"the ambient space" is a correct and usable phrase in written English.
It is often used in technical or scientific contexts to refer to the space or environment surrounding something. Example: In order to accurately measure the temperature of a room, it is important to also consider the ambient space, such as the level of natural sunlight and airflow.
Linear dimensionality reduction will fail when the output space is not well approximated by a linear subspace of the ambient space in which it lies.
Such calculations require computational models of the ambient space radiation environment, particle transport, nuclear and atomic physics, and the human body.
The classic notion of a polar variety of V associated with a given linear subvariety of the ambient space of V was generalized and motivated in Bank et al. (Kybernetika 40 (2004), to appear).
Based on the method of moving frames (MMF) in which the geometry is represented by orthonormal vectors, the proposed scheme not only has the fewest dimensionality both in space and time, but also does not require either of metric tensors, composite meshes, or the ambient space.
They are based on prescribing a suitable vector field in the Euclidean three-dimensional space and then suitably projecting it on the sphere's tangent plane; even when the flux vector in the ambient space is constant, the corresponding flux vector is a non-trivial vector field on the sphere.
The extrinsic mean depends on the geometry of the ambient space and the embedding.
We also incorporated into the track ambient space station noises which Chris had put on his SoundCloud.
Traditional manifold learning methods focus on preserving only the intra-class geometric properties of the manifold embedded in the high-dimensional ambient space, so they cannot fully utilize the underlying discriminative knowledge of the data.
Such constraints are the result of conservation of momentum that limits the mobility of the system in ambient space.
Any geometrical object in this space can be written in terms of the four local intrinsic coordinates X a or in terms of the five global ambient space coordinates x α.
We obtain the solutions in ambient space notation.
