Adaptive Principal Component Extraction Research Articles

Adaptive Recognition of Motion Decomposition Image Based on Adaptive Principal Component Extraction Algorithm

Moving target detection and recognition methods are the foundation and key of modern intelligent video recognition systems. It combines advanced technologies in many fields such as image processing, pattern recognition, and artificial intelligence, and is a research hotspot in computer vision technology. Therefore, it is of great significance to study moving target detection and recognition algorithms. The non-local image extraction algorithm proposed in this paper uses an adaptive clustering method to perform fine cluster analysis on non-local image blocks with different feature types. Through the step-by-step principal component approximation method, we carefully find the features in each class. This progressive principal component approximation implements singular value hard threshold processing based on the Marchenko-Pastur (MP) theorem to select the main part of the feature, and uses special soft thresholds in the principal component transform domain to further improve the extraction performance. The Lower Bound-Based Within-Class Maximum Division (LBWCMD) is proposed, and this method is used as a preprocessing step of robust principal component analysis in moving target detection. This article applies LBWCMD to the video frame set based on the position information of the moving target, and the obtained frame subset meets the signal requirements of Robust Principle Component Analysis (RPCA) to the greatest extent. On this basis, we add frames with smaller motion amplitudes to each frame subset to increase the proportion of background pixels in each subset. Frame set division and low-rank decomposition realize the detection of moving targets under a unified framework. The detection rate of the proposed method is higher than that of the current popular methods in sports video data sets, and the detection accuracy is improved compared with the original RPCA method.

PCA based clustering for brain tumor segmentation of T1w MRI images

Background and objectiveMedical images are huge collections of information that are difficult to store and process consuming extensive computing time. Therefore, the reduction techniques are commonly used as a data pre-processing step to make the image data less complex so that a high-dimensional data can be identified by an appropriate low-dimensional representation. PCA is one of the most popular multivariate methods for data reduction. This paper is focused on T1-weighted MRI images clustering for brain tumor segmentation with dimension reduction by different common Principle Component Analysis (PCA) algorithms. Our primary aim is to present a comparison between different variations of PCA algorithms on MRIs for two cluster methods. MethodsFive most common PCA algorithms; namely the conventional PCA, Probabilistic Principal Component Analysis (PPCA), Expectation Maximization Based Principal Component Analysis (EM-PCA), Generalize Hebbian Algorithm (GHA), and Adaptive Principal Component Extraction (APEX) were applied to reduce dimensionality in advance of two clustering algorithms, K-Means and Fuzzy C-Means. In the study, the T1-weighted MRI images of the human brain with brain tumor were used for clustering. In addition to the original size of 512 lines and 512 pixels per line, three more different sizes, 256 × 256, 128 × 128 and 64 × 64, were included in the study to examine their effect on the methods. ResultsThe obtained results were compared in terms of both the reconstruction errors and the Euclidean distance errors among the clustered images containing the same number of principle components. ConclusionAccording to the findings, the PPCA obtained the best results among all others. Furthermore, the EM-PCA and the PPCA assisted K-Means algorithm to accomplish the best clustering performance in the majority as well as achieving significant results with both clustering algorithms for all size of T1w MRI images.

Applying an Adaptive Principal-Component Extraction Algorithm in Seismic Data Processing

Orthogonal decomposition plays an important role in signal processing. We introduce a neural network learning algorithm for seismic data processing. We present an orthogonal decomposition approach for seismic data via adaptive principal-component extraction. In decomposed eigen-subspace, by means of eigen-extraction, noise is eliminated and the signal-to-noise ratio is enhanced. Compared with the conventional K-L method, the learning algorithm can selectively extract the required few principal components used in eigen-filtering, rather than all principal components of the input data. Therefore, computation costs can be reduced and the more traces there are, the more effective the approach. To demonstrate its effectiveness, we present two real data examples of seismic data processing.

On-line adaptive principal component extraction algorithms using iteration approach

Two new on-line algorithms for adaptive principal component analysis (APCA) are proposed and discussed in order to solve the problem of on-line industrial process monitoring in this paper. Both the algorithms have the capability of extracting principal component eigenvectors on-line in a fixed size sliding data window with high dimensional input data. The first algorithm is based on the steepest gradient descent approach, which updates the covariance matrix with deflation transformation and on-line iteration. Based on neural networks, the second algorithm constructs the input data sequence with an on-line iteration method and trains the neural network in every data frame. The convergence of the two algorithms is then analyzed and the simulations are given to illustrate the effectiveness of the two algorithms. At last, the applications of the two algorithms are discussed.

Fast adaptive principal component extraction based on a generalized energy function

By introducing an arbitrary diagonal matrix, a generalized energy function (GEF) is proposed for searching for the optimum weights of a two layer linear neural network. From the GEF, we derive a recursive least squares (RLS) algorithm to extract in parallel multiple principal components of the input covariance matrix without designing an asymmetrical circuit. The local stability of the GEF algorithm at the equilibrium is analytically verified. Simulation results show that the GEF algorithm for parallel multiple principal components extraction exhibits the fast convergence and has the improved robustness resistance to the eigenvalue spread of the input covariance matrix as compared to the well-known lateral inhibition model (APEX) and least mean square error reconstruction (LMSER) algorithms.

A general class of /spl psi/#x03C8;-APEX PCA neural algorithms

Principal component analysis (PCA) can be successfully applied to a variety of signal processing problems. Different analyzers have been reported in the scientific literature; among others, the Adaptive Principal component EXtractor (APEX) by Kung and Diamantaras has attracted much interest in the scientific community since it involves a specific neural architecture and a specific learning theory. The aim of this brief is to present a general class of APEX-like learning rules (referred to as /spl psi/-APEX) and to illustrate their features by theoretical and numerical analysis.

Robust hebbian learning and noisy principal component analysis

The classical analysis of a stochastic signal into principal components compresses the signal using an optimal selection of linear features. Noisy Principal Component Analysis (NPCA) is an extension of PCA under the assumption that the extracted features are unreliable, and the unreliability is modeled by additive noise. The applications of this assumption appear for instance, in communications problems with noisy channels. The level of noise in the NPCA features affects the reconstruction error in a way resembling the water-filling analogy in information theory. Robust neural network models for Noisy PCA can be defined with respect to certain synaptic weight constraints. In this paper we present the NPCA theory related to a particularly simple and tractable constraint which allows us to evaluate the robustness of old PCA Hebbian learning rules. It turns out that those algorithms are not optimally robust in the sense that they produce a zero solution when the noise power level reaches half the limit set by NPCA. In fact, they are not NPCA-optimal for any other noise levels except zero. Finally, we propose new NPCA-optimal robust Hebbian learning algorithms for multiple adaptive noisy principal component extraction.

Adaptive Principal component EXtraction (APEX) and applications

The authors describe a neural network model (APEX) for multiple principal component extraction. All the synaptic weights of the model are trained with the normalized Hebbian learning rule. The network structure features a hierarchical set of lateral connections among the output units which serve the purpose of weight orthogonalization. This structure also allows the size of the model to grow or shrink without need for retraining the old units. The exponential convergence of the network is formally proved while there is significant performance improvement over previous methods. By establishing an important connection with the recursive least squares algorithm they have been able to provide the optimal size for the learning step-size parameter which leads to a significant improvement in the convergence speed. This is in contrast with previous neural PCA models which lack such numerical advantages. The APEX algorithm is also parallelizable allowing the concurrent extraction of multiple principal components. Furthermore, APEX is shown to be applicable to the constrained PCA problem where the signal variance is maximized under external orthogonality constraints. They then study various principal component analysis (PCA) applications that might benefit from the adaptive solution offered by APEX. In particular they discuss applications in spectral estimation, signal detection and image compression and filtering, while other application domains are also briefly outlined. >