Multimode data analysis

Harchman, R.A. and Lundy, M.E., The PARAFAC model for three-way factor analysis and multidimensional scaling, in Research Methods for Multimode Data Analysis, Law, H.G. et al., Eds., Praeger, New York, 1984. 

Some of the most interesting theoretical developments in chemometrics over the past few years have been in so-called multiway or multimode data analysis. Many such methods have been available for some years, especially in the area of psychometrics, and a few do have relevance to chemistry. It is important, though, not to get too carried away with the excitement of these novel theoretical approaches. We will restrict the discussion here to trilinear PLS1, involving a three-way x block and a single c variable. If there are several known calibrants, the simplest approach is to perform trilinear PLS1 individually on each variable. 

R. A. Harshman, Research Methods for Multimode Data Analysis, Praeger, New York, 1984, p. 566. 

Harshman RA, De Sarbo WS, An application of PARAFAC to a small sample problem, demonstrating preprocessing, orthogonality constraints, and split-half diagnostic techniques, inResearchMethods for Multimode Data Analysis, Law HG, Snyder CW, Jr, Hattie JA and McDonald RP (Eds), Praeger Special Studies, New York, 1984, 602-642. 

Harshman RA, Lundy ME. Data preprocessing and the extended PARAFAC model. In Law HG, Snyder Jr CW, Hattie J, McDonald RP, editors. Research methods for multimode data analysis. New Yrak Praeger 1984. p. 216-84. 

Mixmre models have come up frequently in Bayesian statistical analysis in molecular and structural biology [16,28] as described below, so a description is useful here. Mixture models can be used when simple forms such as the exponential or Dirichlet function alone do not describe the data well. This is usually the case for a multimodal data distribution (as might be evident from a histogram of the data), when clearly a single Gaussian function will not suffice. A mixture is a sum of simple forms for the likelihood ... 

Following the coding of the results above, the Human Resources department undertook to investigate possible causes for the performance anomaly in the indicator of Femmes latales evaded. After careful data analysis across multimodal domains, your failure to achieve a satisfactory result on this performance indicator has been attributed to three possible causes firstly, an inability to identify femmes latales on sight secondly, suboptimal strategic evasion practices and thirdly, overconfidence in ad hoc intimate liaison skilk. 

Fig. 18.14 LC ARROW analysis based on radiation pressure, (a) Time dependent microbead position for extraction of waveguide loss (symbols data, line fit) (b) lateral mode profile determination (bars histogram of measured lateral particle position, line, multimode profile calculated with commercial mode solver...

The analysis of the autocorrelation function data by the Coulter Model N4 is carried out by the Size Distribution Program (SDP), which gives the particle size distribution in the form of various output displays (see Section 10.4). The SDP analysis utilizes the computer program CONTIN developed by S.W. Provencher (ref. 467-470 see also Section 10.2). (This program has been tested on computer-generated data, monomodal polystyrene samples, and a vesicle system (ref. 466-468,471).) Since the SDP does not fit to any specific distribution type, it offers the ability to detect multimodal and very broad distributions. 

Thus, given gparticle size distribution. For narrow size distributions, the autocorrelation function is satisfactorily analyzed by the method of cumulants to give the moments of the particle size distribution.(7) However, the analysis of QELS data for samples with polydisperse or multimodal distributions remains an area of active research.(8)... 

DLS is a technique used in conjunction with -potential measurements to analyze polyplex size (average hydrodynamic diameter) distribution. Because the formation of polyplexes can result in a polydisperse mixture of nanoparticles of different size and shape (induding uncomplexed components), multiple peaks can result. Thus, typical reported data include average hydrodynamic diameter and polydispersity. Most software associated with DLS instmmentation permits assessment of a multimodal size distribution, but such data are often unreported or underreported. The default assumption of a single Gaussian distribution may not be appropriate for the majority of polymer-nucleic add complex formulations that are analyzed by DLS. Also, the analysis of the particle sizes assumes a uniform sphere, which again is not necessarily... 

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