Elimination of Correlations

Most of the feature selection methods neglect second-order effects. If two features are highly correlated both features will be selected if they are valuable for the classification - although the second feature contains the same information as the first one. Optimal methods for the elimination of correlations generate new orthogonal features this can either be effected by the Karhunen-Loeve method (Chapter 8.2) or by the SELECT method (Chapter 9.5 C1583). 

A simpler - but not necessary less laborious - method is the calculation of the correlation coefficients for each possible pair of features in the patterns belonging to a certain class. Pairs of most correlated features are combined or one of them is deleted C55 1993. 

A feature selection method - called attribute inclusion algorithm C3653, ( attribute is equivalent to feature) - for binary encoded patterns was applied to chemical problems by Schechter and Jurs C118, 2603. 

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As we have just emphasized, our main problem is the elimination of correlations to obtain a simple particle description of the time evolution. This presents no problem as long as we deal with averages of the form in... 

The value of DFT is evidently dependent on the accessibility and accuracy of the grand potential functional, Si [p(r)]. The usual practice is to treat the molecules as hard spheres and divide the fluid-fluid potential into attractive and repulsive parts. A mean field approximation is used to simplify the former by the elimination of correlation effects. The hard sphere term is further divided into an ideal gas component and an excess component (Lastoskie etal., 1993). The ideal component is considered to be exactly local, since this part of the Helmholtz free energy per molecule depends only on the density at a particular value of r. 

The dimensionality of a data set is the number of variables that are used to describe eac object. For example, a conformation of a cyclohexane ring might be described in terms c the six torsion angles in the ring. However, it is often found that there are significai correlations between these variables. Under such circumstances, a cluster analysis is ofte facilitated by reducing the dimensionality of a data set to eliminate these correlation Principal components analysis (PCA) is a commonly used method for reducing the dimensior ality of a data set. 

Gas-Film Coefficient Since the gas film is not affected by the liquid-phase reaction, one of the many available correlations for physic absorption may be apphcable. The coefficient also may be found directly after elimination of the hquid-film coefficient by employing a solution that reacts instantaneously and irreversibly with the dissolved gas, thus cancehng out any backpressure. Examples of such systems are SO2 in NaOH and NH3 in H2SO4. 

Data are extant in the literature for two other sets of ethynylene compounds. The sets studied are reported in Table XXXIII. Results of correlation are set forth in Table XXXIV and values of Pr in Table XXXV. The ionization constants of 3-substituted propiolic acids, which were first correlated with the Hammett equation by Charton (18), gave an excellent correlation with eq. (2) (set 22-27-1). The results are very much improved by the elimination of the value for X = H (set 33-27-2). The composition of the electrical effect corresponds approximately to that of the Op constants. The magnitude of the electrical effect is significantly less than that observed for the rrans-3-substituted acrylic acids. 

Time is a fundamental property of the physical world. Because time encompasses the antinomic qualities of transience and duration, the definition of time poses a dilemma for the formulation of a comprehensive physical theory. The partial elimination of time is a common solution to this dilemma. In his mechanical philosophy, Newton appears to resort to the elimination of the transient quality of time by identifying time with duration. It is suggested, however, that the transient quality of time may be identified as the active component of the Newtonian concept of inertia, a quasi occult quality of matter that is correlated with change, and that is essential to defining duration. The assignment of the transient quality of time to matter is a necessary consequence of Newton s attempt to render a world system of divine mathematical order. Newton s interest in alchemy reflects this view that matter is active and mutable in nature... 

Saebe, S., Tong, W. and Pulay, P. Efficient elimination of basis set superposition errors by the local correlation method Accurate ab initio studies of the water dimer, J. Chem. Phys., 98, 2170-2175. 

This belief was further supported by the evidence of a correlation between the clinical response and REM sleep suppression as well as a temporal relationship between the onset of clinical response and REM sleep suppression. However, some of the later studies suggested that REM sleep suppression is not necessary for the antidepressant action (Gillin 1983). For example, some studies show evidence of no change or even an increase in REM sleep with the treatment of depression (Gillin et al. 2001). Recently, Landolt Gillin (Landolt and Gillin 2002) have also demonstrated that the antidepressant response to phenelzine treatment does not depend on elimination of REM sleep or inhibition of slow wave activity in non-REM sleep. However, the generalization of some of these studies is limited because of their small sample size. 

The pores of the silica template can be filled by carbon from a gas or a liquid phase. One may consider an insertion of pyrolytic carbon from the thermal decomposition of propylene or by an aqueous solution of sucrose, which after elimination of water requires a carbonization step at 900°C. The carbon infiltration is followed by the dissolution of silica by HF. The main attribute of template carbons is their well sized pores defined by the wall thickness of the silica matrix. Application of such highly ordered materials allows an exact screening of pores adapted for efficient charging of the electrical double layer. The electrochemical performance of capacitor electrodes prepared from the various template carbons have been determined and are tentatively correlated with their structural and microtextural characteristics. 

The correlation coefficients between a 10 year monthly mean time series of volatilisation rates and SST, 1 Om wind speed and pollutant concentration are used to elucidate which of the parameters drives the volatilisation rate changes and causes the deviations from the long term mean. All of the parameters do not vary independently. Since both SST and wind speed influence the volatilisation rate in a nonlinear manner, it is not intuitive whether an increase in wind speed leads to an increase in volatilisation rate. A raise in wind speed that coincides with a decrease of the sea surface temperature can lead to a negative linear correlation coefficient between volatilisation rate and wind speed. For that reason the partial correlation coefficient is calculated in addition to the simple linear correlation coefficients. It explains the relation between a dependent and one or more independent parameters with reduced danger of spurious correlations due to the elimination of the influence of a third or fourth parameter, by holding it fixed. One important feature of the partial correlation coefficient is, that it is equal to the linear correlation coefficient if both variables... 

If Scheme 2 accurately represented the PhCH2CCl chemistry, curvature in the addn/rearr vs. [alkene] correlation would persist when the carbene was generated from 37. The absence of curvature in this case counts against Scheme 2 (and the CAC mechanism), but accords with the RIES mechanism, Scheme 3. Elimination of the diazirine precursor eliminates the diazirine excited state. From 37, both cyclopropane formation and 1,2-H rearrangement proceed from a single (carbene) intermediate, and addn/rearr vs. [alkene] is linear.25... 

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