Rank algorithm

Fig. 5 Variation of performance of different feature sets for different ranking algorithm obtained with a OVR SVM b OVO SVM c DAG SVM classifiers...

Fixed-size image window-evolving factor analysis (FSIW-EFA) is an evolution of the local rank algorithm fixed size moving window-EFA [111], particularly designed for the study of the local pixel complexity in images [112]. To do so, two main ideas are taken into account the need to divide the image into small areas to get local information and the need to preserve the 2D or 3D spatial... 

A number of approaches to predict ionization based on structure have been published (for a review, see [53]) and some of these are commercially available. Predictions tend to be good for structures with already known and measured functional groups. However, predictions can be poor for new innovative structures. Nevertheless, pfCa predictions can still be used to drive a project in the desired direction and the rank order of the compounds is often correct. More recently training algorithms have also become available which use in-house data to improve the predictions. This is obviously the way forward. 

In 1978, Ho et al. [33] published an algorithm for rank annihilation factor analysis. The procedure requires two bilinear data sets, a calibration standard set Xj and a sample set X . The calibration set is obtained by measuring a standard mixture which contains known amounts of the analytes of interest. The sample set contains the measurements of the sample in which the analytes have to be quantified. Let us assume that we are only interested in one analyte. By a PCA we obtain the rank R of the data matrix X which is theoretically equal to 1 + n, where rt is the number of interfering compounds. Because the calibration set contains only one compound, its rank R is equal to one. 

When several analytes have to be determined, this procedure needs to be repeated for each analyte. Because this algorithm requires that a PCA is calculated for each considered value of k, RAFA is computationally intensive. Sanchez and Kowalski [34] introduced generalized rank annihilation factor analysis (GRAFA). 

In non-metric MDS the analysis takes into account the measurement level of the raw data (nominal, ordinal, interval or ratio scale see Section 2.1.2). This is most relevant for sensory testing where often the scale of scores is not well-defined and the differences derived may not represent Euclidean distances. For this reason one may rank-order the distances and analyze the rank numbers with, for example, the popular method and algorithm for non-metric MDS that is due to Kruskal [7]. Here one defines a non-linear loss function, called STRESS, which is to be minimized ... 

The results presented by Web search engines are generally listed in rank order of most to least relevant. Algorithms used to establish relevance vary. Traditionally relevance has been defined by some measure of content agreement between the search statement and the results however, some of the Web search engines now use measures of site popularity (number of links or number of times accessed) to rank site relevance. Link analysis does temper the artificially high relevance created by sites that optimize their relevance with keywords, multiple titles, and other techniques [50]. However, valuable sites with fewer links or less general interest may be more difficult to find. 

Theorem Let A be an hermitian matrix. Then, the matrix D arising from the algorithm for calculating the rank of a matrix, i.e.,... 

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