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

Quality of fresh-cut carambola (Averrhoa carambola L) is related to many chemical and biochemical variables especially those involved with softening and browning, both influenced by storage temperature. To study these effects, a multivariate analysis was used to evaluate slices packaged in vacuum-sealed polyolefin bags, and stored at 2.5 degrees C, 5 degrees C and 10 degrees C, for up to 16 d. The quality of slices at each temperature was correlated with the duration of storage, O(2) and CO(2) concentration in the package, physical chemical constituents, and activity of enzymes involved in softening (PG) and browning (PPO) metabolism. Three quality groups were identified by hierarchical cluster analysis, and the classification of the components within each of these groups was obtained from a principal component analysis (PCA). The characterization of samples by PCA clearly distinguished acceptable and non-acceptable slices. According to PCA, acceptable slices presented higher ascorbic acid content, greater hue angles ((o)h) and final lightness (L-5) in the first principal component (PC1). On the other hand, non-acceptable slices presented higher total pectin content. PPO activity in the PC1. Non-acceptable slices also presented higher soluble pectin content, increased pectin solubilisation and higher CO(2) concentration in the second principal component (PC2) whereas acceptable slices showed lower total sugar content. The hierarchical cluster and PCA analyses were useful for discriminating the quality of slices stored at different temperatures.

Two Dimensional Principal Component Analysis for Online Tamil Character Recognition

This paper presents a new application of two dimensional Principal Component Analysis (2DPCA) to the problem of online character recognition in Tamil Script. A novel set of features employing polynomial fits and quartiles in combination with conventional features are derived for each sample point of the Tamil character obtained after smoothing and resampling. These are stacked to form a matrix, using which a covariance matrix is constructed. A subset of the eigenvectors of the covariance matrix is employed to get the features in the reduced sub space. Each character is modeled as a separate subspace and a modified form of the Mahalanobis distance is derived to classify a given test character. Results indicate that the recognition accuracy using the 2DPCA scheme shows an approximate 3% improvement over the conventional PCA technique.

Physiological modules for generating discrete and rhythmic movements: Component analysis of EMG signals

A central question in Neuroscience is that of how the nervous system generates the spatiotemporal commands needed to realize complex gestures, such as handwriting. A key postulate is that the central nervous system (CNS) builds up complex movements from a set of simpler motor primitives or control modules. In this study we examined the control modules underlying the generation of muscle activations when performing different types of movement: discrete, point-to-point movements in eight different directions and continuous figure-eight movements in both the normal, upright orientation and rotated 90 degrees. To test for the effects of biomechanical constraints, movements were performed in the frontal-parallel or sagittal planes, corresponding to two different nominal flexion/abduction postures of the shoulder. In all cases we measured limb kinematics and surface electromyographic activity (EMB) signals for seven different muscles acting around the shoulder. We first performed principal component analysis (PCA) of the EMG signals on a movement-by-movement basis. We found a surprisingly consistent pattern of muscle groupings across movement types and movement planes, although we could detect systematic differences between the PCs derived from movements performed in each sholder posture and between the principal components associated with the different orientations of the figure. Unexpectedly we found no systematic differences between the figute eights and the point-to-point movements. The first three principal components could be associated with a general co-contraction of all seven muscles plus two patterns of reciprocal activatoin. From these results, we surmise that both "discrete-rhythmic movements" such as the figure eight, and discrete point-to-point movement may be constructed from three different fundamental modules, one regulating the impedance of the limb over the time span of the movement and two others operating to generate movement, one aligned with the vertical and the other aligned with the horizontal.

Occlusive Components Analysis

We study unsupervised learning in a probabilistic generative model for occlusion. The model uses two types of latent variables: one indicates which objects are present in the image, and the other how they are ordered in depth. This depth order then determines how the positions and appearances of the objects present, specified in the model parameters, combine to form the image. We show that the object parameters can be learnt from an unlabelled set of images in which objects occlude one another. Exact maximum-likelihood learning is intractable. However, we show that tractable approximations to Expectation Maximization (EM) can be found if the training images each contain only a small number of objects on average. In numerical experiments it is shown that these approximations recover the correct set of object parameters. Experiments on a novel version of the bars test using colored bars, and experiments on more realistic data, show that the algorithm performs well in extracting the generating causes. Experiments based on the standard bars benchmark test for object learning show that the algorithm performs well in comparison to other recent component extraction approaches. The model and the learning algorithm thus connect research on occlusion with the research field of multiple-causes component extraction methods.

Refining sparse principal components

In this paper, we discuss methods to refine locally optimal solutions of sparse PCA. Starting from a local solution obtained by existing algorithms, these methods take advantage of convex relaxations of the sparse PCA problem to propose a refined solution that is still locally optimal but with a higher objective value. © 2010 Springer -Verlag Berlin Heidelberg.

Soil differentiation using fingerprint Fourier transform infrared spectroscopy, chemometrics and genetic algorithm-based feature selection

Elliott, G. N., Worgan, H., Broadhurst, D. I., Draper, J. H., Scullion, J. (2007). Soil differentiation using fingerprint Fourier transform infrared spectroscopy, chemometrics and genetic algorithm-based feature selection. Soil Biology & Biochemistry, 39 (11), 2888-2896. Sponsorship: BBSRC / NERC RAE2008

Structural Analysis of Network Traffic Flows

Network traffic arises from the superposition of Origin-Destination (OD) flows. Hence, a thorough understanding of OD flows is essential for modeling network traffic, and for addressing a wide variety of problems including traffic engineering, traffic matrix estimation, capacity planning, forecasting and anomaly detection. However, to date, OD flows have not been closely studied, and there is very little known about their properties. We present the first analysis of complete sets of OD flow timeseries, taken from two different backbone networks (Abilene and Sprint-Europe). Using Principal Component Analysis (PCA), we find that the set of OD flows has small intrinsic dimension. In fact, even in a network with over a hundred OD flows, these flows can be accurately modeled in time using a small number (10 or less) of independent components or dimensions. We also show how to use PCA to systematically decompose the structure of OD flow timeseries into three main constituents: common periodic trends, short-lived bursts, and noise. We provide insight into how the various constituents contribute to the overall structure of OD flows and explore the extent to which this decomposition varies over time.

Fault reconstruction in linear dynamic systems using multivariate statistics

Treasure et al. (2004) recently proposed a new sub space-monitoring technique, based on the N4SID algorithm, within the multivariate statistical process control framework. This dynamic-monitoring method requires considerably fewer variables to be analysed when compared with dynamic principal component analysis (PCA). The contribution charts and variable reconstruction, traditionally employed for static PCA, are analysed in a dynamic context. The contribution charts and variable reconstruction may be affected by the ratio of the number of retained components to the total number of analysed variables. Particular problems arise if this ratio is large and a new reconstruction chart is introduced to overcome these. The utility of such a dynamic contribution chart and variable reconstruction is shown in a simulation and by application to industrial data from a distillation unit.

Application of Nonlinear PCA for Fault Detection in Polymer Extrusion Processes

This paper describes the application of an improved nonlinear principal component analysis (PCA) to the detection of faults in polymer extrusion processes. Since the processes are complex in nature and nonlinear relationships exist between the recorded variables, an improved nonlinear PCA, which incorporates the radial basis function (RBF) networks and principal curves, is proposed. This algorithm comprises two stages. The first stage involves the use of the serial principal curve to obtain the nonlinear scores and approximated data. The second stage is to construct two RBF networks using a fast recursive algorithm to solve the topology problem in traditional nonlinear PCA. The benefits of this improvement are demonstrated in the practical application to a polymer extrusion process.

The size and shape of shells used by hermit crabs: A multivariate analysis of Clibanarius erythropus

Shell attributes Such as weight and shape affect the reproduction, growth, predator avoidance and behaviour of several hermit crab species. Although the importance of these attributes has been extensively investigated, it is still difficult to assess the relative role of size and shape. Multivariate techniques allow concise and efficient quantitative analysis of these multidimensional properties, and this paper aims to understand their role in determining patterns of hermit crab shell use. To this end, a multivariate approach based on a combination of size-unconstrained (shape) PCA and RDA ordination was used to model the biometrics of southern Mediterranean Clibanarius erythropus Populations and their shells. Patterns of shell utilization and morphological gradients demonstrate that size is more important than shape, probably due to the limited availability of empty shells in the environment. The shape (e.g. the degree of shell elongation) and weight of inhabited shells vary considerably in both female and male crabs. However, these variations are clearly accounted for by crab biometrics in males only. Oil the basis of statistical evidence and findings from past studies. it is hypothesized that larger males of adequate size and strength have access to the larger, heavier and relatively more available shells of the globose Osilinus turbinatus, which cannot be used by average-sized males or by females investing energy in egg production. This greater availability allows larger males to select more Suitable Shapes. (C) 2009 Elsevier Masson SAS. All rights reserved.

Application of factor analysis and geostatistics to identify processes controlling the distribution and bioaccessibility of trace elements in Northern Ireland soils

Geologic and environmental factors acting over varying spatial scales can control
trace element distribution and mobility in soils. In turn, the mobility of an element in soil will affect its oral bioaccessibility. Geostatistics, kriging and principal component analysis (PCA) were used to explore factors and spatial ranges of influence over a suite of 8 element oxides, soil organic carbon (SOC), pH, and the trace elements nickel (Ni), vanadium (V) and zinc (Zn). Bioaccessibility testing was carried out previously using the Unified BARGE Method on a sub-set of 91 soil samples from the Northern Ireland Tellus1 soil archive. Initial spatial mapping of total Ni, V and Zn concentrations shows their distributions are correlated spatially with local geologic formations, and prior correlation analyses showed that statistically significant controls were exerted over trace element bioaccessibility by the 8 oxides, SOC and pH. PCA applied to the geochemistry parameters of the bioaccessibility sample set yielded three principal components accounting for 77% of cumulative variance in the data
set. Geostatistical analysis of oxide, trace element, SOC and pH distributions using 6862 sample locations also identified distinct spatial ranges of influence for these variables, concluded to arise from geologic forming processes, weathering processes, and localised soil chemistry factors. Kriging was used to conduct a spatial PCA of Ni, V and Zn distributions which identified two factors comprising the majority of distribution variance. This was spatially accounted for firstly by basalt rock types, with the second component associated with sandstone and limestone in the region. The results suggest trace element bioaccessibility and distribution is controlled by chemical and geologic processes which occur over variable spatial ranges of influence.

Material Identification of Loose Particles in Sealed Electronic Devices Using PCA and SVM

The existence of loose particles left inside the sealed electronic devices is one of the main factors affecting the reliability of the whole system. It is important to identify the particle material for analyzing their source. The conventional material identification algorithms mainly rely on time, frequency and wavelet domain features. However, these features are usually overlapped and redundant, resulting in unsatisfactory material identification accuracy. The main objective of this paper is to improve the accuracy of material identification. First, the principal component analysis (PCA) is employed to reselect the nine features extracted from time and frequency domains, leading to six less correlated principal components. And then the reselected principal components are used for material identification using a support vector machine (SVM). Finally, the experimental results show that this new method can effectively distinguish the type of materials including wire, aluminum and tin particles.

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