The method of EOF analysis is similar in spirit to harmonic analysis, but harmonic analysis typically uses predetermined orthogonal functions, for example, sine and cosine functions at fixed frequencies.
12.
It has been shown, using both artificial and real geophysical data, that SOM has many advantages over the conventional feature extraction methods such as Empirical Orthogonal Functions ( EOF ) or PCA.
13.
Similar formulae hold for many other sequences of orthogonal functions arising from Sturm-Liouville equations, and these are also called the Rodrigues formula for that case, especially when the resulting sequence is polynomial.
14.
Therefore, the quasi-orthogonal function ( QOF ), which can process optimal cross-correlation with Walsh code has been used as a method to get around the limitations of the Walsh Codes.
15.
Measured via an empirical orthogonal function analysis, the mode of variability with the greatest effect on climates worldwide is the seasonal cycle, followed by El Ni�o-Southern Oscillation, followed by thermohaline circulation.
16.
However, in most cases the functions f ( x ) can be written in terms of an infinite series of orthogonal functions such as f ( x ) = f _ n H _ n ( x ) and then the definition becomes:
17.
To enhance the overall capacity in such scenarios, alternative sets of orthogonal functions called the quasi-orthogonal functions ( QOF ), which possess optimal minimax cross correlation with Walsh code sets of variable length, have been incorporated in IS-2000.
18.
To enhance the overall capacity in such scenarios, alternative sets of orthogonal functions called the quasi-orthogonal functions ( QOF ), which possess optimal minimax cross correlation with Walsh code sets of variable length, have been incorporated in IS-2000.
19.
Correlation coefficients are calculated between the six time-series and the principal components are the eigenvectors of the resulting correlation matrix . ( Empirical orthogonal function analysis proceeds instead from the variance-covariance matrix which again is biased to the eastern longitudes .)
20.
Even though the source terms ( such as the masses, charges, or currents ) may not be symmetrical, one can expand them in terms of irreducible representations of the rotational symmetry group, which leads to spherical harmonics and related sets of orthogonal functions.
