Probabilistic principal component analysis

Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum-likelihood estimation of parameters in a latent variable model closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the principal subspace iteratively, and discuss the advantages conveyed by the definition of a probability density function for PCA.

Probabilistic principal component analysis

Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum-likelihood estimation of parameters in a latent variable model closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the principal subspace iteratively, and discuss the advantages conveyed by the definition of a probability density function for PCA.

Extended principal component analysis and its applications to image analysis

The objectives of this research are to analyze and develop a modified Principal Component Analysis (PCA) and to develop a two-dimensional PCA with applications in image processing. PCA is a classical multivariate technique where its mathematical treatment is purely based on the eigensystem of positive-definite symmetric matrices. Its main function is to statistically transform a set of correlated variables to a new set of uncorrelated variables over $\IR\sp{n}$ by retaining most of the variations present in the original variables.^ The variances of the Principal Components (PCs) obtained from the modified PCA form a correlation matrix of the original variables. The decomposition of this correlation matrix into a diagonal matrix produces a set of orthonormal basis that can be used to linearly transform the given PCs. It is this linear transformation that reproduces the original variables. The two-dimensional PCA can be devised as a two successive of one-dimensional PCA. It can be shown that, for an $m\times n$ matrix, the PCs obtained from the two-dimensional PCA are the singular values of that matrix.^ In this research, several applications for image analysis based on PCA are developed, i.e., edge detection, feature extraction, and multi-resolution PCA decomposition and reconstruction. ^

Principal component analysis and assessment of language network activation patterns in pediatric epilepsy

This dissertation establishes a novel data-driven method to identify language network activation patterns in pediatric epilepsy through the use of the Principal Component Analysis (PCA) on functional magnetic resonance imaging (fMRI). A total of 122 subjects’ data sets from five different hospitals were included in the study through a web-based repository site designed here at FIU. Research was conducted to evaluate different classification and clustering techniques in identifying hidden activation patterns and their associations with meaningful clinical variables. The results were assessed through agreement analysis with the conventional methods of lateralization index (LI) and visual rating. What is unique in this approach is the new mechanism designed for projecting language network patterns in the PCA-based decisional space. Synthetic activation maps were randomly generated from real data sets to uniquely establish nonlinear decision functions (NDF) which are then used to classify any new fMRI activation map into typical or atypical. The best nonlinear classifier was obtained on a 4D space with a complexity (nonlinearity) degree of 7. Based on the significant association of language dominance and intensities with the top eigenvectors of the PCA decisional space, a new algorithm was deployed to delineate primary cluster members without intensity normalization. In this case, three distinct activations patterns (groups) were identified (averaged kappa with rating 0.65, with LI 0.76) and were characterized by the regions of: (1) the left inferior frontal Gyrus (IFG) and left superior temporal gyrus (STG), considered typical for the language task; (2) the IFG, left mesial frontal lobe, right cerebellum regions, representing a variant left dominant pattern by higher activation; and (3) the right homologues of the first pattern in Broca's and Wernicke's language areas. Interestingly, group 2 was found to reflect a different language compensation mechanism than reorganization. Its high intensity activation suggests a possible remote effect on the right hemisphere focus on traditionally left-lateralized functions. In retrospect, this data-driven method provides new insights into mechanisms for brain compensation/reorganization and neural plasticity in pediatric epilepsy.

Principal Component Analysis and Assessment of Language Network Activation Patterns in Pediatric Epilepsy

This dissertation establishes a novel data-driven method to identify language network activation patterns in pediatric epilepsy through the use of the Principal Component Analysis (PCA) on functional magnetic resonance imaging (fMRI). A total of 122 subjects’ data sets from five different hospitals were included in the study through a web-based repository site designed here at FIU. Research was conducted to evaluate different classification and clustering techniques in identifying hidden activation patterns and their associations with meaningful clinical variables. The results were assessed through agreement analysis with the conventional methods of lateralization index (LI) and visual rating. What is unique in this approach is the new mechanism designed for projecting language network patterns in the PCA-based decisional space. Synthetic activation maps were randomly generated from real data sets to uniquely establish nonlinear decision functions (NDF) which are then used to classify any new fMRI activation map into typical or atypical. The best nonlinear classifier was obtained on a 4D space with a complexity (nonlinearity) degree of 7. Based on the significant association of language dominance and intensities with the top eigenvectors of the PCA decisional space, a new algorithm was deployed to delineate primary cluster members without intensity normalization. In this case, three distinct activations patterns (groups) were identified (averaged kappa with rating 0.65, with LI 0.76) and were characterized by the regions of: 1) the left inferior frontal Gyrus (IFG) and left superior temporal gyrus (STG), considered typical for the language task; 2) the IFG, left mesial frontal lobe, right cerebellum regions, representing a variant left dominant pattern by higher activation; and 3) the right homologues of the first pattern in Broca's and Wernicke's language areas. Interestingly, group 2 was found to reflect a different language compensation mechanism than reorganization. Its high intensity activation suggests a possible remote effect on the right hemisphere focus on traditionally left-lateralized functions. In retrospect, this data-driven method provides new insights into mechanisms for brain compensation/reorganization and neural plasticity in pediatric epilepsy.

Visualization of learning in multilayer perceptron networks using principal component analysis

This paper is concerned with the use of scientific visualization methods for the analysis of feedforward neural networks (NNs). Inevitably, the kinds of data associated with the design and implementation of neural networks are of very high dimensionality, presenting a major challenge for visualization. A method is described using the well-known statistical technique of principal component analysis (PCA). This is found to be an effective and useful method of visualizing the learning trajectories of many learning algorithms such as back-propagation and can also be used to provide insight into the learning process and the nature of the error surface.

Multivariate Analysis for Animal Selection in Experimental Research

Background: Several researchers seek methods for the selection of homogeneous groups of animals in experimental studies, a fact justified because homogeneity is an indispensable prerequisite for casualization of treatments. The lack of robust methods that comply with statistical and biological principles is the reason why researchers use empirical or subjective methods, influencing their results. Objective: To develop a multivariate statistical model for the selection of a homogeneous group of animals for experimental research and to elaborate a computational package to use it. Methods: The set of echocardiographic data of 115 male Wistar rats with supravalvular aortic stenosis (AoS) was used as an example of model development. Initially, the data were standardized, and became dimensionless. Then, the variance matrix of the set was submitted to principal components analysis (PCA), aiming at reducing the parametric space and at retaining the relevant variability. That technique established a new Cartesian system into which the animals were allocated, and finally the confidence region (ellipsoid) was built for the profile of the animals’ homogeneous responses. The animals located inside the ellipsoid were considered as belonging to the homogeneous batch; those outside the ellipsoid were considered spurious. Results: The PCA established eight descriptive axes that represented the accumulated variance of the data set in 88.71%. The allocation of the animals in the new system and the construction of the confidence region revealed six spurious animals as compared to the homogeneous batch of 109 animals. Conclusion: The biometric criterion presented proved to be effective, because it considers the animal as a whole, analyzing jointly all parameters measured, in addition to having a small discard rate.

Characterization of soil chemical properties of strawberry fields using principal component analysis

One of the largest strawberry-producing municipalities of Rio Grande do Sul (RS) is Turuçu, in the South of the State. The strawberry production system adopted by farmers is similar to that used in other regions in Brazil and in the world. The main difference is related to the soil management, which can change the soil chemical properties during the strawberry cycle. This study had the objective of assessing the spatial and temporal distribution of soil fertility parameters using principal component analysis (PCA). Soil sampling was based on topography, dividing the field in three thirds: upper, middle and lower. From each of these thirds, five soil samples were randomly collected in the 0-0.20 m layer, to form a composite sample for each third. Four samples were taken during the strawberry cycle and the following properties were determined: soil organic matter (OM), soil total nitrogen (N), available phosphorus (P) and potassium (K), exchangeable calcium (Ca) and magnesium (Mg), soil pH (pH), cation exchange capacity (CEC) at pH 7.0, soil base (V%) and soil aluminum saturation(m%). No spatial variation was observed for any of the studied soil fertility parameters in the strawberry fields and temporal variation was only detected for available K. Phosphorus and K contents were always high or very high from the beginning of the strawberry cycle, while pH values ranged from very low to very high. Principal component analysis allowed the clustering of all strawberry fields based on variables related to soil acidity and organic matter content.

REDUÇÃO DE VARIÁVEIS DE ENTRADA DE REDES NEURAIS ARTIFICIAIS A PARTIR DE DADOS DE ANÁLISE DE COMPONENTES PRINCIPAIS NA MODELAGEM DE OXIGÊNIO DISSOLVIDO

The objective of this work is to demonstrate the efficient utilization of the Principal Components Analysis (PCA) as a method to pre-process the original multivariate data, that is rewrite in a new matrix with principal components sorted by it's accumulated variance. The Artificial Neural Network (ANN) with backpropagation algorithm is trained, using this pre-processed data set derived from the PCA method, representing 90.02% of accumulated variance of the original data, as input. The training goal is modeling Dissolved Oxygen using information of other physical and chemical parameters. The water samples used in the experiments are gathered from the Paraíba do Sul River in São Paulo State, Brazil. The smallest Mean Square Errors (MSE) is used to compare the results of the different architectures and choose the best. The utilization of this method allowed the reduction of more than 20% of the input data, which contributed directly for the shorting time and computational effort in the ANN training.

Analysis of diffusion tensor magnetic resonance imaging data using principal component analysis

An analysis method for diffusion tensor (DT) magnetic resonance imaging data is described, which, contrary to the standard method (multivariate fitting), does not require a specific functional model for diffusion-weighted (DW) signals. The method uses principal component analysis (PCA) under the assumption of a single fibre per pixel. PCA and the standard method were compared using simulations and human brain data. The two methods were equivalent in determining fibre orientation. PCA-derived fractional anisotropy and DT relative anisotropy had similar signal-to-noise ratio (SNR) and dependence on fibre shape. PCA-derived mean diffusivity had similar SNR to the respective DT scalar, and it depended on fibre anisotropy. Appropriate scaling of the PCA measures resulted in very good agreement between PCA and DT maps. In conclusion, the assumption of a specific functional model for DW signals is not necessary for characterization of anisotropic diffusion in a single fibre.

Ecological niche modeling and principal component analysis of Krameria Loefl. (Krameriaceae)

Krameria plants are found in arid regions of the Americas and present a floral system that attracts oil-collecting bees. Niche modeling and multivariate tools were applied to examine ecological and geographical aspects of the 18 species of this genus, using occurrence data obtained from herbaria and literature. Niche modeling showed the potential areas of occurrence for each species and the analysis of climatic variables suggested that North American species occur mostly in deserted or xeric ecoregions with monthly precipitation below 140 mm and large temperature ranges. South American species are mainly found in deserted ecoregions and subtropical savannas where monthly precipitation often exceeds 150 mm and temperature ranges are smaller. Principal Component Analysis (PCA) performed with values of temperature and precipitation showed that the distribution limits of Krameria species are primarily associated with maximum and minimum temperatures. Modeling of Krameria species proved to be a useful tool for analyzing the influence of the ecological niche variables in the geographical distribution of species, providing new information to guide future investigations. (C) 2011 Elsevier Ltd. All rights reserved.

3D face computational photography using PCA spaces

In this paper, we present a 3D face photography system based on a facial expression training dataset, composed of both facial range images (3D geometry) and facial texture (2D photography). The proposed system allows one to obtain a 3D geometry representation of a given face provided as a 2D photography, which undergoes a series of transformations through the texture and geometry spaces estimated. In the training phase of the system, the facial landmarks are obtained by an active shape model (ASM) extracted from the 2D gray-level photography. Principal components analysis (PCA) is then used to represent the face dataset, thus defining an orthonormal basis of texture and another of geometry. In the reconstruction phase, an input is given by a face image to which the ASM is matched. The extracted facial landmarks and the face image are fed to the PCA basis transform, and a 3D version of the 2D input image is built. Experimental tests using a new dataset of 70 facial expressions belonging to ten subjects as training set show rapid reconstructed 3D faces which maintain spatial coherence similar to the human perception, thus corroborating the efficiency and the applicability of the proposed system.

Chemosystematic studies of natural compounds isolated from Asteraceae: characterization of tribes by principal component analysis

This work describes an application of principal component analysis (PCA) on a database of secondary metabolites from the Asteraceae family. The numbers of occurrences of metabolites in 11 chemical classes for the different vibes of the family were used as variables, PCA allows the identification of chemical classes that contribute most to the subgroups classification within the family. Relationships between chemical composition and botanical classification were made. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Genetic parameters and principal component analysis for egg production from White Leghorn hens

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Classificador Fisherface Fuzzy para o reconhecimento de faces

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)