the columns of a matrix A one at a time and attempt to build a basis for a low-dimensional subspace that spans the dominant subspace of A. We present a unified framework for IPCA algorithms, show that many existing ones are parameterizations of it, propose new sophisticated algorithms, and show that both the new algorithms and many existing ones can be implemented more efficiently than was previously known. We also show that many existing algorithms can fail even in easy cases and we show experimentally that our new algorithms outperform existing ones.

This study presents a seismic transformer model designed to enhance the accuracy of mud weight prediction for drilling operations in the overpressured formation. By analysis of seismic data that implicitly characterize formation pressure, the model helps prevent blowouts, well collapses, mud leaks, and expensive managed pressure drilling. A dataset from some oil filed is used to validate this approach, demonstrating the potential for improved subsurface pressure prediction. The workflow processes post-stack time migrated seismic cubes as sequences of seismic traces. Each trace is segmented into samples in the target geological horizon. A Vision Transformer Masked Autoencoder (ViTMAE)-based model extracts robust features by reconstructing masked portions of traces, leveraging seismic data's inherent pressure-related signals. Incremental Principal Component Analysis (IPCA) compresses the extracted features into smaller dimensions. The model ties seismic and spatial characteristics with a mud weight prediction. The seismic transformer model, trained with a 75% masking ratio and mean squared error loss, generated 96 encoded features, which were reduced to 24 principal components using IPCA. This compression retained 90% of the encoded information, preserving crucial seismic characteristic of the formation pressure state while ensuring computational efficiency with batch processing. By better capturing the relationship between seismic data and formation pressure, the model allows for improved mud weight predictions, reducing the risk of operational hazards and unnecessary drilling costs. Statistical tests further confirm the geological significance of the extracted features, demonstrating their ability to represent subsurface pressure conditions accurately. This work introduces a novel adaptation of ViTMAE for seismic data processing in drilling operations, explicitly connecting seismic feature extraction to formation pressure modeling. The study provides a practical framework for engineers to improve mud weight prediction, enhancing safety and cost-efficiency in drilling.

Appearance-based image analysis techniques require fast computation of principal components of high-dimensional image vectors. We introduce a fast incremental principal component analysis (IPCA) algorithm, called candid covariance-free IPCA (CCIPCA), used to compute the principal components of a sequence of samples incrementally without estimating the covariance matrix (so covariance-free). The new method is motivated by the concept of statistical efficiency (the estimate has the smallest variance given the observed data). To do this, it keeps the scale of observations and computes the mean of observations incrementally, which is an efficient estimate for some well known distributions (e.g., Gaussian), although the highest possible efficiency is not guaranteed in our case because of unknown sample distribution. The method is for real-time applications and, thus, it does not allow iterations. It converges very fast for high-dimensional image vectors. Some links between IPCA and the development of the cerebral cortex are also discussed.

Background subtraction is one of commonly used techniques for many applications such as human detection in images. For background estimation, principal component analysis (PCA) is an available method. Since the background sometimes changes according to illumination change or due to a newly appeared stationary article, the eigenspace should be updated momentarily. A naïve algorithm for eigenspace updating is to update the covariance matrix. Then, the eigenspace is updated by solving the eigenvalue problem for the covariance matrix. But this procedure is very time consuming because covariance matrix is a very large size matrix. In this paper we propose a novel method to update the eigenspace approximately with exceedingly low computational cost. Main idea to decrees computational cost is to approximate the covariance matrix by low dimensional matrix. Thus, computational cost to solve eigenvalue problem becomes exceedingly decrease. A merit of the proposed method is discussed.

Field of medical image analysis is evolving at a rapid pace. New advancements have introduced big challenges in analysis and information extraction from the generated images. Usually the scale of input data is so immense that it needs very efficient and smart algorithms to process intended outcomes. Magnetic Resonance Images (MRI) is one of the primary sources for morphometric analysis. Frequently used techniques for this kind of analysis are Principal Component analysis (PCA) and a more robust Incremental Principal Component Analysis (IPCA). Both these techniques apply complex algorithms for producing statistical shape models which ultimately show variance in clinical images. Variance is primarily detected and measured in the articular cartilage. Statistical assessment of cartilage volume and surface area estimation gives an indication of osteoarthritis severity. This research paper proposes an agile framework for segmentation of images of the knee by using Active contour model. Image texture information is merged in the model with the help of effective mathematical functions. Vector valued geodesic was used during segmentation and also to detect and measure variance in the image at pixel level. By use of efficient algorithms and mathematical tools this technique showed promising results in handling noise and nonuniform intensities within the image. The algorithm effectively provided a quantitative cartilage assessment which could help physicians in classifying osteoarthritis stages.

Flexible fitting in 3D-EM with incomplete data on superfamily variability

This paper presents a novel Gabor-based kernel Principal Component Analysis (PCA) method by integrating the Gabor wavelet representation of face images and the kernel PCA method for face recognition. Gabor wavelets first derive desirable facial features characterized by spatial frequency, spatial locality, and orientation selectivity to cope with the variations due to illumination and facial expression changes. The kernel PCA method is then extended to include fractional power polynomial models for enhanced face recognition performance. A fractional power polynomial, however, does not necessarily define a kernel function, as it might not define a positive semidefinite Gram matrix. Note that the sigmoid kernels, one of the three classes of widely used kernel functions (polynomial kernels, Gaussian kernels, and sigmoid kernels), do not actually define a positive semidefinite Gram matrix either. Nevertheless, the sigmoid kernels have been successfully used in practice, such as in building support vector machines. In order to derive real kernel PCA features, we apply only those kernel PCA eigenvectors that are associated with positive eigenvalues. The feasibility of the Gabor-based kernel PCA method with fractional power polynomial models has been successfully tested on both frontal and pose-angled face recognition, using two data sets from the FERET database and the CMU PIE database, respectively. The FERET data set contains 600 frontal face images of 200 subjects, while the PIE data set consists of 680 images across five poses (left and right profiles, left and right half profiles, and frontal view) with two different facial expressions (neutral and smiling) of 68 subjects. The effectiveness of the Gabor-based kernel PCA method with fractional power polynomial models is shown in terms of both absolute performance indices and comparative performance against the PCA method, the kernel PCA method with polynomial kernels, the kernel PCA method with fractional power polynomial models, the Gabor wavelet-based PCA method, and the Gabor wavelet-based kernel PCA method with polynomial kernels.

In the era of smart digital transformation, automatic face recognition is the way of identification and verification of a person in many applications of security and authentication. If the person's 2D still image or 3D video frame is taken under controlled lighting and frontal face poses, then today automatic face recognition is a solved problem with more than 98 % accuracy. Under ideal condition of images, automatic face recognition outperforms manual face recognition rate. But the problem of uncontrolled illumination, occlusion, tilting of faces, different expressions of faces, use of accessories and hair color, growth of facial hair, aging effect of a person and low-resolution images makes automatic face recognition underperform; it gets defeated by human. Unless this problem is solved on real time, automatic face recognition system cannot be trusted for crucial security applications like e-passport, fraud detection, counter terrorism and mug-shot verification etc. Extensive research is underway to improve this technology. Traditionally Harr cascade classifier methods, histogram of oriented gradients (HoG), principal component analysis (PCA), Eigen-faces, and support vector machine (SVM) classifier are used in face recognition. Now modern deep learning innovation has superseded those traditional machine learning techniques with more computing power in GPUs and TPUs to tackle all variations in input image quality and ever-growing face database. The goal of this paper is to report the journey of face recognition system from traditional to modern techniques to increase precision and recall of the system.

“Principal Component Analysis” (PCA) is an established linear technique for dimensionality reduction. It performs an orthonormal transformation to replace possibly correlated variables with a smaller set of linearly independent variables, the so-called principal components, which capture a large portion of the data variance. The problem of finding the optimal number of principal components has been widely studied for offline PCA. However, when working with streaming data, the optimal number changes continuously. This requires to update both the principal components and the dimensionality in every timestep. While the continuous update of the principal components is widely studied, the available algorithms for dimensionality adjustment are limited to an increment of one in neural network-based and incremental PCA. Therefore, existing approaches cannot account for abrupt changes in the presented data. The contribution of this work is to enable in neural network-based PCA the continuous dimensionality adjustment by an arbitrary number without the necessity to learn all principal components. A novel algorithm is presented that utilizes several PCA characteristics to adaptivly update the optimal number of principal components for neural network-based PCA. A precise estimation of the required dimensionality reduces the computational effort while ensuring that the desired amount of variance is kept. The computational complexity of the proposed algorithm is investigated and it is benchmarked in an experimental study against other neural network-based and incremental PCA approaches where it produces highly competitive results.

This study proposes a Fusion, Feature-Level, Face Recognition System (FFLFRS) that is based on the Multi-Resolution, Singular Value Decomposition (MSVD) fusion technique. Face recognition in the FFLFRS is achieved via four processes: face detection, feature extraction, feature fusion, and face classification. In this system, the most significant face features (that is, the eyes, nose, and mouth) are first detected. Then, local and global features are extracted by the Local Binary Pattern (LBP) and Principal Component Analysis (PCA) extraction approaches. Afterwards, the extracted features are fused by the MSVD method and classified by the Artificial Neural Network (ANN). The proposed FFLFRS was verified on 10,000 face images drawn from the face images database of the Olivetti Research Laboratory (ORL). Face recognition performance of this system was contrasted with levels of performance of three state of the art, fusion-level, face recognition systems (FRSs) depending on the Frequency Partition (FP), Laplacian Pyramid (LP), and Covariance Intersection (CI) fusion methods. Ten-thousand images were employed to test the proposed model and assess its performance, which was evaluated in terms of changes in pose, illumination, and expression, besides low resolution and presence of occlusion. The face recognition results of the proposed FFLFRS are encouraging. This system proved to be effective in dealing with images having challenges to face recognition and it could achieve a recognition accuracy as high as 97.78%.

Facial expressions are the most visual method to convey emotions. Facial expressions of a person at different instances are not same. Automatic recognition of facial expressions is important for natural human-machine interfaces. Although human recognize facial expressions without delay, however expression reorganization by computer is still a challenge. In this proposed method Log Gabor filter bank of 5 scales and 8 different orientations is used. To reduce the dimensionality PCA (Principal Component Analysis) is then applied to Log- Gabor filtered images. The database used was JAFFE (Japanese female facial expression). The process involves detection of face, feature extraction using Log-Gabor filter, dimensionality reduction by PCA and classification of emotion using Euclidean distance metric. The work had been carried out in two stages. In stage I firstly, all the 7 emotions were detected using Log Gabor filter bank of 5 scales and 8 orientations. Secondly PCA was applied to compress 8 orientations and finally PCA was applied to compress 5 scales. In this stage the images of the training persons were included in the Test database. In stage II, 5 emotions angry, disgust, happy, neutral and surprise were detected by using Log Gabor filter bank of 5 scales and 8 orientations. In this stage images of training persons were not included in the Test database.

One of the most successful process to accomplish human face recognition are the methods based on the principal component analysis (PCA), also known as eigenfaces. Recently, novel PCA approaches have been proposed: modular (MPCA) and two-dimensional (IMPCA). These approaches have achieved outstanding result in feature extraction and recognition. IMPCA is used for feature extraction based on 2D matrix representation and MPCA is based on image division to improve face recognition with variations like facial expressions, light and head pose. In this work we use some aspects of these methods to build a new technique called modular Image PCA (MIMPCA). The results achieved with the proposed method are superior in all experiments compared with the original techniques under different conditions of head pose angle, illumination and facial expression.

Face recognition has been very important issue in computer vision and pattern recognition over the last several decades. One difficulty in face recognition is how to handle the variations in the expression, pose and illumination when only a limited number of training samples are available. In this project, we performed Real Time Facial Expression Analysis Using PCA. Initially the Eigen space was created with Eigen values and eigenvectors. From this space, the Eigen faces are constructed, and the most relevant Eigen faces have been selected using Principal Component Analysis (PCA). With these Eigen faces the input test images are classified based on Facial Expression Classifier. The proposed method was carried out by taking the picture database. The database was obtained with 10 photographs of each person at different expressions. These expressions can be classified into some discrete classes like happy, anger, disgust, sad and neutral. Absence of any expression is the "neutral" expression. There are 30 persons in database. The database is kept in the train folder which contains each person having all his/her photographs.