Distinct Variation Pattern Discovery Using Alternating Nonlinear Principal Component Analysis.

Latent autoimmune diabetes in adults (LADA) which accounts for more than 10% of all cases of diabetes is characterized by onset after age 30, absence of ketoacidosis, insulin independence for at least 6 months, and presence of circulating islet-cell antibodies. Its marked heterogeneity in clinical features and immunological markers suggests the existence of multiple mechanisms underlying its pathogenesis. The principal component (PC) analysis is a statistical approach used for finding patterns in data of high dimension. In this study the PC analysis was applied to a set of variables from a cohort of Sardinian LADA patients to identify a smaller number of latent patterns. A list of 11 variables including clinical (gender, BMI, lipid profile, systolic and diastolic blood pressure and insulin-free time period), immunological (anti-GAD65, anti-IA-2 and anti-TPO antibody titers) and genetic features (predisposing gene variants previously identified as risk factors for autoimmune diabetes) retrieved from clinical records of 238 LADA patients referred to the Internal Medicine Unit of University of Sassari, Italy, were analyzed by PC analysis. The predictive value of each PC on the further development of insulin dependence was evaluated using Kaplan-Meier curves. Overall 4 clusters were identified by PC analysis. In component PC-1, the dominant variables were: BMI, triglycerides, systolic and diastolic blood pressure and duration of insulin-free time period; in PC-2: genetic variables such as Class II HLA, CTLA-4 as well as anti-GAD65, anti-IA-2 and anti-TPO antibody titers, and the insulin-free time period predominated; in PC-3: gender and triglycerides; and in PC-4: total cholesterol. These components explained 18, 15, 12, and 12%, respectively, of the total variance in the LADA cohort. The predictive power of insulin dependence of the four components was different. PC-2 (characterized mostly by high antibody titers and presence of predisposing genetic markers) showed a faster beta-cells failure and PC-3 (characterized mostly by gender and high triglycerides) and PC-4 (high cholesterol) showed a slower beta-cells failure. PC-1 (including dislipidemia and other metabolic dysfunctions), showed a mild beta-cells failure. In conclusion variable clustering might be consistent with different pathogenic pathways and/or distinct immune mechanisms in LADA and could potentially help physicians improve the clinical management of these patients.

In many fields such as data mining, machine learning, pattern recognition and signal processing, data sets containing huge number of features are often involved. Feature selection is an essential data preprocessing technique for such high-dimensional data classification tasks. Traditional dimensionality reduction approach falls into two categories: Feature Extraction (FE) and Feature Selection (FS). Principal component analysis is an unsupervised linear FE method for projecting high-dimensional data into a low-dimensional space with minimum loss of information. It discovers the directions of maximal variances in the data. The Rough set approach to feature selection is used to discover the data dependencies and reduction in the number of attributes contained in a data set using the data alone, requiring no additional information. For selecting discriminative features from principal components, the Rough set theory can be applied jointly with PCA, which guarantees that the selected principal components will be the most adequate for classification. We call this method Rough PCA. The proposed method is successfully applied for choosing the principal features and then applying the Upper and Lower Approximations to find the reduced set of features from a gene expressiondata.

Hyperspectral imaging was explored to detect Sclerotinia stem rot (SSR) on oilseed rape leaves with chemometric methods, and the influences of variable selection, machine learning, and calibration transfer methods on detection performances were evaluated. Three different sample sets containing healthy and infected oilseed rape leaves were acquired under different imaging acquisition parameters. Four discriminant models were built using full spectra, including partial least squares-discriminant analysis (PLS-DA), support vector machine (SVM), soft independent modeling of class analogies (SIMCA), and k-nearest neighbors (KNN). PLS-DA and SVM models were also built with the optimal wavelengths selected by principal component analysis (PCA) loadings, second derivative spectra, competitive adaptive reweighted sampling (CARS), and successive projections algorithm (SPA). The optimal wavelengths selected for each sample set by different methods were different; however, the optimal wavelengths selected by PCA loadings and second derivative spectra showed similarity between different sample sets. Direct standardization (DS) was successfully applied to reduce spectral differences among different sample sets. Overall, the results demonstrated that using hyperspectral imaging with chemometrics for plant disease detection can be efficient and will also help in the selection of optimal variable selection, machine learning, and calibration transfer methods for fast and accurate plant disease detection.

In recent year, stock investor in Indonesia increased rapidly, so it is required to do analysis about the stock that helps the investor in their investment plan. Clustering is beneficial to select the appropriate stock for investors. Unfortunately, stock prices keep varying from time to time. Consequently, it is not an easy work to select the stock for investment. In addition, stock price time series data are high dimensional data that influenced by many factors. In this study, high dimensional data are obtained by the time frame of each factor. Therefore, it is important to use a suitable technique to cluster high dimensional data. This paper presents High Dimensional Data Clustering (HDDC), a model-based clustering based on Gaussian Mixture Model, using the Expectation-Maximization (EM) algorithm. HDDC via EM algorithm gives a more robust result, and it possible to make an additional assumption. Moreover, this paper combines a high-dimensional clustering technique HDDC via EM algorithm and the most popular feature extraction technique Principal Component Analysis (PCA). This paper comparing methods of clustering technique HDDC and the combination between HDDC and PCA to know the most effective method which gives better result in clustering high-dimensional time series data. The 155 data features are reduced to 7 principal components using PCA analysis. Despite PCA has increased the time efficiency of building the model, clustering technique HDDC via EM algorithm enables to handle the high-dimensional data better than the combination with PCA.

In the oil and gas industry, an extensive volume of logging data is routinely generated and acquired during operations. This data is accumulated across various phases of exploration, production, and subsequent operations. The challenge lies in extracting meaningful insights from this high-dimensional dataset. Constraints in data visualization (such as the three spatial axes, x, y, and z) and manipulation further complicate the process of drawing valuable conclusions. As a method to tackle this challenge, a technique has been devised to streamline data visualization by reducing high-dimensional data to a lower dimensionality, while retaining vital features crucial for big data analysis. Principal component analysis (PCA) emerges as a prominent approach employed for data dimensionality reduction. PCA simplifies multivariate datasets encompassing well-logging tools (e.g., gamma ray, density, neutron porosity, and resistivity) and drilling parameters such as rate of penetration, weight on bit, and vibration data, condensing them into a reduced number of factors known as principal components (PCs). The results of the dimensionality reduction technique show that various logging data and drilling parameters were condensed into a set of principal components (PC1, PC2…PCx), where x corresponds to the number of utilized variables. The analysis indicates that the first two components (PC1, PC2) capture most of data patterns. The graphical representation of these components (PCA biplot) reveals distinct clusters with clear patterns, facilitating the identification of separate electro-facies. Moreover, PC1 exhibits a strong correlation with lithology variations, enabling its utilization in well-to-well correlation. Additionally, regression analysis demonstrates a significant predictive relationship between PCA components and well logging variables, allowing the use of the R-squared regression technique to forecast a result curve based on PCA input. Higher principal components are found to be more associated with formation fluid, thus complementing the standard petrophysical analysis. The industry's current shift is from data collection to practical applications. By employing diverse dimensionality reduction techniques, the workflow enables the analysis of big data in a more comprehensive manner, unveiling concealed trends and insights. This approach not only facilitates machine-learning and artificial-intelligence applications but also enables a deeper understanding of the data through descriptive forms, thereby supporting industry advancements.

In the last decade, many approaches have been developed to solve one-class classification (OCC) problems for anomaly detection. Many of them rely on estimating the statistical distribution of the data, find hidden patterns, or remap the data in advantageous feature spaces. This kind of techniques usually needs some a priori knowledge of the data distribution (i.e., Gaussian) or the setting of some parameters to achieve good classification performance, making their use less effective when the data distribution is unknown. In this paper, we propose a novel blind anomaly detection for low dimensional feature spaces, that exploits the flexibility of the neural network (NN) structure to find the class boundaries without any information about the shape of the data distribution. To prove the generality of the solution, we tested many different class shapes, and we applied it to a structural health monitoring (SHM) case study. Without requiring the tuning of hyperparameters, the performance of the proposed algorithm overcomes that of some known approaches like principal component analysis (PCA), kernel principal component analysis (KPCA), Gaussian mixture model (GMM), and autoassociative neural network (ANN) in many cases, and performs well in the specific SHM setting.

A new approach to identifying nonlinear principal component models is presented. This involves the application of linear principal component analysis (PCA) prior to the identification of a modified autoassociative neural network (AAN) that represents the required nonlinear PCA model. The benefits of this new approach are that (i) the size of the reduced set of linear principal components (PCs) is smaller than the set of recorded process variables, and (ii) the set of PCs is better conditioned as redundant and insignificant information is removed. The result is a new set of input data for a modified network. The usefulness of this approach is illustrated using a recorded industrial data that relates to crack detection in an industrial melter process.

In the last decade there has been a considerable development of spaceborne SAR sensors. All the major space agencies are planning future SAR missions with polarimetric capabilities. However there is still a need to guide electromagnetic and statistics theories that take advantage of this kind of information towards operational applications. The use of contextual information is often required for automatic interpretation and target detection. The implementation of fast and reliable algorithms that exploit both polarimetric and contextual information can be limited by the increased dimensionality of the problem. Principal Component Analysis (PCA) is a data analysis technique that relies on a simple transformation of recorded observation, stored in a vector, to produce statistically independent variables. Non-Linear PCA is commonly seen as a non-linear generalization and extension of standard PCA. If non-linear correlations between variables exist, NLPCA will describe the data with greater accuracy and/or by fewer factors than PCA. In this work a combination of polarimetric and contextual information is performed using an Auto Associative Neural Network. A set of polarimetric input features were chosen together with contextual descriptors in order to produce an information set having lower dimensionality that can be exploited in a classification problem.

In this paper, a novel apple Physalospora recognition approach based on the Gabor feature-based principal component analysis (GBPCA) is proposed. In this method, the principal component analysis (PCA) is a powerful technique for finding patterns in data of high dimensionality and can reduce the high dimensionality of the data space to the low dimensionality of feature space effectively. Gabor filter is an effective tool because of its accurate time-frequency localization and robustness against variations caused by illumination and rotation. Three main steps are taken in the proposed GBPCA: Firstly, Gabor features of different scales and orientations are extracted by convoluting the Gabor filter bank and the original gray images. Then eigenvectors in the direction of the largest variance of the training vectors is computed by PCA. An eigenspace is composed of these eigenvectors. Thirdly, we project the testing images into the constructed eigenspace and the Euclidean distance and nearest neighbor classifier are adopted for classification. Therefore, the proposed method is not only insensitive to illumination and rotation, but also efficient in feature matching. Experimental results demonstrate the effectiveness of the proposed GBPCA.

Principal Components Analysis

The identification of between-group differences and changes in gait mechanics are useful for injury prevention. Previous studies suggest the differences in gait biomechanical variables may interact in a complex non-linear fashion rather than a simple linear fashion. A non-linear multivariate analysis technique is therefore necessary to unravel the inherent structure in the gait data. Kernel principal component analysis (KPCA) is an extension of principal component analysis (PCA), the most widely used method in this field, and can provide inside into non-linear relationships of the variables of interest. Despite the growing use of PCA in running gait research, no prior studies have evaluated the utility of KPCA in determining the between-group differences in running gait patterns. Therefore, the objective of this study was to compare the performance of KPCA and PCA in identifying differences between male and female runners and as well between young and older runners in running gait kinematics. Running kinematic data were analysed on a gender group (female, n = 50; male, n = 50) and an age group (young, n = 50; older, n = 50) for discrete variables and waveform data. The following key results were obtained: (1) the performance of the KPCA for the identification of gender and age differences in running gait kinematics increased as compared to using the linear PCA; (2) the Gaussian function often performed better than the polynomial function for these two experiments; (3) there was no consistent optimal value of either the width σ of the Gaussian kernel or the degree d of the polynomial kernel for different data types and experiments. These results suggest that non-linear features extracted by KPCA could be potentially useful in identifying and discriminating between-group differences and changes in running gait patterns, and could provide useful information about the intrinsic non-linear dynamics of running movement.

This overview of process fault diagnosis concentrates on steady-state processes, continuous dynamic processes and batch processes. In steady-state processes, the classic linear model for process fault diagnosis based on the use of principal component analysis is discussed in some detail, followed by extensions of this model to nonlinear steady-state (non)Gaussian processes. These extensions include higher-order statistical models, such as based on the use of independent components, the use of principal curves and surfaces as well as neural networks as nonlinear extensions of principal component analysis. Likewise, innovations and applications of kernel methods are among other considered, including kernel principal component analysis, kernel partial least squares, kernel independent component analysis as well as multiple kernel learning variants of some of these approaches. Continuous dynamic processes are considered in terms of manifold models, adaptive methods and phase space methods, where the application of process diagnostics, such as correlation dimension and recurrence quantitative analyses, has been proposed. The multitude of recent developments in batch processing are similarly reviewed in terms of the multiway principal component model, extended to multiphase and multiblock models. These developments are considered in the broad framework outlined in Chap. 1.

Compressing movement information via principal components analysis (PCA): Contrasting outcomes from the time and frequency domains

Near infrared reflectance spectroscopy was used to discriminate different species of freshwater fish samples. Samples from seven freshwater fish species of the family Cyprinidae (black carp ( Mylopharyngodon piceus), grass carp ( Ctenopharyngodon idellus), silver carp ( Hypophthalmichthys molitrix), bighead carp ( Aristichthys nobilis), common carp ( Cyprinus carpio), crucian ( Carassius auratus), and bream ( Parabramis pekinensis)) were scanned by near infrared reflectance spectroscopy from 1000 nm to 1799 nm. Linear discriminant analysis models were built for the classification of species. We inspected the effect of partial least square, principal component analysis, competitive adaptive reweighted sampling, and fast Fourier transform on linear discriminant analysis. The results showed that the dimension reduction methods worked very well for this example. Linear discriminant analysis models which were combined with principal component analysis and fast Fourier transform could classify accurately all the samples under multiplicative scatter correction pre-processing. According to the loadings in principal component analysis, spectra wavelengths 1000, 1001, 1154, 1208, 1284, 1288, 1497, 1665, and 1770 nm were selected as effective wavelengths in linear discriminant analysis. The discriminant analysis was simplified by using effective wavelengths as independent variables in a linear discriminant analysis model. This study indicated that linear discriminant analysis combined with near infrared reflectance spectroscopy could be an effective strategy for the classification of freshwater fish species.

Unsupervised classification of multichannel profile data using PCA: An application to an emission control system