Data reduction methods

There are a number of factors contributing to this discrepancy, such as a lack of standardization in specimen preparation, the loading method, the measurement and data reduction methods. Details of major contributors to the large data scatter are summarized for each testing method in the following ... 

The potential of modern chemical instrumentation to detect and measure the conposition of coirplex mixtures has made it necessary to consider the use of methods of multivariable data analysis in the overall evaluation of environmental measurements. In a number of instances, the category (chemical class) of the compound that has given rise to a series of signals may be known but the specific entity responsible for a given signal may not be. This is true, for example, for the polychlorinated biphenyls (PCB s) in which the clean-up procedure and use of specific detectors eliminates most possibilities except PCB s. Such hierarchical procedures simplify the problem somewhat but it is still advantageous to apply data reduction methods during the course of the interpretation process. 

There are two primary difficulties in directly inverting equation (12.7). First, the system is usually underdetermined, which means there are more variables (e.g., wavelengths) than equations (e.g., number of calibration samples). Thus, direct inversion does not always yield a unique solution. Second, even if a pseudoinverse exists and results in a unique solution, the solution tends to be unstable because all measurements contain noise and error. That is, small variations in c or S can lead to large variations in b. Underdetermined and unstable models can be avoided by using data reduction methods, such as factor analysis, which reduce the dimensionality of the spectral data and much of the underlying noise within each spectrum. 

Chapter 4 describes the polymer data bases. This chapter is organized into sections discussing the experimental methods available for measuring the thermodynamic data of polymer solutions with an overview of the advantages and disadvantages of each method. The next section, Data Reduction Methods, describes how the experimental measurements from these experiments can be used to calculate the activity coefficients that are necessary for phase equilibria calculations. Finally, a summary of all the systems that are available on the data diskettes is provided. A user can scan this section or use the computer program POLYDATA to find if data are available for a particular system. 

Due to the low thickness of this sample, approximately 25pm, no determination of a lag time was possible. Testing using mass spectrometer generally indicated hydrogen at near saturation levels within the first sampling frequency, which is limited to about 15 seconds for the instrumentation used. The data were analyzed using the standard data reduction method and the permeability of this alloy is indicated in Table 3. 

Unsupervised Data Mining. Searching large volumes of data for hidden descriptive relationships. Unlike supervised data mining, no response variables are used. The techniques used include various display and data reduction methods, as well as cluster analysis and association analysis. 

Another important class of MVA is represented by cluster analysis methods and principal component analysis (PCA). The latter is a representative of data reduction methods that exploit linear algebra. We do not, however, believe all the important patterns can be captured by linear algebraic methods. Finear mathematical methods are ideal for data compression, because to recover the original data distortion is undesirable. Thus, data compression is essentially applied Fourier analysis [2], In contrast, data mining is a kind of pattern... 

We are interested in a data-mining or data reduction method that is as unsupervised as possible. In other words, we are interested in the data analysis method that is maximally data-driven. We do not mean that we insist that data-mining methods must be unsupervised, but we believe that supervising or guidance could do best with methods that can already allow sufficiently powerful data reduction in the unsupervised mode. 

The automation of the torsion pendulum utilizing a desktop computer eliminates the tedious data analysis previously associated with that technique. Any one of four data reduction methods can be used the experimental conditions will determine which is the optimum one to employ. The torsion pendulum technique provides quantitative values of shear modulus and logarithmic decrement and in the torsion braid mode provides a qualitative analysis of materia i, especially in the liquid-to-solid transition region. 

Fig. 8 Data reduction methods to linearize immunoassay concentration-response curves. (From Ref. 647.)...

Hill, R.B., and Klewicki, J.C., Data reduction methods for flow tagging velocity measurements, Exps. in Fluids, 2Q, 142-152 (1996). 

Farges F (2002) Improving data reduction methods in X-ray absorption fine structure spectroscopy. Part 1 pre-edge and XANES, resolution, convolution and component analyses. Phys Chem Minerals... 

As the science, technology, and an of vollammciric instrumentation and data reduction methods have developed, so too have the time and spatial regimes of voltammetry decreased in scale. Traditionally, voltam-metric measurements were made at dc and relatively low frequency. As a result, only relatively slow electron-transfer processes could he explored using these methods. 

Kemsley, E. K. (1996). Discriminant analysis of high-dimensional data a comparison of principal components analysis and partial least squares data reduction methods, Chemom. Intell. Lab. Syst. 33 47-61. 

All compression, denoising, and data reduction methods retain the largest Nx number of coefficients depending on the choice of appropriate threshold k. These methods follow the principle assuming that large wavelet coefficients characterize signal better in the sense of its energy and thus retain more information. 

The aim of denoising methods consist in reducing the modeling errors (noises) while data reduction methods aim to reduce data as much as possible by preserving key data characteristics for subsequent analysis. For example data reduction methods RREi,(k) design in (leong et al. 2006) is developed to balance the relative retained data energy and the relative number of retained coefficients (the data reduction ratio). 

Data reduction methods which are widely used in library search have also been tested for pattern recognition- The k largest peaks in a spectrum (k = 5 to 50), or selection of the k largest peaks in mass intervals of length I (k = 1 to 2, I = 7 or 14) were utilized for... 

Pitzer s equations can be used for mixtures of electrolyes. Thermodynamic functions are obtained in the usual way as the derivatives of the chemical potential with respect to temperature or pressure. However, a considerable number of empirically adjusted parameters is needed to obtain satisfactory data description. The Pitzer approach is used as a self-standing data-reduction method, but it is also embedded by engineers in the so-called NRTL (nonrandom two liquid) electfolyte models. 

SENSOR CALIBRATION DATA HANDLING. Another important aspect of the over-all calibration job was the adapting of accepted laboratory and data reduction methods to a procedure that would facilitate raw data reduction and analysis on a production basis. This was accomplished by programming all computations and comparison steps such that they could be handled by an IBM 704 computer. The program calls for determination of the temperature, from the resistance readings on the standards, at the time the resistance was measured on each test probe tabulation of the resistance vs. temperature relationship of each probe through the temperature range of interest comparison of this calibrated relationship with the specification relationship for the particular probe and finally, tabulation of the deviation of the actual calibration from the specification at the calibration points taken. 

The process of constructing a QSPR model includes the following steps, summarized in Fig.5.1 (1) selection of a data set (2) generation of various structural descriptors by means of MD simulations application of variable selection or/and data reduction methods on the calculated descriptors in order to identify a small subset of these descriptors that are relevant to the macroscopic material properties being modeled (in some cases this step may not be required) (3) generation of linear/multilinear or non-Unear relationship between the descriptors and the global material property (4) validation of the model to assess its reliability, robustness, predictivity, and domain of applicability. 

More attention must be given to data reduction methods. 

It would be useful if VLE experimentalists could define by mutual agreement half a dozen or so referee test systems, as the calorimetry people have done. These would be binary systems for which pure-component vapor pressures were well known, and which had been carefully studied by several investigators on different types of equipment of proven reliability. The systems would be used for testing new equipment designs and new VLE data-reduction methods. 

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