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Discover LudwigThe phrase "as a manifold" is correct and usable in written English.
It can be used in contexts related to mathematics, physics, or philosophy, where "manifold" refers to a mathematical space or a complex structure.
Example: "The universe can be understood as a manifold, where each point represents a different state of existence."
Alternatives: "as a complex structure" or "as a multi-dimensional space".
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Pipes and hoses emanating from the trucks connect to a metal apparatus known as a manifold, which looks like a giant insect.
Each domain is modeled as a manifold.
Given an arbitrary affine space, its associated projective space is the space of all such lines, understood as a manifold.
This covariance matrix can be viewed as a manifold point in the space of SPD matrices.
Beyond those, in consideration of most features in nature distributing as a manifold structure, the manifold-based feature extraction algorithms become a new trend [10, 11].
The idea of a warped product manifold was first discovered by Bishop and O'Neil (cf. [1]) as a manifold of negative curvature.
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Thus, we aim to utilize the diffusion embedding as a manifold-adaptive projection operator, where the states of each speaker are detected by an FHMM in its manifold.
As such a manifold provides the relative potentials to all possible hosts available for selection, we construct a phase-dependent dynamic decision-making mechanism in a form of a self-adaptive conditional probabilistic model.
Then, subspace set is viewed as a Grassmann manifold, and the manifold is modeled by Grassmann kernel-based SVM classifier to describe its nonlinear characteristics.
The manifold M can be interpreted as a Riemannian manifold (M, g) where g is the metric generated by a x, D).
The neighborhood graph so constructed is naturally configured as a smooth manifold, and hence complies with the effectiveness condition underlying manifold learning.
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