Data array

R(,) data array, Nrows (samples), M columns (attributes)... 

Instructions) and (Import Data from Excel) allow a portion of an Excel spreadsheet to be copied into a SMAC-data file the necessary steps are as follows (1) open the Excel file, mark the range to be copied and press [Copy] (2) open DATA and create a new or open an existing data file (3) select (Input Data) (Import Data from Excel) and position the cursor on an appropriate cell, e.g. cell (1,1). The imported data replaces any data that was in that cell range. If the imported cell range needs more columns or rows than are presently available, the data array is correspondingly increased in size. Headers and dimensions can be added later. 

In the present terminology, a three-way data array is defined by n rows, p columns and q layers, with indices i,j and k, respectively. 

The expressions for the forward and backward Fourier transforms of a data array of 2N+ 1 data points with the origin in the centre point are [3] ... 

The data array Xmyriyqy which may be preprocessed by standardisation and transformation, is decomposed in a set of three-way products of score images, T, loading vectors, p, and the residual, Emytlyq ... 

The first PC provides a set of d-dimensional loadings, which can be transformed by (2) into a compositional data array, L, and a PC score, S, for each y. The first PC expressed as compositional data is calculated by the perturbation operation... 

Another possibility is the Tucker3 model where a decomposition of the array into sets of scores and loadings is performed that should describe the data in a more condensed form than the original data array. For the sake of simplicity we will describe the model for a three-way array, but it is easy to extend the idea to multiway data. Let xijk denote an element of a three-way array X of dimension I/J/K. Basic assumption is that the data are influenced by a relatively small set of driving forces (factors). Then the Tucker3 model is defined as... 

The data modeled are from gas chromatograms obtained for Aroclors 1242, 1248, 1254 and 1260. The unknown samples are from the anaysis of used transformer oil obtained from a waste dump in New Jersey. The concentration of individual isomers in selected Aroclor and transformer oil samples are given in Appendix I. The data are organized in a matrix in which the first four data entries for each sample in row 1 of the data array (Table 2, Apendix I) designate the composition of the sample. For standards, these four variables represent the fractional parts of Aroclor 1242, 1248, 1254, or 1260, respectively, that were combined. Results from the analysis of transformer oil (samples 21-23) are of unknown fractional composition and variables 1 through 4 are null entries. In the examples that follow data from samples analyzed (Table 1, Appendix I) were used in part or in total to illustrate the PLS method. 

For a data array X containing responses of M variables over N different samples, this method involves the calculation of the mean response of each of the M variables over the N samples, and, for each of the M variables, subsequent subtraction of this mean from the original responses. Mean-centering can be represented by the following equation ... 

The modulus data are then used to estimate the total signal amount by means of various algorithms. The simplest one uses the average of the modulus over a pre-defined data-array window. 

The result is an enhancement of all the advantages of spin-echo detection. The number of usable data points in each acquired data array can in this case exceed in an FID by a factor much larger than two. Since T2 relaxation is going on during the detection, it is again important to keep 8 rigorously constant during the whole multi-block experiment. 

Each batch experiment or each step of a semi-batch experiment results in a data array Ai, . This matrix is often rather smooth in the time direction, especially if rather fast spectra are taken compared to the evolving chemistry. If one follows any particular channel of data in the time direction, it may slowly increase or de-... 

Once the data array has been probed and the minimum number of descriptors that differentiate activity from inactivity has been ascertained, a prediction algorithm is deduced. This algorithm attempts to quantify the bioactivity in terms of the relevant descriptors. The predictive usefulness of this algorithm is then validated by being applied to the test set compounds. If the prediction algorithm is sufficiently robust, it can be used to direct the syntheses of optimized compounds. 

Multivariate Image Analysis Strong and Weak Multiway Methods Strong and weak -way methods analyze 3D and 2D matrices, respectively. Hyperspectral data cube structure is described using chemometric vocabulary [17]. A two-way matrix, such as a classical NIR spectroscopy data set, has two modes object (matrix lines) and V variables (matrix columns). Hyperspectral data cubes possess two object modes and one variable mode and can be written as an OOV data array because of their two spatial directions. 

D image is extracted from individual points along the spectral range (2.4-5 ppm). Three series of images are shown within each series the chemical shift separation between images is 0.065 ppm. This complete data set took approximately 27 h to acquire—as a 128 x 128 data array with in-plane resolution of 140 pm x 140 pm for an image slice thickness of 1mm. 

Because of the more extensive data array obtained by voltammetric detection, other data manipulation techniques to improve selectivity or sensitivity can also be devised. One example is to measure the difference in response at two different potentials in order to gain selectivity for compounds that are more difficult to oxidize. Compounds that are easily oxidized will give the same response at both potentials, and the difference signal will therefore be zero. Only... 

There are several other chemometric approaches to calibration transfer that will only be mentioned in passing here. An approach based on finite impulse response (FIR) filters, which does not require the analysis of standardization samples on any of the analyzers, has been shown to provide good results in several different applications.81 Furthermore, the effectiveness of three-way chemometric modeling methods for calibration transfer has been recently discussed.82 Three-way methods refer to those methods that apply to A -data that must be expressed as a third-order data array, rather than a matrix. Such data include excitation/emission fluorescence data (where the three orders are excitation wavelength, emission wavelength, and fluorescence intensity) and GC/MS data (where the three orders are retention time, mass/charge ratio, and mass spectrum intensity). It is important to note, however, that a series of spectral data that are continuously obtained on a process can be constructed as a third-order array, where the three orders are wavelength, intensity, and time. 

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