On the use of principal components in contemporany population genetics: a case study

In human Population Genetics, routine applications of principal component techniques are oftenrequired. Population biologists make widespread use of certain discrete classifications of humansamples into haplotypes, the monophyletic units of phylogenetic trees constructed from severalsingle nucleotide bimorphisms hierarchically ordered. Compositional frequencies of the haplotypesare recorded within the different samples. Principal component techniques are then required as adimension-reducing strategy to bring the dimension of the problem to a manageable level, say two,to allow for graphical analysis.Population biologists at large are not aware of the special features of compositional data and normally make use of the crude covariance of compositional relative frequencies to construct principalcomponents. In this short note we present our experience with using traditional linear principalcomponents or compositional principal components based on logratios, with reference to a specificdataset

Intelligent PCA contribution analysis for quality estimation in batch processes. Application in a sequencing batch reactor for wastewater treatment

En aquest treball, es proposa un nou mètode per estimar en temps real la qualitat del producte final en processos per lot. Aquest mètode permet reduir el temps necessari per obtenir els resultats de qualitat de les anàlisi de laboratori. S'utiliza un model de anàlisi de componentes principals (PCA) construït amb dades històriques en condicions normals de funcionament per discernir si un lot finalizat és normal o no. Es calcula una signatura de falla pels lots anormals i es passa a través d'un model de classificació per la seva estimació. L'estudi proposa un mètode per utilitzar la informació de les gràfiques de contribució basat en les signatures de falla, on els indicadors representen el comportament de les variables al llarg del procés en les diferentes etapes. Un conjunt de dades compost per la signatura de falla dels lots anormals històrics es construeix per cercar els patrons i entrenar els models de classifcació per estimar els resultas dels lots futurs. La metodologia proposada s'ha aplicat a un reactor seqüencial per lots (SBR). Diversos algoritmes de classificació es proven per demostrar les possibilitats de la metodologia proposada.

On-line event detection by recursive dynamic principal component analysis and gas sensor arrays under drift conditions

Leakage detection is an important issue in many chemical sensing applications. Leakage detection hy thresholds suffers from important drawbacks when sensors have serious drifts or they are affected by cross-sensitivities. Here we present an adaptive method based in a Dynamic Principal Component Analysis that models the relationships between the sensors in the may. In normal conditions a certain variance distribution characterizes sensor signals. However, in the presence of a new source of variance the PCA decomposition changes drastically. In order to prevent the influence of sensor drifts the model is adaptive and it is calculated in a recursive manner with minimum computational effort. The behavior of this technique is studied with synthetic signals and with real signals arising by oil vapor leakages in an air compressor. Results clearly demonstrate the efficiency of the proposed method.

Improving a leaves automatic recognition process using PCA

In this work we present a simulation of a recognition process with perimeter characterization of a simple plant leaves as a unique discriminating parameter. Data coding allowing for independence of leaves size and orientation may penalize performance recognition for some varieties. Border description sequences are then used, and Principal Component Analysis (PCA) is applied in order to study which is the best number of components for the classification task, implemented by means of a Support Vector Machine (SVM) System. Obtained results are satisfactory, and compared with [4] our system improves the recognition success, diminishing the variance at the same time.

Avaliação da qualidade do corpo hídrico do rio Tibagi na região de Ponta Grossa utilizando análise de componentes principais (PCA)

The aim of this paper was to evaluate alterations in the quality of the water of the Tibagi River caused by the urban and industrial activities in the region of Ponta Grossa. The study involved the monitoring of physico-chemical and microbiological parameters of the water body, which were evaluated by a principal components analysis routine. Sample collections were carried out monthly during one year (October of 2005 to September of 2006), at 3 sampling points: upstream and downstream of the industrial district and downstream from the city of Ponta Grossa. The principal components analysis showed the effect of point sources associated with industrial activity, which contribute to the rise of total concentration of amoniacal nitrogen and the reduction of dissolved oxygen in the studied region.

Compositional analysis of archaeological glasses

At CoDaWork'03 we presented work on the analysis of archaeological glass composi- tional data. Such data typically consist of geochemical compositions involving 10-12 variables and approximates completely compositional data if the main component, sil- ica, is included. We suggested that what has been termed `crude' principal component analysis (PCA) of standardized data often identi ed interpretable pattern in the data more readily than analyses based on log-ratio transformed data (LRA). The funda- mental problem is that, in LRA, minor oxides with high relative variation, that may not be structure carrying, can dominate an analysis and obscure pattern associated with variables present at higher absolute levels. We investigate this further using sub- compositional data relating to archaeological glasses found on Israeli sites. A simple model for glass-making is that it is based on a `recipe' consisting of two `ingredients', sand and a source of soda. Our analysis focuses on the sub-composition of components associated with the sand source. A `crude' PCA of standardized data shows two clear compositional groups that can be interpreted in terms of di erent recipes being used at di erent periods, re ected in absolute di erences in the composition. LRA analysis can be undertaken either by normalizing the data or de ning a `residual'. In either case, after some `tuning', these groups are recovered. The results from the normalized LRA are di erently interpreted as showing that the source of sand used to make the glass di ered. These results are complementary. One relates to the recipe used. The other relates to the composition (and presumed sources) of one of the ingredients. It seems to be axiomatic in some expositions of LRA that statistical analysis of compositional data should focus on relative variation via the use of ratios. Our analysis suggests that absolute di erences can also be informative

On the use of principal components in contemporany population genetics: a case study

In human Population Genetics, routine applications of principal component techniques are often required. Population biologists make widespread use of certain discrete classifications of human samples into haplotypes, the monophyletic units of phylogenetic trees constructed from several single nucleotide bimorphisms hierarchically ordered. Compositional frequencies of the haplotypes are recorded within the different samples. Principal component techniques are then required as a dimension-reducing strategy to bring the dimension of the problem to a manageable level, say two, to allow for graphical analysis. Population biologists at large are not aware of the special features of compositional data and normally make use of the crude covariance of compositional relative frequencies to construct principal components. In this short note we present our experience with using traditional linear principal components or compositional principal components based on logratios, with reference to a specific dataset

Analysis of Pleistocene paleodrainage evolution in the Po Basin (Italy) by multivariate statistical techniques

In order to obtain a high-resolution Pleistocene stratigraphy, eleven continuously cored boreholes, 100 to 220m deep were drilled in the northern part of the Po Plain by Regione Lombardia in the last five years. Quantitative provenance analysis (QPA, Weltje and von Eynatten, 2004) of Pleistocene sands was carried out by using multivariate statistical analysis (principal component analysis, PCA, and similarity analysis) on an integrated data set, including high-resolution bulk petrography and heavy-mineral analyses on Pleistocene sands and of 250 major and minor modern rivers draining the southern flank of the Alps from West to East (Garzanti et al, 2004; 2006). Prior to the onset of major Alpine glaciations, metamorphic and quartzofeldspathic detritus from the Western and Central Alps was carried from the axial belt to the Po basin longitudinally parallel to the SouthAlpine belt by a trunk river (Vezzoli and Garzanti, 2008). This scenario rapidly changed during the marine isotope stage 22 (0.87 Ma), with the onset of the first major Pleistocene glaciation in the Alps (Muttoni et al, 2003). PCA and similarity analysis from core samples show that the longitudinal trunk river at this time was shifted southward by the rapid southward and westward progradation of transverse alluvial river systems fed from the Central and Southern Alps. Sediments were transported southward by braided river systems as well as glacial sediments transported by Alpine valley glaciers invaded the alluvial plain. Kew words: Detrital modes; Modern sands; Provenance; Principal Components Analysis; Similarity, Canberra Distance; palaeodrainage

Constrained principal component analysis reveals functionally connected load-dependent networks involved in multiple stages of working memory

Constrained principal component analysis (CPCA) with a finite impulse response (FIR) basis set was used to reveal functionally connected networks and their temporal progression over a multistage verbal working memory trial in which memory load was varied. Four components were extracted, and all showed statistically significant sensitivity to the memory load manipulation. Additionally, two of the four components sustained this peak activity, both for approximately 3 s (Components 1 and 4). The functional networks that showed sustained activity were characterized by increased activations in the dorsal anterior cingulate cortex, right dorsolateral prefrontal cortex, and left supramarginal gyrus, and decreased activations in the primary auditory cortex and "default network" regions. The functional networks that did not show sustained activity were instead dominated by increased activation in occipital cortex, dorsal anterior cingulate cortex, sensori-motor cortical regions, and superior parietal cortex. The response shapes suggest that although all four components appear to be invoked at encoding, the two sustained-peak components are likely to be additionally involved in the delay period. Our investigation provides a unique view of the contributions made by a network of brain regions over the course of a multiple-stage working memory trial.

Method for exploratory cluster analysis and visualisation of single-trial ERP ensembles

Background: The validity of ensemble averaging on event-related potential (ERP) data has been questioned, due to its assumption that the ERP is identical across trials. Thus, there is a need for preliminary testing for cluster structure in the data. New method: We propose a complete pipeline for the cluster analysis of ERP data. To increase the signalto-noise (SNR) ratio of the raw single-trials, we used a denoising method based on Empirical Mode Decomposition (EMD). Next, we used a bootstrap-based method to determine the number of clusters, through a measure called the Stability Index (SI). We then used a clustering algorithm based on a Genetic Algorithm (GA)to define initial cluster centroids for subsequent k-means clustering. Finally, we visualised the clustering results through a scheme based on Principal Component Analysis (PCA). Results: After validating the pipeline on simulated data, we tested it on data from two experiments – a P300 speller paradigm on a single subject and a language processing study on 25 subjects. Results revealed evidence for the existence of 6 clusters in one experimental condition from the language processing study. Further, a two-way chi-square test revealed an influence of subject on cluster membership.

PCA Tomography: how to extract information from data cubes

Astronomy has evolved almost exclusively by the use of spectroscopic and imaging techniques, operated separately. With the development of modern technologies, it is possible to obtain data cubes in which one combines both techniques simultaneously, producing images with spectral resolution. To extract information from them can be quite complex, and hence the development of new methods of data analysis is desirable. We present a method of analysis of data cube (data from single field observations, containing two spatial and one spectral dimension) that uses Principal Component Analysis (PCA) to express the data in the form of reduced dimensionality, facilitating efficient information extraction from very large data sets. PCA transforms the system of correlated coordinates into a system of uncorrelated coordinates ordered by principal components of decreasing variance. The new coordinates are referred to as eigenvectors, and the projections of the data on to these coordinates produce images we will call tomograms. The association of the tomograms (images) to eigenvectors (spectra) is important for the interpretation of both. The eigenvectors are mutually orthogonal, and this information is fundamental for their handling and interpretation. When the data cube shows objects that present uncorrelated physical phenomena, the eigenvector`s orthogonality may be instrumental in separating and identifying them. By handling eigenvectors and tomograms, one can enhance features, extract noise, compress data, extract spectra, etc. We applied the method, for illustration purpose only, to the central region of the low ionization nuclear emission region (LINER) galaxy NGC 4736, and demonstrate that it has a type 1 active nucleus, not known before. Furthermore, we show that it is displaced from the centre of its stellar bulge.

Solid phase microextraction as a reliable alternative to conventional extraction techniques to evaluate the pattern of hydrolytically released components in Vitis vinifera L. grapes

In present research, headspace solid-phase microextraction (HS-SPME) followed by gas chromatography–mass spectrometry (GC–qMS), was evaluated as a reliable and improved alternative to the commonly used liquid–liquid extraction (LLE) technique for the establishment of the pattern of hydrolytically released components of 7 Vitis vinifera L. grape varieties, commonly used to produce the world-famous Madeira wine. Since there is no data available on their glycosidic fractions, at a first step, two hydrolyse procedures, acid and enzymatic, were carried out using Boal grapes as matrix. Several parameters susceptible of influencing the hydrolytic process were studied. The best results, expressed as GC peak area, number of identified components and reproducibility, were obtained using ProZym M with b-glucosidase activity at 35 °C for 42 h. For the extraction of hydrolytically released components, HS-SPME technique was evaluated as a reliable and improved alternative to the conventional extraction technique, LLE (ethyl acetate). HS-SPME using DVB/CAR/PDMS as coating fiber displayed an extraction capacity two fold higher than LLE (ethyl acetate). The hydrolyzed fraction was mainly characterized by the occurrence of aliphatic and aromatic alcohols, followed by acids, esters, carbonyl compounds, terpenoids, and volatile phenols. Concerning to terpenoids its contribution to the total hydrolyzed fraction is highest for Malvasia Cândida (23%) and Malvasia Roxa (13%), and their presence according previous studies, even at low concentration, is important from a sensorial point of view (can impart floral notes to the wines), due to their low odor threshold (μg/L). According to the obtained data by principal component analysis (PCA), the sensorial properties of Madeira wines produced by Malvasia Cândida and Malvasia Roxa could be improved by hydrolysis procedure, since their hydrolyzed fraction is mainly characterized by terpenoids (e.g. linalool, geraniol) which are responsible for floral notes. Bual and Sercial grapes are characterized by aromatic alcohols (e.g. benzyl alcohol, 2-phenylethyl alcohol), so an improvement in sensorial characteristics (citrus, sweet and floral odors) of the corresponding wines, as result of hydrolytic process, is expected.

Neuronal Assembly Detection and Cell Membership Specification by Principal Component Analysis

LOPES-DOS-SANTOS, V. , CONDE-OCAZIONEZ, S. ; NICOLELIS, M. A. L. , RIBEIRO, S. T. , TORT, A. B. L. . Neuronal assembly detection and cell membership specification by principal component analysis. Plos One, v. 6, p. e20996, 2011.

Multivariate analysis of fresh-cut carambola slices stored under different temperatures

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Short communication: Principal components and factor analytic models for test-day milk yield in Brazilian Holstein cattle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)