Nonlinear PCA & Feature Extraction

Principal Components Analysis (PCA) is an invaluable statistical tool in signal processing. In many cases, an on-line algorithm to adapt the PCA network to determine the principal projections in the input space is desired. Algorithms proposed until now use the traditional deflation or the inflation procedure to determine the intermediate components sequentially, after the convergence of the principal or minor component is achieved. In this paper, we propose a constrained linear network and a robust cost function to determine any number of principal components simultaneously. The topology exploits the fact that the eigenvector matrix sought is orthonormal. A gradient-based algorithm named SIPEX-G is also presented.

Genome-wide association studies (GWAS) are susceptible to bias due to population stratification (PS). The most widely used method to correct bias due to PS is principal components (PCs) analysis (PCA), but there is no objective method to guide which PCs to include as covariates. Often, the ten PCs with the highest eigenvalues are included to adjust for PS. This selection is arbitrary, and patterns of local linkage disequilibrium may affect PCA corrections. To address these limitations, we estimate genomic propensity scores based on all statistically significant PCs selected by the Tracy-Widom (TW) statistic. We compare a principal components and propensity scores (PCAPS) approach to PCA and EMMAX using simulated GWAS data under no, moderate, and severe PS. PCAPS reduced spurious genetic associations regardless of the degree of PS, resulting in odds ratio (OR) estimates closer to the true OR. We illustrate our PCAPS method using GWAS data from a study of testicular germ cell tumors. PCAPS provided a more conservative adjustment than PCA. Advantages of the PCAPS approach include reduction of bias compared to PCA, consistent selection of propensity scores to adjust for PS, the potential ability to handle outliers, and ease of implementation using existing software packages.

Based on the linear unmixing images of different surface objects, online dictionary learning algorithm was utilized to compute the sparse dictionaries for multispectral linear unmixing images and panchromatic images. Principal component analysis (PCA) was then utilized to generate united sparse PCA dictionaries through the extraction of the first principal components of panchromatic images and unmixing image dictionaries. The number of dictionaries is determined to be 480 after taking into consideration of the limitation in computing power and root-mean-square error of restructured images. Based on these dictionaries, orthogonal matching pursuit method was utilized to calculate the sparse coefficients of multispectral and panchromatic images, separately, while nonnegative matrix factorization fusion algorithm was utilized to calculate multispectral and panchromatic sparse coefficients to obtain sparse coefficient of the fusional image on all bands, with the resulted matrix having a size of 480 × 255 025. These united sparse PCA dictionaries and fusion sparse coefficients were then used to reconstruct the fusional image. Through the analysis of five quantitative indices of fusion assessment, the proposed fusion algorithm has retained the multispectral information of images and enhanced the detailed information in image texture.

A unified learning algorithm to extract principal and minor components

In this paper, a condition monitoring and fault diagnosis system for induction motors is proposed by integrating artificial intelligence algorithms: principal component analysis (PCA), genetic algorithm (GA) and an artificial neural network (ANN). As main diagnosis media of fault motor, three-direction vibration signals and three-phase stator current signals are selected to measure. Multi-sensor measurement results in lots of data transfer that makes on-line or continuous condition monitoring and fault diagnosis difficult. Data transform into feature information provides a solution. Features are calculated from many domains to keep original data information at the highest level. In order to avoid the curse of dimensionality phenomenon and improve fault identification accuracy rate, PCA and GA are employed to reduce the feature dimensionality of the measured data. PCA removes the relative features, and extracts the principal components (PCs) from the original features. Then the significant features are selected from the extracted features by GA as inputs to the neural network. GA is also used to optimize the ANN parameters. The efficiency of the proposed system is validated through monitoring and diagnosing induction motor conditions, and comparing with other systems. The results show good performance of the proposed system and promising application

Breast cancer is the leading cancer among females, the key technology of preventing breast cancers is early detection. Based on the advantage of support vector machine (SVM), finding global solution and possessing higher generalization capability on dealing with the small sample, a new method of diagnosing breast cancer by CAD is proposed in this paper. Firstly, a principal component analysis is used to represent the information of ROI image, which account for most of the variance of the original data set while significantly reducing the data dimension. After the extraction of principal components, only those data of which account for most part of variance were retained as the feature vector and input into a SVM classification and BP neural network classification to classify. Finally, the results of experiment show that the accuracy and specificity for the diagnosis of breast cancer using SVM classification is good.

Groundwater is considered as one of the most important sources for water supply in Iran. The Fasa Plain in Fars Province, Southern Iran is one of the major areas of wheat production using groundwater for irrigation. A large population also uses local groundwater for drinking purposes. Therefore, in this study, this plain was selected to assess the spatial variability of groundwater quality and also to identify main parameters affecting the water quality using multivariate statistical techniques such as Cluster Analysis (CA), Discriminant Analysis (DA), and Principal Component Analysis (PCA). Water quality data was monitored at 22 different wells, for five years (2009-2014) with 10 water quality parameters. By using cluster analysis, the sampling wells were grouped into two clusters with distinct water qualities at different locations. The Lasso Discriminant Analysis (LDA) technique was used to assess the spatial variability of water quality. Based on the results, all of the variables except sodium absorption ratio (SAR) are effective in the LDA model with all variables affording 92.80% correct assignation to discriminate between the clusters from the primary 10 variables. Principal component (PC) analysis and factor analysis reduced the complex data matrix into two main components, accounting for more than 95.93% of the total variance. The first PC contained the parameters of TH, Ca2+, and Mg2+. Therefore, the first dominant factor was hardness. In the second PC, Cl-, SAR, and Na+ were the dominant parameters, which may indicate salinity. The originally acquired factors illustrate natural (existence of geological formations) and anthropogenic (improper disposal of domestic and agricultural wastes) factors which affect the groundwater quality.

The principal components, i.e. the eigenvectors corresponding to the largest eigenvalues of an autocorrelation matrix, contain the desired information of the considered signal. The principal component analysis (PCA) algorithms have a widespread application field in signal and image processing. We propose an invariant-norm algorithm with complex values. The solutions of the corresponding averaging differential equations converge to the principal eigenvectors of the autocorrelation matrix. This PCA algorithm is suitable for complex values of the input and the weight vectors. In addition, we consider a possibility to reduce the computational complexity of the proposed algorithm.

Principal Component Analysis (PCA), also known as Proper Orthogonal Decomposition (POD), is one of the prevailing Reduced Order Modeling (ROM) techniques for aerodynamic data analysis. Along with the PCA, its variant for missing data, gappy POD, has recently found its application by transforming problems into missing data problems. In this paper, an alternative based on probability theory, i.e., Probabilistic Principal Component Analysis (PPCA), is employed for aerodynamic data reconstruction problems in lieu of the PCA and the gappy POD. Unlike the PCA, the PPCA generates spanning vectors of low-dimensional space iteratively with an Expectation Maximization (EM) algorithm. The combined algorithm, termed as Expectation-Maximization Probabilistic Principal Component Analysis (EM-PCA), can deal with not only complete data but also incomplete data sets, since the EM algorithm naturally incorporates missing data in its formulation. Therefore, the EM-PCA has potential to be a substitute for both PCA and gappy POD. For illustration, the EM-PCA is applied to complete as well as incomplete snapshot ensembles compiled from aerodynamic simulations, and acquired modes and restored data are verified with those obtained by the PCA and the gappy POD.

Principal component analysis and hierarchical cluster analysis were applied to investigate physicochemical and instrumental textural properties of fresh kashar cheese. Four different principal components sufficiently explained the variability in the cheese samples. In addition, hierarchical cluster analysis was performed to group the kashar cheese samples regarding physicochemical and instrumental textural properties. Instrumental textural properties indicated greater variability than chemical composition of cheese samples. Principal component analysis revealed that color parameters were positively correlated with textural and chemical parameters. The results of this study revealed that other parameters rather than chemical composition would be effective on the instrumental textural properties. It was proved that principal component analysis was a very effective statistical tool to determine quality of cheese samples. According to the principal component analysis and hierarchical cluster analysis results, the attributes defining the kashar cheese samples were determined to be primarily the texture profile analysis parameters.

Early prediction of the shelf-life of medium-heat whole milk powders using stepwise multiple regression and principal component analysis

Improving the classification of Landsat data using standardized principal components analysis

Principal component analysis (PCA) and minor component analysis (MCA) are two important statistical tools which have many applications in the fields of signal processing and data analysis. PCA and MCA neural networks (NNs) can be used to online extract principal component and minor component from input data. It is interesting to develop generalized learning algorithms of PCA and MCA NNs. Some novel generalized PCA and MCA learning algorithms are proposed in this paper. Convergence of PCA and MCA learning algorithms is an essential issue in practical applications. Traditionally, the convergence is studied via deterministic continuous-time (DCT) method. The DCT method requires the learning rate of the algorithms to approach to zero, which is not realistic in many practical applications. In this paper, deterministic discrete-time (DDT) method is used to study the dynamical behaviors of the proposed algorithms. The DDT method is more reasonable for the convergence analysis since it does not require constraints as that of the DCT method. It is proven that under some mild conditions, the weight vector in these proposed algorithms will converge exponentially to principal or minor component. Simulation results are further used to illustrate the theoretical results.

This study integrated conventional statistical tools with neighbourhood linkage to propose the statistical diagnosis approach. Fourteen monitoring wells in Kaohsiung Science Park were selected as study case, and lab data of routine groundwater analysis including pH, EC, hardness, TDS, TOC, ammonia, nitrate, nitrite, chloride, sulphate, fluoride, phenols, Fe, Mn, As, and temperature were subjected to principal component and cluster analysis. Principal component analysis (PCA) was utilized to reflect those chemical data with the greatest correlation, and PCA results identified five major principal components (PCs) representing 74.6% of cumulative variance. Based on the monitoring data between 2005 and 2008, the extracted information from the PCA mirrored the potential sources of groundwater contamination as acid leakage, arsenic dissolution, salinization, mineralization, and fluoride release. Cluster analysis (CA) was used to evaluate the similarities of water quality in groundwater samples, and five clusters were assigned in two-step clustering for corresponding with the number of PCs, i.e. the potential sources of groundwater contamination. The interpreted facts from CA illustrated that the classified monitoring wells in each cluster properly match up with the identified processes. With the aid of neighbourhood linkage, the domain of groundwater contamination can be spatially outlined by mapping the neighbouring wells within the identical cluster. Therefore, the nature of underlying processes affecting groundwater quality was explored by statistical diagnosis.

The aim of the present article was to reconsider several conclusions by Velicer and Jackson (1990a) in their review of issues that arise when comparing common factor analysis and principal component analysis. Specifically, the three conclusions by Velicer and Jackson that are considered in the present article are: (a) that common factor and principal component solutions are similar, (b) that differences between common factor and principal component solutions appear only when too many dimensions are extracted, and (c) that common factor and principal component parameters are equally generalizable. In contrast, Snook and Gorsuch (1989) argued recently that principal component analysis and common factor analysis led to different, dissimilar estimates of pattern loadings, terming the principal component loadings biased and the common factor loadings unbiased. In the present article, after replicating the Snook and Gorsuch results, an extension demonstrated that the difference between common factor and principal component pattern loadings is inversely related to the number of indicators per factor, not to the total number of observed variables in the analysis, countering claims by both Snook and Gorsuch and Velicer and Jackson. Considering the more general case of oblique factors, one concomitant of overrepresentation of pattern loadings is an underrepresentation of intercorrelations among dimensions represented by principal component analysis, whereas comparable values obtained using factor analysis are accurate. Differences in parameters deriving from principal component analysis and common factor analysis were explored in relation to several additional aspects of population data, such as variation in the level of communality of variables on a given factor and the moving of a variable from one battery of measures to another. The results suggest that principal component analysis should not be used if a researcher wishes to obtain parameters reflecting latent constructs or factors.