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.

Supervisory control of wastewater treatment plants by combining principal component analysis and fuzzy c-means clustering

In this paper a methodology for integrated multivariate monitoring and control of biological wastewater treatment plants during extreme events is presented. To monitor the process, on-line dynamic principal component analysis (PCA) is performed on the process data to extract the principal components that represent the underlying mechanisms of the process. Fuzzy c-means (FCM) clustering is used to classify the operational state. Performing clustering on scores from PCA solves computational problems as well as increases robustness due to noise attenuation. The class-membership information from FCM is used to derive adequate control set points for the local control loops. The methodology is illustrated by a simulation study of a biological wastewater treatment plant, on which disturbances of various types are imposed. The results show that the methodology can be used to determine and co-ordinate control actions in order to shift the control objective and improve the effluent quality.

Drying process of microcrystalline cellulose studied by attenuated total reflection IR spectroscopy with two-dimensional correlation spectroscopy and principal component analysis

Molecular interactions between microcrystalline cellulose (MCC) and water were investigated by attenuated total reflection infrared (ATR/IR) spectroscopy. Moisture-content-dependent IR spectra during a drying process of wet MCC were measured. In order to distinguish overlapping O–H stretching bands arising from both cellulose and water, principal component analysis (PCA) and, generalized two-dimensional correlation spectroscopy (2DCOS) and second derivative analysis were applied to the obtained spectra. Four typical drying stages were clearly separated by PCA, and spectral variations in each stage were analyzed by 2DCOS. In the drying time range of 0–41 min, a decrease in the broad band around 3390 cm−1 was observed, indicating that bulk water was evaporated. In the drying time range of 49–195 min, decreases in the bands at 3412, 3344 and 3286 cm−1 assigned to the O6H6cdots, three dots, centeredO3′ interchain hydrogen bonds (H-bonds), the O3H3cdots, three dots, centeredO5 intrachain H-bonds and the H-bonds in Iβ phase in MCC, respectively, were observed. The result of the second derivative analysis suggests that water molecules mainly interact with the O6H6cdots, three dots, centeredO3′ interchain H-bonds. Thus, the H-bonding network in MCC is stabilized by H-bonds between OH groups constructing O6H6cdots, three dots, centeredO3′ interchain H-bonds and water, and the removal of the water molecules induces changes in the H-bonding network in MCC.

Genetic variability in cultivated common bean beyond the two major gene pools

It is generally accepted that two major gene pools exist in cultivated common bean (Phaseolus vulgaris L.), a Middle American and an Andean one. Some evidence, based on unique phaseolin morphotypes and AFLP analysis, suggests that at least one more gene pool exists in cultivated common bean. To investigate this hypothesis, 1072 accessions from a common bean core collection from the primary centres of origin, held at CIAT, were investigated. Various agronomic and morphological attributes (14 categorical and 11 quantitative) were measured. Multivariate analyses, consisting of homogeneity analysis and clustering for categorical data, clustering and ordination techniques for quantitative data and nonlinear principal component analysis for mixed data, were undertaken. The results of most analyses supported the existence of the two major gene pools. However, the analysis of categorical data of protein types showed an additional minor gene pool. The minor gene pool is designated North Andean and includes phaseolin types CH, S and T; lectin types 312, Pr, B and K; and mostly A5, A6 and A4 types alpha-amylase inhibitor. Analysis of the combined categorical data of protein types and some plant categorical data also suggested that some other germplasm with C type phaseolin are distinguished from the major gene pools.

Are wing size, wing shape and asymmetry related to field fitness of Trichogramma egg parasitoids?

The effects of wing shape, wing size, and fluctuating asymmetry in these measures oil the field fitness of T. nr. brassicae and T. pretiosum were investigated. Trichogramma wasps mass-reared on eggs of the factitious host Sitotroga cerealella were released in tomato paddocks and those females ovipositing on Helicoverpo spp. eggs were recaptured. Comparisons of the recaptured group with a sample from the release population were used to assess fitness. Wing data were obtained by positioning landmarks on mounted forewings. Size was then measured as the centroid size computed from landmark distances, while Procrustes analysis followed by principal component analysis was used to assess wing shape. Similar findings were obtained for both Trichogramma species: fitness of wasps was strongly related to wing size and some shape dimensions, but not to the asymmetries of these measures. Wasps which performed well in the field had larger wings and a different wing shape compared to wasps from the mass reared population. Both size and the shape dimensions were linearly associated with fitness although there was also some evidence for non-linear selection on shape. The results suggest that wing shape and wing size are reliable predictors of field fitness for these Trichogramma wasps.

Chemical analysis of powdered metallurgical slags by X-ray fluorescence spectrometry

Slag composition determines the physical and chemical properties as well as the application performance of molten oxide mixtures. Therefore, it is necessary to establish a routine instrumental technique to produce accurate and precise analytical results for better process and production control. In the present paper, a multi-component analysis technique of powdered metallurgical slag samples by X-ray Fluorescence Spectrometer (XRFS) has been demonstrated. This technique provides rapid and accurate results, with minimum sample preparation. It eliminates the requirement for a fused disc, using briquetted samples protected by a layer of Borax(R). While the use of theoretical alpha coefficients has allowed accurate calibrations to be made using fewer standard samples, the application of pseudo-Voight function to curve fitting makes it possible to resolve overlapped peaks in X-ray spectra that cannot be physically separated. The analytical results of both certified reference materials and industrial slag samples measured using the present technique are comparable to those of the same samples obtained by conventional fused disc measurements.

Evaluation of eight spring onion genotypes, sulphur nutrition and soil-type effects with an electronic nose

Genotype, sulphur (S) nutrition and soil-type effects on spring onion quality were assessed using a 32-conducting polymer sensor E-nose. Relative changes in sensor resistance ratio (% dR/R) varied among eight spring onion genotypes. The % dR/R was reduced by S application in four of the eight genotypes. For the other four genotypes, S application gave no change in % dR/R in three, and increased % dR/R in the other. E-nose classification of headspace volatiles by a two-dimensional principal component analysis (PCA) plot for spring onion genotypes differed for S fertilisation vs. no S fertilisation. Headspace volatiles data set clusters for cv. 'White Lisbon' grown on clay or on sandy loam overlapped when 2.9 [Mahalanobis distance value (D2) = 1.6], or 5.8-(D2 = 0.3) kg S ha-1 was added. In contrast, clear separation (D2 = 7.5) was recorded for headspace volatile clusters for 0 kg S hd-1 on clay vs. sandy loam. Addition of 5.8 kg S ha-1 increased pyruvic acid content (mmole g-1 fresh weight) by 1.7-fold on average across the eight genotypes. However, increased S from 2.9 to 5.8 kg ha-1 did not significantly (P > 0.05) influence % dR/R, % dry matter (DM) or total soluble solids (TSS) contents, but significantly (P < 0.05) increased pyruvic acid content. TSS was significantly (P < 0.05) reduced by S addition, while % DM was unaffected. In conclusion, the 32-conducting polymer E-nose discerned differences in spring onion quality that were attributable to genotype and to variations in growing conditions as shown by the significant (P < 0.05) interaction effects for % dR/R.

Non-linear principal components analysis: an alternative method for finding patterns in environmental data

The main purpose of this article is to gain an insight into the relationships between variables describing the environmental conditions of the Far Northern section of the Great Barrier Reef, Australia, Several of the variables describing these conditions had different measurement levels and often they had non-linear relationships. Using non-linear principal component analysis, it was possible to acquire an insight into these relationships. Furthermore. three geographical areas with unique environmental characteristics could be identified. Copyright (c) 2005 John Wiley & Sons, Ltd.

Using multivariate analysis to predict the behaviour of soils under effluent irrigation

Onsite wastewater treatment systems aim to assimilate domestic effluent into the environment. Unfortunately failure of such systems is common and inadequate effluent treatment can have serious environmental implications. The capacity of a particular soil to treat wastewater will change over time. The physical properties influence the rate of effluent movement through the soil and its chemical properties dictate the ability to renovate effluent. A research project was undertaken to determine the role that physical and chemical soil properties play in predicting the long-term behaviour of soil under effluent irrigation and to determine if they have a potential function as early indicators of adverse effects of effluent irrigation on treatment sustainability. Principal Component Analysis (PCA) and Cluster Analysis grouped the soils independently of their soil classifications and allowed us to distinguish the most suitable soils for sustainable long term effluent irrigation and determine the most influential soil parameters to characterise them. Multivariate analysis allowed a clear distinction between soils based on the cation exchange capacities. This in turn correlated well with the soil mineralogy. Mixed mineralogy soils in particular sodium or magnesium dominant soils are the most susceptible to dispersion under effluent irrigation. The soil Exchangeable Sodium Percentage (ESP) was identified as a crucial parameter and was highly correlated with percentage clay, electrical conductivity, exchangeable sodium, exchangeable magnesium and low Ca:Mg ratios (less than 0.5).

The stability of P in coral reef fishes

The constancy of phenotypic variation and covariation is an assumption that underlies most recent investigations of past selective regimes and attempts to predict future responses to selection. Few studies have tested this assumption of constancy despite good reasons to expect that the pattern of phenotypic variation and covariation may vary in space and time. We compared phenotypic variance-covariance matrices (P) estimated for Populations of six species of distantly related coral reef fishes sampled at two locations on Australia's Great Barrier Reef separated by more than 1000 km. The intraspecific similarity between these matrices was estimated using two methods: matrix correlation and common principal component analysis. Although there was no evidence of equality between pairs of P, both statistical approaches indicated a high degree of similarity in morphology between the two populations for each species. In general, the hierarchical decomposition of the variance-covariance structure of these populations indicated that all principal components of phenotypic variance-covariance were shared but that they differed in the degree of variation associated with each of these components. The consistency of this pattern is remarkable given the diversity of morphologies and life histories encompassed by these species. Although some phenotypic instability was indicated, these results were consistent with a generally conserved pattern of multivariate selection between populations.

Predictors of osteoarthritis(OA) improvement in patients treated with Hylan G-F for knee OA.

Aim of study: Different criteria for treatment response were explored to identify predictors of OA improvement. Analyses were based on data from a previously reported 1-year randomized controlled trial of appropriate care with or without hylan G-F 20 in patients with knee OA. Methods: Five definitions of ‘‘patient responder’’ from baseline to month 12 were examined: at least 20% reduction in WOMAC pain score; at least 20% reduction in WOMAC pain score and at least 20% reduction in either the WOMAC stiffness or function score; OARSI responder criteria (Propositions A and B) for intra-articular drugs; and OMERACT-OARSI responder criteria (Proposition D). As an a posteriori analysis, multivariable logistic regression models for each definition of patient responder were developed using a forward selection method. The following variables were defined prior to modeling and considered in the model along with two-way interactions: age (O65 years), BMI, gender, X-ray grade (0, I, II vs III, IV), co-morbidity (1 or 2 conditions vs 3 or more), duration of OA in study knee (years), previous surgery of study knee, hylan G-F 20 injection technique, WOMAC pain, stiffness and function, and treatment group. Results: Hylan G-F 20 was a predictor of improvement for all patient responder definitions P ! 0.001; odds of improvement were 2.7 or higher for patients in the hylan G-F 20 group compared to appropriate care without hylan G-F 20. For three of the five patient responder definitions, X-ray grade was a predictor of improvement (P ! 0.10; lower X-ray grade increased the odds of improvement). For four of the five patient responder definitions, duration of OA was a predictor of improvement (P ! 0.10; shorter duration of OA increased the odds of improvement). Conclusion: Analyses showed that appropriate care with hylan G-F 20 is the dominant predictor of patient improvement. While high grade structural damage does not preclude a response, patients who are targeted early in the disease process when less structural damage has occurred, may have a greater chance of improvement.

Performance analysis using equivariant kernel density estimator in nonlinear mixture

This paper investigates the performance analysis of separation of mutually independent sources in nonlinear models. The nonlinear mapping constituted by an unsupervised linear mixture is followed by an unknown and invertible nonlinear distortion, are found in many signal processing cases. Generally, blind separation of sources from their nonlinear mixtures is rather difficult. We propose using a kernel density estimator incorporated with equivariant gradient analysis to separate the sources with nonlinear distortion. The kernel density estimator parameters of which are iteratively updated to minimize the output independence expressed as a mutual information criterion. The equivariant gradient algorithm has the form of nonlinear decorrelation to perform the convergence analysis. Experiments are proposed to illustrate these results.

Investigating the performance analysis of EASI algorithm and EKENS algorithm in nonlinear model

This paper investigates the performance of EASI algorithm and the proposed EKENS algorithm for linear and nonlinear mixtures. The proposed EKENS algorithm is based on the modified equivariant algorithm and kernel density estimation. Theory and characteristic of both the algorithms are discussed for blind source separation model. The separation structure of nonlinear mixtures is based on a nonlinear stage followed by a linear stage. Simulations with artificial and natural data demonstrate the feasibility and good performance of the proposed EKENS algorithm.