A new incremental principal component analysis with a forgetting factor for background estimation

Face recognition efficiency is extremely challenged by image corruption, noise, shadowing and variant face expressions. In this paper, we propose a reliable incremental face recognition algorithm to address this problem. The algorithm is robust to face image misalignment, occlusion, corruption and different style variations. To apply this for large face data streams, the proposed algorithm uses incremental robust principal component analysis (PCA) to regain the intrinsic data of a bunch of images regarding one subject. A novel similarity metric is defined for face recognition and classification. Five different databases and a base of four different criteria are used in the experiments to illustrate the reliability of the proposed method. Experiments point that it outperforms other existing incremental PCA approaches namely incremental singular value decomposition, add block singular value decomposition and candid covariance-free incremental PCA in terms of recognition rate under occlusions, facial expressions and image perspectives.

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.

Human detection in images using deep learning has been a popular research topic in recent years and has achieved remarkable performance. Training a human detection network is useful for first responders to search for trapped victims in debris after a disaster. In this paper, we focus on the detection of such victims using deep learning, and we find that state-of-the-art detection models pre-trained on the well-known COCO dataset fail to detect victims. This is because all the people in the training set are shown in photos of daily life or sports activities, while people in the debris after a disaster usually only have parts of their bodies exposed. In addition, because of the dust, the colors of their clothes or body parts are similar to those of the surrounding debris. Compared with collecting images of common objects, images of disaster victims are extremely difficult to obtain for training. Therefore, we propose a framework to generate harmonious composite images for training. We first paste body parts onto a debris background to generate composite victim images and then use a deep harmonization network to make the composite images look more harmonious. We select YOLOv5l as the most suitable model, and experiments show that using composite images for training improves the AP (average precision) by 19.4% (15.3%→34.7%). Furthermore, using the harmonious images is of great benefit to training a better victim detector, and the AP is further improved by 10.2% (34.7%→44.9%). This research is part of the EU project INGENIOUS. Our composite images and code are publicly available on our website.

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.

For multivariate analysis with p variables the problem that often arises is the ambiguous nature of the correlation or covariance matrix. When p is moderately or very large it is generally difficult to identify the true nature of relationship among the variables as well as observations from the covariance or correlation matrix. Under such situations a very common way to simplify the matter is to reduce the dimension by considering only those variables (actual or derived) which are truly responsible for the overall variation. Important and useful dimension reduction techniques are Principal Component Analysis (PCA), Factor Analysis, Multidimensional Scaling, Independent Component Analysis (ICA), etc. Among them PCA is the most popular one. One may look at this method in three different ways. It may be considered as a method of transforming correlated variables into uncorrelated one or a method of finding linear combinations with relatively small or large variability or a tool for data reduction. The third criterion is more data oriented. In PCA primarily it is not necessary to make any assumption regarding the underlying multivariate distribution but if we are interested in some inference problems related to PCA then assumption of multivariate normality is necessary. The eigen values and eigen vectors of the covariance or correlation matrix are the main contributors of a PCA. The eigen vectors determine the directions of maximum variability whereas the eigen values specify the variances. In practice, decisions regarding the quality of the principal component approximation should be made on the basis of eigen value–eigen vector pairs.

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.

The covariance matrix (or its inverse, the precision matrix) is central to many chemometric techniques. Traditional sample estimators perform poorly for high‐dimensional data such as metabolomics data. Because of this, many traditional inference techniques break down or produce unreliable results. In this paper, we selectively review several modern estimators of the covariance and precision matrix that improve upon the traditional sample estimator. We focus on 3 general techniques: eigenvalue‐shrinkage estimation, ridge‐type estimation, and structured estimation. These methods rely on different assumptions regarding the structure of the covariance or precision matrix. Various examples, in particular using metabolomics data, are used to compare these techniques and to demonstrate that in concert with, eg, principal component analysis, multivariate analysis of variance, and Gaussian graphical models, better results are obtained.

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.

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.

We examined the ability of eigenvalue tests to distinguish field—collected from random, assemblage structure data sets. Eight published time series of species abundances were used in the analysis, including data sets for: fishes, birds, mammals, stream benthos, and crabs. To test the efficacy of eigenvalue tests, we constructed 1000 randomly generated data sets for each real data set, whose means and variances were identical to the means and variances of the original data matrices. The data sets were then subjected to a principal components analysis (PCA) and eigenvalue tests used to identify significant eigenvalues for both correlation and covariance matrix solutions. We also examined the effects of: (1) number of species (= number of variables), (2) number of samples (= replication), (3) variance structure, on the performance of the test. Using PCA's based on the correlation matrix and with sample sizes typically encountered in the field, the eigenvalue tests generally performed at the .05 level when a = .01. Slightly poorer results were obtained with the covariance matrix. Increasing the number of samples to at least three times the number of species generally gave a level coverage of an a level test (i.e., a = .05, .01). Increasing variance in the data set only affected test outcomes at levels of replication less than twice the number of species. We conclude that the eigenvalue tests can be used to detect patterns in PCA's of assemblage structure data, if the number of samples is at least three times the number of species and either a covariance or correlation matrix solution is used. It is assumed that these patterns represent ecologically meaningful patterns of variation.

Upcoming and existing large-scale surveys of galaxies require accurate theoretical predictions of the dark matter clustering statistics for thousands of mock galaxy catalogs. We demonstrate that this goal can be achieve with our new Parallel Particle-Mesh (PM) Nbody code (PPM-GLAM) at a very low computational cost. We run about 15,000 simulations with ~2 billion particles that provide ~1% accuracy of the dark matter power spectra P(k) for wave-numbers up to k~ 1h/Mpc. Using this large data-set we study the power spectrum covariance matrix, the stepping stone for producing mock catalogs. In contrast to many previous analytical and numerical results, we find that the covariance matrix normalised to the power spectrum C(k,k')/P(k)P(k') has a complex structure of non-diagonal components. It has an upturn at small k, followed by a minimum at k=0.1-0.2h/Mpc. It also has a maximum at k=0.5-0.6h/Mpc. The normalised covariance matrix strongly evolves with redshift: C(k,k')~delta(t)^alpha P(k)P(k'), where delta is the linear growth factor and alpha ~ 1-1.25, which indicates that the covariance matrix depends on cosmological parameters. We also show that waves longer than 1Gpc have very little impact on the power spectrum and covariance matrix. This significantly reduces the computational costs and complexity of theoretical predictions: relatively small volume ~ (1Gpc)^3 simulations capture the necessary properties of dark matter clustering statistics. All the power spectra obtained from many thousands of our simulations are publicly available.

Biometric Authentication (BA) has been recently identified as a significant paradigm on maintaining the security level to improve individual person's authenticity. With more and more advanced technology, the BA has to be enhanced to cope up with the increased insecure environment. Several schemes employing multimodal biometric system fuses the face image with certain other traditional biometric modalities to ensure security. However changes in the facial expression significantly updates the facial geometry, thereby reduces the ranking score level. Some of the multimodal biometric research group has designed different algorithms on personal biometric feature based authentication. But, fusion multimodal biometric system did not provide robustness compromising the security level. To develop high robust multimodal biometric system, person multimodal biometric using Covariance Matrix Incremental Principal Component Analysis (CMI-PCA) method is proposed in this paper. The main goal of CMI-PCA method is to work with three principle steps and attain rank level fusion integration on the faces, ears and hand dorsal vein. First, the person's multimodal biometric features are sensed and feature extraction is performed using Gabor Filter based Incremental PCA to improve robustness level. Second step is to match the extracted features with stored test image from the database using Score Matching based on Covariance Matrix Incremental PCA. The score matching based on Covariance Matrix Incremental PCA maintain the scale of extracted features and compute the mean score value to match with test images without any Covariance Matrix range. Finally, the CMI-PCA method involves combining different biometric identification ranks for making final decision. The extended Borda Count Multimodal Ranking system is used in CMI-PCA to determine the integrated biometric outcome and ensures higher security level for individual information. Experiment is conducted on factors such as robustness level, multimodal matching score rate, rank level fusion efficiency rate.

BackgroundIdentifying lncRNA-disease associations not only helps to better comprehend the underlying mechanisms of various human diseases at the lncRNA level but also speeds up the identification of potential biomarkers for disease diagnoses, treatments, prognoses, and drug response predictions. However, as the amount of archived biological data continues to grow, it has become increasingly difficult to detect potential human lncRNA-disease associations from these enormous biological datasets using traditional biological experimental methods. Consequently, developing new and effective computational methods to predict potential human lncRNA diseases is essential.ResultsUsing a combination of incremental principal component analysis (IPCA) and random forest (RF) algorithms and by integrating multiple similarity matrices, we propose a new algorithm (IPCARF) based on integrated machine learning technology for predicting lncRNA-disease associations. First, we used two different models to compute a semantic similarity matrix of diseases from a directed acyclic graph of diseases. Second, a characteristic vector for each lncRNA-disease pair is obtained by integrating disease similarity, lncRNA similarity, and Gaussian nuclear similarity. Then, the best feature subspace is obtained by applying IPCA to decrease the dimension of the original feature set. Finally, we train an RF model to predict potential lncRNA-disease associations. The experimental results show that the IPCARF algorithm effectively improves the AUC metric when predicting potential lncRNA-disease associations. Before the parameter optimization procedure, the AUC value predicted by the IPCARF algorithm under 10-fold cross-validation reached 0.8529; after selecting the optimal parameters using the grid search algorithm, the predicted AUC of the IPCARF algorithm reached 0.8611.ConclusionsWe compared IPCARF with the existing LRLSLDA, LRLSLDA-LNCSIM, TPGLDA, NPCMF, and ncPred prediction methods, which have shown excellent performance in predicting lncRNA-disease associations. The compared results of 10-fold cross-validation procedures show that the predictions of the IPCARF method are better than those of the other compared methods.

Normally in Principal Component Analysis (PCA) (Sirovich & Kirby, 1987; Turk & Pentland, 1991), the 2D image matrices are firstly transformed to 1D image vectors by vectorization. The vectorization of a matrix is the column vector obtain by stacking the columns of the matrix on top of one another. The covariance or scatter matrix are formulated from the these image vectors. The covariance matrix will be well estimated if and only if the number of available training samples is not far smaller than the dimension of this matrix. In fact, it is too hard to collect this the number of samples. Then, normally in 1D subspace analysis, the estimated covariance matrix is not well estimated and not full rank.