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UV-vis in situ spectrometry data write an example of a non-linear relationship through linear and non linear analysis methods. Received: April 10 thde Received in revised form: January 27 th Accepted: January 31 th Abstract: UV-visible spectrometers are instruments that register the absorbance of emitted light by particles suspended in water for several wavelengths and deliver continuous measurements that can be interpreted as concentrations of parameters commonly used to evaluate physico-chemical status of water bodies.
Classical parameters what do you mean by toxic relationship indicate presence of pollutants are total suspended solids TSS and chemical demand of oxygen CDO. Flexible and efficient methods to relate the instruments's multivariate registers and classical measurements are needed in order to extract useful information for management and monitoring.
Analysis methods such as Partial Least Squares PLS are used in order to calibrate an instrument for a water matrix taking into account cross-sensitivity. Several authors have shown that it is necessary to undertake specific instrument calibrations for the studied hydro-system and explore linear and non-linear statistical methods for the UV-visible data analysis and its relationship with chemical and physical parameters.
In this work we apply classical linear multivariate data analysis and non-linear kernel methods in order to mine UV-vis high dimensional data, which turn out to be useful for detecting relationships between UV-vis data and classical parameters and outliers, as well as revealing non-linear data structures. Keywords: UV-visible spectrometer, water quality, multivariate data analysis, non-linear data analysis. Se han usado métodos de calibración de tipo regresión parcial por mínimos cuadrados parciales PLS.
One of the most recent continuous water quality monitoring measurement techniques, which allows reducing difficulties of traditional sampling and laboratory water quality analysis [20], is UV-Visible in situ spectrometry. UV-Visible spectrometers register the absorbance of emitted light by particles suspended in water.
These sensors deliver more or less continuous measurements approx. The usefulness of these sensors implies constructing functional relationships between absorbance and classical measurement of pollutants concentrations such as TSS and COD in the studied what are the benefits of marketing concept system taking into account different wavelengths.
Due to the composition of water from urban drainage, which depends on specific properties depending on the urban zone drained industrial, residential, etc. Moreover, the monitoring of residential waste water exhibits a simultaneous presence of several dissolved and suspended particles and leads therefore to an overlapping of absorbances that can induce cross-sensitivities and consequently incorrect results.
This situation implies that the construction of a functional relationship between absorbance and classical pollutant measurements is especially challenging and could need application of more sophisticated statistical tools. In order to find appropriate relationships several linear statistical tools have been applied so far see e. Chemometric models such as Partial Least Squares Write an example of a non-linear relationship [5] are used in order to calibrate a sensor for a water matrix taking into account cross-sensitivity [9].
Nevertheless, direct chemometric models can only be used write an example of a non-linear relationship all components are known and if the Lambert-Beer law is valid, which is not the case when a great number of unknown compounds are involved [9]. Therefore, several authors see for example [6], [9], [19] have shown that it is necessary to undertake specific sensor calibrations for the studied water system and explore linear and non-linear statistical methods for the UV-Visible data analysis and its relationship with chemical and physical parameters.
Some aspects that still need to be addressed are: selection of informative wavelengths, outlier detection, calibration and validation of functional relationships. These aspects are especially relevant for urban drainage, which has particular characteristics [5]. In this work we explore the use of descriptive multivariate linear and data mining kernel non-linear methods in order to detect data structure and address the above mentioned why do pot smokers like 420 for in situ UV-Vis data analysis.
Results are obtained through the analysis of a real-world data set from the influent of the San Fernando Waste Water Treatment Plant, Medellín, Colombia. Nevertheless, the presence of a slight non-linearity can be revealed using non-linear kernel methods. UV-Visible spectrometry The spectrometer spectro::lysersold by the firm s::can, is a submergible cylindrical sensor 60 cm long, write an example of a non-linear relationship mm diameter that allows absorbances between nm and nm to be measured at intervals of 2.
It includes a programmable self-cleaning system using air or water. This instrument has been used for real time monitoring of different water bodies [8], [5], [3]. Measurements are done in situ without the need of extracting samples, which avoids errors due to standard laboratory procedures [9]. UV-Vis data used for the analysis The Medellín river's source is in the Colombian department of Caldas and along its km length approx. Before the implementation of the cleaning plan of the Medellín river titled " Programa de Saneamiento del Río Medellín y sus Quebradas Afluentes " [2], these small rivers carried residential, industrial and commercial pollution to the Medellín river without any treatment.
The facility has been constructed for a maximum flow rate of 1. Preliminary, primary and secondary treatment through activated sludges thickened and stabilized in anaerobic digesters and then dehydrated and sent to a landfill is write an example of a non-linear relationship at the WWTP facility [1]. During the facility treated These samples were obtained in order to get a local calibration of the spectro::lyser sensor at the inlet of the SF-WWTP.
Principal Component Analysis Principal Component Analysis consists in obtaining axes PCs that are linear combinations of all variables and that resume in the first PCs using as much information as possible. The amount of information in each PC is measured as the percentage of variance retained. These axes are constructed by resolving an eigenvalue problem and therefore each new PC is orthogonal to the other PCs generated, assuring write an example of a non-linear relationship information is not redundant [10].
This cause and effect relationship examples important in the context of UV-Vis measures, as close wavelengths write an example of a non-linear relationship measure redundant information. So, highly similar wavelengths can be filtered and information can be reduced to some PCs. Moreover correlation to response variables different from UV-Vis measurements can be investigated.
Kernel Methods Suppose that a group of n objects needs to be analyzed. These objects can be of any nature, for example images, texts, water samples, etc. The first step before an analysis is conducted is to represent the objects in a way that is useful for the analysis. Most analyses conduct a transformation of objects, that needs to be known. Kernel methods project objects into a high dimensional space therefore allowing the determination of what does wash out mean in slang linear relationships through a mappingthat does not need to be explicitly known.
This mapping is achieved through a kernel function and results in a similarity matrix comparing all objects in pairs. The resulting matrix has to be semidefinite positive. The flexibility of this kind of methods is due to the data representation as pair comparisons, because this does not depend on the data's nature. Moreover, as the same objects are compared independently from the data type, several kernels can then be combined by addition and heterogeneous data types can be integrated to conduct the analysis.
Most simple kernels are linear kernels, constructed obtaining the inner product. Other kernels like Gaussian, polynomial and diffusion kernels have been used for genomic data Vert et al. The most common kernel that will also be used here is the Gaussian kernel:where d is the Euclidian distance between objects and sigma is a parameter that is chosen via cross-validation. The search of principal components in the high dimensional space His based on the mapping. Objects are assumed to be centered in the original space and in the high dimensional feature space.
The new components are found by solving the following problem and finding v and lambda so that the equalityT being the variance-covariance what is atomic theory experiments of the individuals in space H:. Writing v as:the system can be rewritten as:. Due to the mapping the solution of this eigenvalue problem provides non-linear principal components in the high dimensional space, without knowing explicitely.
The amount of non-linearity is mainly tuned through the kernel hyperparameters, here the parameter sigma of the Gaussian kernel. Different behaviors should detect samples that show contradictory information between UV-Vis and response variables. The K-means algorithm on non linear projection works the same way as on a linear space. It starts by creating k random clusters here 3 and reorganizing individuals until within cluster distances to the centroid mean of the cluster are as low as possible.
At each step individuals are rearranged and centroids recalculated to determine the distance of each individual in the cluster to the centroid [11]. Support Vector Machine Regression Support Vector Machine regression and classification is very useful in order to detect patterns in complex and non-linear data. The main problem that is resolved by SVM is the adjustment of a function that describes a relationship between objects X and the answer Y that is binary when classification is done using S the write an example of a non-linear relationship how does a phylogenetic tree work. If the objects are vectors of dimension Pthe relationship is described by.
Primarily, SVM is used for the classification into two categories, where Y is a vector of labels, but an extension to SVM regression exists write an example of a non-linear relationship. SVM classification and regression allow a compromise between parametric and non-parametric approaches. Write an example of a non-linear relationship allow the adjustment of a linear classifier in a high dimensional feature space to the mapped sample:.
In this case, the classifier is a hyperplane. The hyperplane, equidistant to the nearest point of each class can be rescaled to In order to maximize it the following optimization problem has to be solved: min w 2 subject to. In order to solve this optimization problem, that apparently has no local minima, and leads to a unique solution, a loss function is introduced:. This function penalizes large values of f x with opposite sign of y. Points that are on the boundaries of the classifier and therefore satisfy the equality are called the support vectors.
In SVM regression the loss function differs and a new parameter e appears:. In classification, when a pattern is far from the margin it does not contribute to the loss function. The basic SV regression seeks to estimate the linear functionwhere x and b are elements of Hthe high dimensional space. A function minimizing error is adjusted, controlling training error and model complexity. Small w indicates a flat function in the H space. In nu-SVM regression, e is calculated automatically making a trade-off between model complexity and slack variables variables added for the optimization to work.
So, nu should be lower than 1. Here we used SVM regression to adjust a model for the prediction write an example of a non-linear relationship response values. Therefore, we divided the samples randomly into approx. For the SVM regression the R [15] kernlab [7] package was used. To adjust the sigma parameter based on differential evolution [14] we used the DEoptim package [13].
This procedure was done only food processing technology courses in coimbatore the calibration data, using as the objective function the what is commutative and associative in maths differences between observed and SVM-regression estimated data for the water quality parameter TSS, COD and fCOD independently.
Independent intensity values of the data set show a decrease in intensity when wavelength increases. Variability is similar for all wavelengths but is slightly higher for lower wavelengths. Few extreme values are present at the univariate level, but no evidence exists that they could be due to which is better serif or sans serif errors and therefore no data filtering was undertaken.
Extreme high values are also found at the univariate level, but were not filtered either for the same reasons as before. PCA conducted on all UV-Vis data showed that these data are extremely correlated and therefore redundant as they can be resumed in the first PC with The first two PCs resume The most important variables on the first PC contributing with highest variance are the following wavelengths in nm : This result indicates that only with these wavelengths, enough information on samples could be obtained, because approx.
Most samples are very similar showing projections with very similar coordinates on the PC space.