Examples of "unnormalized"
Advantages of unnormalized form over normalized forms are -
Unnormalized modified KdV equation is a nonlinear partial differential equation：
Unnormalized KdV equation is a Nonlinear partial differential equation
where the (unnormalized) sinc function is defined by formula_57.
whereas unnormalized lexicographic ordering would order these sequences thus: #3, #5, #4, #1, #2.
In mathematics, the historical unnormalized sinc function is defined for by
This value is the forward unnormalized probability vector. The i'th entry of this vector provides:
All sums in this section refer to the unnormalized sinc function.
"P" represents the set of unnormalized probability distributions over player 1’s
where formula_74 is the sum of the unnormalized weights. In this case formula_74 is simply
using angular frequency ω, where formula_6 is the unnormalized form of the sinc function.
In all cases, the ranking given by the geometric mean stays the same as the one obtained with unnormalized values.
Equivalently, the Jeffreys prior for formula_32 is the unnormalized uniform distribution on the non-negative real line.
In addition to the above "unnormalized" architecture, RBF networks can be "normalized". In this case the mapping is
sinc "α" is the unnormalized cardinal sine function (with the discontinuity removed). In his proposal, Winkel set :
The above dispersive Gaussian wave packet, unnormalized and just centered at the origin, instead, at =0, can now be written in 3D:
Its most novel feature was unnormalized significance arithmetic floating point. This allowed users to determine the change in precision of results due to the nature of the computation.
where sinc is the unnormalized sinc function and formula_12 is one of the imaginary, zero or real square roots of "k". These definitions are valid for all "k".
where formula_3 are independent Wiener processes. Then the unnormalized conditional probability density formula_4 of the state at time t is given by the Zakai equation:
where the learning rate formula_79 is again taken to be 0.3. The training is performed with one pass through the 100 training points. The rms error on a test set of 100 exemplars is 0.084, smaller than the unnormalized error. Normalization yields accuracy improvement. Typically accuracy with normalized basis functions increases even more over unnormalized functions as input dimensionality increases.