Sentence examples similar to as dimensions increase from inspiring English sources

As the number of dimensions increase, the concept of proximity or distance becomes less precise; this is especially true for spatial data [13].

As state dimensions increase, the time to calculate the decision grows exponentially.

Similarly, explosive driven systems have their own set of limiting conditions due to limitations in explosive energy and size of devices required as engineering dimensions increase.

This has to do with the curse of dimensionality, which simply means that the same number of points quickly become more scarcely packed as the dimensions increase, and that a corresponding density estimation will be based on fewer and fewer neighboring points.

In addition, ripples in the graphene sheet stabilize the giant "D" family as the crystal cell dimensions increase.

It is found that the number of eigen frequencies that should be taken into account increases as the number of dimensions increases.

This adaptive WSP algorithm will be very useful as the number of dimensions increases and can solve the problem of the "hollow" center.

They also often involve the computation of gradients and/or Laplacians, which can become very complicated to compute as the number of dimensions increases.

Liao et al. [17] stated that as the number of dimensions increases, such techniques need an exponentially larger amount of CPU time.

However, the coordinate-search method searches points using each vector of the positive basis; thus, convergence speed is reduced as the number of dimensions increases.

The emergence of high-dimensional datasets poses challenges for the analysis and identifications of dynamical network patterns, because many traditional statistical tools may lose their efficiency dramatically as the numbers of dimensions increases.