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In uniform scaling with a non-zero scale factor, all non-zero vectors retain their direction (as seen from the origin), or all have the direction reversed, depending on the sign of the scaling factor. In non-uniform scaling only the vectors that belong to an eigenspace will retain their direction. A vector that is the sum of two or more non ...
The sampling theory of Shannon can be generalized for the case of nonuniform samples, that is, samples not taken equally spaced in time. The Shannon sampling theory for non-uniform sampling states that a band-limited signal can be perfectly reconstructed from its samples if the average sampling rate satisfies the Nyquist condition. [1]
The antithetic variates technique consists, for every sample path obtained, in taking its antithetic path — that is given a path {, …,} to also take {, …,}.The advantage of this technique is twofold: it reduces the number of normal samples to be taken to generate N paths, and it reduces the variance of the sample paths, improving the precision.
The second requirement ensures that the average of the corresponding distribution is equal to that of the sample used. If K is a kernel, then so is the function K* defined by K*(u) = λK(λu), where λ > 0. This can be used to select a scale that is appropriate for the data.
In some physical systems, the term scaling is used interchangeably with nondimensionalization, in order to suggest that certain quantities are better measured relative to some appropriate unit. These units refer to quantities intrinsic to the system, rather than units such as SI units.
As an example, consider a dataset of birds for classification. The feature space for the minority class for which we want to oversample could be beak length, wingspan, and weight (all continuous). To then oversample, take a sample from the dataset, and consider its k nearest neighbors (in feature space).
Example of a regular grid. A regular grid is a tessellation of n-dimensional Euclidean space by congruent parallelotopes (e.g. bricks). [1] Its opposite is irregular grid.. Grids of this type appear on graph paper and may be used in finite element analysis, finite volume methods, finite difference methods, and in general for discretization of parameter spaces.
In Latin hypercube sampling one must first decide how many sample points to use and for each sample point remember in which row and column the sample point was taken. Such configuration is similar to having N rooks on a chess board without threatening each other. In orthogonal sampling, the sample space is partitioned into equally probable ...