Data analysis methods

To enable the application of electronic data analysis methods, the chemical structures have to be coded as vectors see Chapter 8). Thus, a chemical data set consists of data vectors, where each vector, i.e., each data object, represents one chemical structure. 

Sections 9A.2-9A.6 introduce different multivariate data analysis methods, including Multiple Linear Regression (MLR), Principal Component Analysis (PCA), Principal Component Regression (PCR) and Partial Least Squares regression (PLS). 

The electronic data analysis service (ELECTRAS), which was developed at the Com-puter-Chemie-Centrum of the University of Erlangen-Ntlmberg through a project supported by the DFN-Verein and the BMBF, is a web-based application which presents an interface to various kinds of data analysis methods. It offers the methods... 

An additional feature of ELECTRAS is a module which provides an introduction to various data analysis techniques One part of this module provides a typical work flow for data analysis. It explains the important steps when conducting a data analysis and describes the output of the data analysis methods. The second part gives a description of the methods offered. This modvJe can be used both as a guideline for novice users and as a reference for experts. 

Despite the variety of methods that had been developed, by 1960 kinetic methods were no longer in common use. The principal limitation to a broader acceptance of chemical kinetic methods was their greater susceptibility to errors from uncontrolled or poorly controlled variables, such as temperature and pH, and the presence of interferents that activate or inhibit catalytic reactions. Many of these limitations, however, were overcome during the 1960s, 1970s, and 1980s with the development of improved instrumentation and data analysis methods compensating for these errors. ... 

Data analysis, methods for (see Least-squares regression)... 

It is felt that the use of electron microbeam methods offers the basis for a revolutionary new approach to the study of catalyst particles. Some results can be obtained immediately but to realise the full potential of the method a considerable amount of further exploration of data collection and data analysis methods will be needed. 

More specifically, input data analysis methods are similar to input-output methods, but rely on different strategies for extracting the relevant information. With reference to the general expression in Eq. (4), the resulting analyzed or latent variable for all input methods can be represented as... 

Specific data analysis methods can be derived from Eqs. (5) and (6) depending on decisions about the input transformation, type of activation or basis functions, and optimization criteria. These decisions form the basis of a common framework for comparing all empirical modeling methods (Bakshi and Utojo, 1999). 

An optimization criterion for determining the output parameters and basis functions is to minimize the output prediction error and is common to all input-output modeling methods. The activation or basis functions used in data analysis methods may be broadly divided into the following two categories ... 

If the probability distribution of the data is or assumed Gaussian, several statistical measures are available for interpreting the data. These measures can be used to interpret the latent variables determined by a selected data analysis method. Those described here are a combination of statistical measures and graphical analysis. Taken together they provide an assessment of the statistical significance of the analysis. 

Using the conventional data analysis methods of PCA, DFA, and HCA, studies have indicated that the role of PyMS in microbiology may extend beyond... 

Order and polydispersity are key parameters that characterize many self-assembled systems. However, accurate measurement of particle sizes in concentrated solution-phase systems, and determination of crystallinity for thin-film systems, remain problematic. While inverse methods such as scattering and diffraction provide measures of these properties, often the physical information derived from such data is ambiguous and model dependent. Hence development of improved theory and data analysis methods for extracting real-space information from inverse methods is a priority. 

In this example, we apply D-PLS (PLS discriminant analysis, see Section 5.2.2) for the recognition of a chemical substructure from low-resolution mass spectral data. This type of classification problems stood at the beginning of the use of multivariate data analysis methods in chemistry (see Section 1.3). 

Basic understanding and efficient use of multivariate data analysis methods require some familiarity with matrix notation. The user of such methods, however, needs only elementary experience it is for instance not necessary to know computational details about matrix inversion or eigenvector calculation but the prerequisites and the meaning of such procedures should be evident. Important is a good understanding of matrix multiplication. A very short summary of basic matrix operations is presented in this section. Introductions to matrix algebra have been published elsewhere (Healy 2000 Manly 2000 Searle 2006). 

Smyth GK, Yang YH, Speed T. 2003. Statistical issues in cDNA microarray data analysis. Methods Mol Biol 224 111. 

Because of space limitations, PK/PD data analysis methods are not described in detail here. Some of the most commonly used PK/PD tools are hsted in Table 1.5. 

In addition to the physical data analysis methods, traditional engineering analysis tools and methods are also useful during incident investigations. Traditional analysis tools can he used to determine the following. 

A better data analysis method, as yet unused, might be to use the area under the step response curve. It can be shown that the moments are related to the step response by... 

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