Statnote 27: Principal components analysis (PCA)

In Statnotes 24 and 25, multiple linear regression, a statistical method that examines the relationship between a single dependent variable (Y) and two or more independent variables (X), was described. The principle objective of such an analysis was to determine which of the X variables had a significant influence on Y and to construct an equation that predicts Y from the X variables. ‘Principal components analysis’ (PCA) and ‘factor analysis’ (FA) are also methods of examining the relationships between different variables but they differ from multiple regression in that no distinction is made between the dependent and independent variables, all variables being essentially treated the same. Originally, PCA and FA were regarded as distinct methods but in recent times they have been combined into a single analysis, PCA often being the first stage of a FA. The basic objective of a PCA/FA is to examine the relationships between the variables or the ‘structure’ of the variables and to determine whether these relationships can be explained by a smaller number of ‘factors’. This statnote describes the use of PCA/FA in the analysis of the differences between the DNA profiles of different MRSA strains introduced in Statnote 26.

Fluorescence and reflectance spectroscopy for identification of atherosclerosis in human carotid arteries using principal components analysis

Objectives: The aim of this work was to verify the differentiation between normal and pathological human carotid artery tissues by using fluorescence and reflectance spectroscopy in the 400- to 700-nm range and the spectral characterization by means of principal components analysis. Background Data: Atherosclerosis is the most common and serious pathology of the cardiovascular system. Principal components represent the main spectral characteristics that occur within the spectral data and could be used for tissue classification. Materials and Methods: Sixty postmortem carotid artery fragments (26 non-atherosclerotic and 34 atherosclerotic with non-calcified plaques) were studied. The excitation radiation consisted of a 488-nm argon laser. Two 600-mu m core optical fibers were used, one for excitation and one to collect the fluorescence radiation from the samples. The reflectance system was composed of a halogen lamp coupled to an excitation fiber positioned in one of the ports of an integrating sphere that delivered 5 mW to the sample. The photo-reflectance signal was coupled to a 1/4-m spectrograph via an optical fiber. Euclidean distance was then used to classify each principal component score into one of two classes, normal and atherosclerotic tissue, for both fluorescence and reflectance. Results: The principal components analysis allowed classification of the samples with 81% sensitivity and 88% specificity for fluorescence, and 81% sensitivity and 91% specificity for reflectance. Conclusions: Our results showed that principal components analysis could be applied to differentiate between normal and atherosclerotic tissue with high sensitivity and specificity.

Adaptive multiscale principal components analysis for online monitoring of wastewater treatment

Fault detection and isolation (FDI) are important steps in the monitoring and supervision of industrial processes. Biological wastewater treatment (WWT) plants are difficult to model, and hence to monitor, because of the complexity of the biological reactions and because plant influent and disturbances are highly variable and/or unmeasured. Multivariate statistical models have been developed for a wide variety of situations over the past few decades, proving successful in many applications. In this paper we develop a new monitoring algorithm based on Principal Components Analysis (PCA). It can be seen equivalently as making Multiscale PCA (MSPCA) adaptive, or as a multiscale decomposition of adaptive PCA. Adaptive Multiscale PCA (AdMSPCA) exploits the changing multivariate relationships between variables at different time-scales. Adaptation of scale PCA models over time permits them to follow the evolution of the process, inputs or disturbances. Performance of AdMSPCA and adaptive PCA on a real WWT data set is compared and contrasted. The most significant difference observed was the ability of AdMSPCA to adapt to a much wider range of changes. This was mainly due to the flexibility afforded by allowing each scale model to adapt whenever it did not signal an abnormal event at that scale. Relative detection speeds were examined only summarily, but seemed to depend on the characteristics of the faults/disturbances. The results of the algorithms were similar for sudden changes, but AdMSPCA appeared more sensitive to slower changes.

Forest soil short term response to prescribed fire: an approach by Principal Components Analysis

In the current context of serious climate changes, where the increase of the frequency of some extreme events occurrence can enhance the rate of periods prone to high intensity forest fires, the National Forest Authority often implements, in several Portuguese forest areas, a regular set of measures in order to control the amount of fuel mass availability (PNDFCI, 2008). In the present work we’ll present a preliminary analysis concerning the assessment of the consequences given by the implementation of prescribed fire measures to control the amount of fuel mass in soil recovery, in particular in terms of its water retention capacity, its organic matter content, pH and content of iron. This work is included in a larger study (Meira-Castro, 2009(a); Meira-Castro, 2009(b)). According to the established praxis on the data collection, embodied in multidimensional matrices of n columns (variables in analysis) by p lines (sampled areas at different depths), and also considering the quantitative data nature present in this study, we’ve chosen a methodological approach that considers the multivariate statistical analysis, in particular, the Principal Component Analysis (PCA ) (Góis, 2004). The experiments were carried out in a soil cover over a natural site of Andaluzitic schist, in Gramelas, Caminha, NW Portugal, who was able to maintain itself intact from prescribed burnings from four years and was submit to prescribed fire in March 2008. The soils samples were collected from five different plots at six different time periods. The methodological option that was adopted have allowed us to identify the most relevant relational structures inside the n variables, the p samples and in two sets at the same time (Garcia-Pereira, 1990). Consequently, and in addition to the traditional outputs produced from the PCA, we have analyzed the influence of both sampling depths and geomorphological environments in the behavior of all variables involved.

Increased audiovisual integration in cochlear-implanted deaf patients: independent components analysis of longitudinal positron emission tomography data.

It has been demonstrated in earlier studies that patients with a cochlear implant have increased abilities for audio-visual integration because the crude information transmitted by the cochlear implant requires the persistent use of the complementary speech information from the visual channel. The brain network for these abilities needs to be clarified. We used an independent components analysis (ICA) of the activation (H2 (15) O) positron emission tomography data to explore occipito-temporal brain activity in post-lingually deaf patients with unilaterally implanted cochlear implants at several months post-implantation (T1), shortly after implantation (T0) and in normal hearing controls. In between-group analysis, patients at T1 had greater blood flow in the left middle temporal cortex as compared with T0 and normal hearing controls. In within-group analysis, patients at T0 had a task-related ICA component in the visual cortex, and patients at T1 had one task-related ICA component in the left middle temporal cortex and the other in the visual cortex. The time courses of temporal and visual activities during the positron emission tomography examination at T1 were highly correlated, meaning that synchronized integrative activity occurred. The greater involvement of the visual cortex and its close coupling with the temporal cortex at T1 confirm the importance of audio-visual integration in more experienced cochlear implant subjects at the cortical level.

Diagnosing Patients Combining Principal Components Analysis and Case Based Reasoning

This paper addresses the application of a PCA analysis on categorical data prior to diagnose a patients data set using a Case-Based Reasoning (CBR) system. The particularity is that the standard PCA techniques are designed to deal with numerical attributes, but our medical data set contains many categorical data and alternative methods as RS-PCA are required. Thus, we propose to hybridize RS-PCA (Regular Simplex PCA) and a simple CBR. Results show how the hybrid system produces similar results when diagnosing a medical data set, that the ones obtained when using the original attributes. These results are quite promising since they allow to diagnose with less computation effort and memory storage

Diagnosing Patients Combining Principal Components Analysis and Case Based Reasoning

This paper addresses the application of a PCA analysis on categorical data prior to diagnose a patients data set using a Case-Based Reasoning (CBR) system. The particularity is that the standard PCA techniques are designed to deal with numerical attributes, but our medical data set contains many categorical data and alternative methods as RS-PCA are required. Thus, we propose to hybridize RS-PCA (Regular Simplex PCA) and a simple CBR. Results show how the hybrid system produces similar results when diagnosing a medical data set, that the ones obtained when using the original attributes. These results are quite promising since they allow to diagnose with less computation effort and memory storage

Fuzzy Principal Components Analysis

Due to the large number of characteristics, there is a need to extract the most relevant characteristicsfrom the input data, so that the amount of information lost in this way is minimal, and the classification realized with the projected data set is relevant with respect to the original data. In order to achieve this feature extraction, different statistical techniques, as well as the principal components analysis (PCA) may be used. This thesis describes an extension of principal components analysis (PCA) allowing the extraction ofa finite number of relevant features from high-dimensional fuzzy data and noisy data. PCA finds linear combinations of the original measurement variables that describe the significant variation in the data. The comparisonof the two proposed methods was produced by using postoperative patient data. Experiment results demonstrate the ability of using the proposed two methods in complex data. Fuzzy PCA was used in the classificationproblem. The classification was applied by using the similarity classifier algorithm where total similarity measures weights are optimized with differential evolution algorithm. This thesis presents the comparison of the classification results based on the obtained data from the fuzzy PCA.

Principal components analysis for quality evaluation of cooled banana 'Nanicão' in different packing

This work aims determinate the evaluation of the quality of 'Nanicão' banana, submitted to two conditions of storage temperature and three different kinds of package, using the technique of the Analysis of Principal Components (ACP), as a basis for an Analysis of Variance. The fruits used were 'Nanicão' bananas, at ripening degree 3, that is, more green than yellow. The packages tested were: "Torito" wood boxes, load capacity: 18 kg; "½ box" wood boxes, load capacity: 13 kg; and cardboard boxes, load capacity: 18 kg. The temperatures assessed were: room temperature (control); and (13±1ºC), with humidity controlled to 90±2,5%. Fruits were discarded when a sensory analysis determined they had become unfit for consumption. Peel coloration, percentages of imperfection, fresh mass, total acidity, pH, total soluble solids and percentages of sucrose were assessed. A completely randomized design with a 2-factorial treatment structure (packing X temperature) was used. The obtained data were analyzed through a multivariate analysis known as Principal Components Analysis, using S-plus 4.2. The conclusion was that the best packages to preserve the fruit were the ½ box ones, which proves that it is necessary to reduce the number of fruits per package to allow better ventilation and decreases mechanical injuries and ensure quality for more time.

Identifying the component structure of job satisfaction by principal components analysis among extension officers in North West Province, South Africa

The component structure of a 34-item scale measuring different aspects of job satisfaction was investigated among extension officers in North West Province, South Africa. A simple random sampling technique was used to select 40 extension officers from which data were collected. A structured questionnaire consisting of 34 job satisfaction and 10 personal characteristic items was administered to the extension officers. Items on job satisfaction were measured at interval level and analyzedwith Principal ComponentAnalysis. Most of the respondents (82.5%) weremales, between 40 to 45 years, 85% were married and 87.5% had a diploma as their educational qualification. Furthermore, 54% of the households size between 4 to 6 persons, whereas 75% were Christians. The majority of the extension officers lived in their job area (82.5), while 80% covered at least 3 communities and 3 farmer groups. In terms of number of farmers covered, only 40% of the extension officers covered more than 500 farmers and 45% travelled more than 40 km to reach their farmers. From the job satisfaction items 9 components were extracted to show areas for job satisfaction among extension officers. These were in-service training, research policies, communicating recommended practices, financial support for self and family, quality of technical help, opportunity to advance education, management and control of operations, rewarding system and sanctions. The results have several implications for motivating extension officers for high job performance especially with large number of clients and small number of extension agents.

Diagnosing Patients Combining Principal Components Analysis and Case Based Reasoning

This paper addresses the application of a PCA analysis on categorical data prior to diagnose a patients data set using a Case-Based Reasoning (CBR) system. The particularity is that the standard PCA techniques are designed to deal with numerical attributes, but our medical data set contains many categorical data and alternative methods as RS-PCA are required. Thus, we propose to hybridize RS-PCA (Regular Simplex PCA) and a simple CBR. Results show how the hybrid system produces similar results when diagnosing a medical data set, that the ones obtained when using the original attributes. These results are quite promising since they allow to diagnose with less computation effort and memory storage

Two Novel Methods For The Determination Of The Number Of Components In Independent Components Analysis Models

Independent Components Analysis is a Blind Source Separation method that aims to find the pure source signals mixed together in unknown proportions in the observed signals under study. It does this by searching for factors which are mutually statistically independent. It can thus be classified among the latent-variable based methods. Like other methods based on latent variables, a careful investigation has to be carried out to find out which factors are significant and which are not. Therefore, it is important to dispose of a validation procedure to decide on the optimal number of independent components to include in the final model. This can be made complicated by the fact that two consecutive models may differ in the order and signs of similarly-indexed ICs. As well, the structure of the extracted sources can change as a function of the number of factors calculated. Two methods for determining the optimal number of ICs are proposed in this article and applied to simulated and real datasets to demonstrate their performance.