For technical reasons it is also often convenient only to consider positive weight functions.

Some common local weighting functions are defined in the following table.

They are defined by the use of weight functions.

Weight functions can be employed in both discrete and continuous settings.

The choice of weighting function will be discussed later.

Such a W is called a weight function.

In this context, the weight function ' is sometimes referred to as a density.

Here we introduce a nonnegative weight function in the definition of this inner product.

However, any other weight function that satisfies the properties listed in Cleveland (1979) could also be used.

The technique arranges the network into a hierarchy of groups according to a specified weight function.

Additionally, the communities found in the network are highly dependent on the choice of weighting function.

So as to control the convergence, the weighting function of the first type is always chosen .

The most common case is , as above, but in certain applications a different weight function is desirable.

Each weighting function or "kernel" has its own characteristics.

The term weighting function they used is similar to the language model and the binary independence model.

These functions are orthogonal with respect to a unit weight function on the interval from 1 to 1.

The weight function corresponds to the unweighted situation in which all elements have equal weight.

For the purpose of facilitating the expression, a weighting function is defined:

Note that Gaussian quadrature can also be adapted for various weight functions, but the technique is somewhat different.

The following key elements distinguish the modified weight function from the criterion of optimality:

With the weighting function, the summation can be replaced by a contour integral in the complex plane.

As in Fig. 1, the weighting function generates poles (red crosses) on the imaginary axis.

Once a term-document matrix is constructed, local and global weighting functions can be applied to it to condition the data.

Here is a weight function that typically goes to zero or quickly approaches zero at some finite radius.

The proposed weighting function had the form: