Nonlinear Kernel Principal Component Analysis Research Articles

The use of measurable traits of trunk and crown to assess the biosocial classes of oak trees (Quercus robur L.)

The crown class assessment is a key element in forestry practice. It is a traditional method that finds application in thinning plans, assessment of site index, tree competition, or crown condition. Assigning trees into a given class is done during field surveys and requires precision and experience to avoid inaccuracy. Therefore, Kraft’s system has often been criticized and modified. Thus, in our study, we aimed to analyse whether the directly measured traits of trunk and crown of oak trees (Quercus robur L.) can be applied to crown class assessment. For this purpose, we used the principal component analysis (PCA) and nonlinear kernel principal component analysis (KPCA) based on measurable traits of trunk and crown, i.e., the height of the tree, the diameter at breast height, the length of the crown, and the field crown projection area. In total, we measured 286 mature trees in three oak stands located in western Poland. Results indicate that all chosen traits of trunk and crown allowed, though not always perfect, to assign the trees into given crown classes. The greatest contribution to crown class distinction had the diameter at breast height and the parameters of crown, i.e., and the field crown projection area. Furthermore, results show that the best method of assigning the trees into biosocial classes is the KPCA Gauss, considering the percentage explanation of the total variability, and KPCA Laplace, considering the visual division. In the latter, the multivariate analysis resulted in a similar crown class assignment as the field-assigned method. However, its application requires measurements that make it neither cheaper nor faster than a traditional crown class assessment. It indicates that a traditional field-assigned method, despite its subjectivity, should continue to be of great importance in forestry practice. Moreover, the alternative traits of trunk and crown can be a potentially useful statistical substitute for crown class assessment. Keywords: crown class, oak stand, trunk and crown traits, multivariate methods

A NEW AUTO-SCORING ALGORITHM FOR BALANCE ASSESSMENT WITH WEARABLE IMU DEVICE BASED ON NONLINEAR MODEL

In this paper, a new auto-scoring algorithm that automatically evaluates the Berg balance scale (BBS) tasks is proposed. The BBS can be used as an indicator for patients to analyze their rehabilitation status by themselves. In the proposed method, the patient must use a wearable inertial measurement unit (IMU) sensor, and the result of the patient’s BBS task execution would be scored automatically by the evaluation algorithm. The proposed evaluation algorithm involves only few computations and has high scoring accuracy. Nonlinear kernel principal component analysis and a small number of linear features were combined to reduce the features from each sensor, and the algorithm model was implemented using a support vector machine (SVM), a machine learning technique with low computational complexity. The effectiveness of the algorithm was evaluated through clinical evaluation of 53 subjects with up to eight IMU sensors. The average accuracy of the proposed algorithm using eight sensors was 93.2%, and that using five sensors was 91.5%. There was a 12.6% and 10.9% increase in accuracy, respectively, compared to a previous study. The training and testing times of the proposed SVM model were over 38 times faster than the multi-layer perceptron model used in a previous study.

HybridCNN based hyperspectral image classification using multiscale spatiospectral features

Hyperspectral images (HSIs) are contiguous band images widely used in remote sensing applications. The evolution of deep learning techniques made a significant impact on HSI classification. Several HSI processing applications rely on various Convolutional Neural Network (CNN) models. However, the higher dimensionality nature of HSIs increases the computational complexity and leads to the Hughes phenomenon. Therefore most of the CNN models perform dimensionality reduction (DR) as a preprocessing step. Another challenge in HSI classification is the consideration of both spatial and spectral features for obtaining accurate results. A few 3-D-CNN models are designed to overcome this challenge, but it takes more execution time than other methods. This research work proposes a multiscale spatio-spectral feature based hybrid CNN model for hyperspectral image classification. Hybrid DR used for optimal band extraction, which performs linear Gaussian Random Projection (GRP) and non-linear Kernel Principal Component Analysis (KPCA). The proposed hybrid CNN classification technique extracts the spectral and spatial features for different window sizes using 3D-CNN. These features concatenated and fed into a 2D-CNN for further feature extraction and classification. The hybrid model is compared against various state-of-the-art CNN based techniques and found to showcase a satisfactory result with less computational complexity.

Nonlinear Process Fault Diagnosis Based on Serial Principal Component Analysis.

Many industrial processes contain both linear and nonlinear parts, and kernel principal component analysis (KPCA), widely used in nonlinear process monitoring, may not offer the most effective means for dealing with these nonlinear processes. This paper proposes a new hybrid linear-nonlinear statistical modeling approach for nonlinear process monitoring by closely integrating linear principal component analysis (PCA) and nonlinear KPCA using a serial model structure, which we refer to as serial PCA (SPCA). Specifically, PCA is first applied to extract PCs as linear features, and to decompose the data into the PC subspace and residual subspace (RS). Then, KPCA is performed in the RS to extract the nonlinear PCs as nonlinear features. Two monitoring statistics are constructed for fault detection, based on both the linear and nonlinear features extracted by the proposed SPCA. To effectively perform fault identification after a fault is detected, an SPCA similarity factor method is built for fault recognition, which fuses both the linear and nonlinear features. Unlike PCA and KPCA, the proposed method takes into account both linear and nonlinear PCs simultaneously, and therefore, it can better exploit the underlying process's structure to enhance fault diagnosis performance. Two case studies involving a simulated nonlinear process and the benchmark Tennessee Eastman process demonstrate that the proposed SPCA approach is more effective than the existing state-of-the-art approach based on KPCA alone, in terms of nonlinear process fault detection and identification.

Nonlinear gradient denoising: Finding accurate extrema from inaccurate functional derivatives

A method for nonlinear optimization with machine learning (ML) models, called nonlinear gradient denoising (NLGD), is developed, and applied with ML approximations to the kinetic energy density functional in an orbital‐free density functional theory. Due to systematically inaccurate gradients of ML models, in particular when the data is very high‐dimensional, the optimization must be constrained to the data manifold. We use nonlinear kernel principal component analysis (PCA) to locally reconstruct the manifold, enabling a projected gradient descent along it. A thorough analysis of the method is given via a simple model, designed to clarify the concepts presented. Additionally, NLGD is compared with the local PCA method used in previous work. Our method is shown to be superior in cases when the data manifold is highly nonlinear and high dimensional. Further applications of the method in both density functional theory and ML are discussed. © 2015 Wiley Periodicals, Inc.

A Cellular Automata Model Based on Nonlinear Kernel Principal Component Analysis for Urban Growth Simulation

In this paper we present a cellular automata (CA) model based on nonlinear kernel principal component analysis (KPCA) to simulate the spatiotemporal process of urban growth. As a generalisation of the linear principal component analysis (PCA) method, the KPCA method was developed to extract the nonspatially correlated principal components amongst the various spatial variables which affect urban growth in high-dimensional feature space. Compared with the linear PCA method, the KPCA approach is superior as it generates fewer independent components while still maintaining its capacity to reduce the noise level of the original input datasets. The reduced number of independent components can be used to better reconstruct the nonlinear transition rules of a CA model. In addition, the principal components extracted through the KPCA approach are not linearly related to the input spatial variables, which accords well with the nonlinear nature of complex urban systems. The KPCA-based CA model (KPCA-CA) developed was fitted to a fast-growing region in China's Shanghai Metropolis for the sixteen-year period 1992–2008. The simulated patterns of urban growth matched well with the observed urban growth, as determined from historical remotely sensed images for the same period. The KPCA-CA model resulted in significant improvements in locational accuracy when compared with conventional CA models and acted to reduce simulation uncertainty.

MO‐D‐L100J‐06: Evaluation of An Automatic Algorithm Based On Kernel Principal Component Analysis for Segmentation of the Bladder and Prostate in CT Scans of Prostate Radiotherapy Patients

Purpose: to evaluate the performance of an automatic segmentation algorithm used to segment the prostate and bladder in CT scans of patients undergoing external beam radiotherapy. Method and Materials: A nonlinear kernel principal component analysis (KPCA) based algorithm has been developed to model the surface shapes of soft tissue organs in the pelvis of prostate patients. A library of 25 patients, each with approximately 13 CT scans acquired during their treatment, has been manually segmented by a physician. The library is used to both train and evaluate the algorithm. In this preliminary analysis, the training sets consisted of the contours from 8 to 10 scans of a single patient. Evaluation was performed using 3 CT studies previously unseen by the system from each patient, from the beginning, middle and end of treatment. Performance was measured by comparing the volumes and center‐of‐gravity positions of the generated surfaces with those of the physician‐drawn surfaces. The prostate shapes were also compared by generating maps of the surface separation after center‐of‐mass alignment. Three models were evaluated: a prostate‐only model, a bladder‐only model, and a joint prostate‐bladder model. Results: All models demonstrate the ability to successfully segment the soft tissue structures in the majority of cases. The average ratios of the prostate and bladder overlap volumes to the references volumes for the first seven patients were found to be 0.829 and 0.868 for the prostate only and bladder only models. The joint model results are similar, the corresponding ratios being 0.853 and 0.844. Surface separations for the two models were similar, the models generally being within 1 mm of the physician‐drawn shapes at mid‐organ, and along the right and left sides. Conclusion: Preliminary results from the proposed automatic segmentation method indicate it is sufficiently accurate for radiotherapy applications.

Principal manifolds and probabilistic subspaces for visual recognition

Investigates the use of linear and nonlinear principal manifolds for learning low-dimensional representations for visual recognition. Several leading techniques - principal component analysis (PCA), independent component analysis (ICA) and nonlinear kernel PCA (KPCA) - are examined and tested in a visual recognition experiment using 1,800+ facial images from the "FERET" (FacE REcognition Technology) database. We compare the recognition performance of nearest-neighbor matching with each principal manifold representation to that of a maximum a-posteriori (MAP) matching rule using a Bayesian similarity measure derived from dual probabilistic subspaces. The experimental results demonstrate the simplicity, computational economy and performance superiority of the Bayesian subspace method over principal manifold techniques for visual matching.