… an unknown manifold M embedded in a high-dimensional observation space X. Let xci)
denote the coordinates of the ith observation. We seek a mapping I : X - Y from the observation …

… In order to state the problem more precisely, we need to describe the class of manifolds within
which we will search for the existence of a manifold which satisfies the manifold hypothesis…

… asymptotic observers for nonlinear discrete-time systems. It is argued that instead of trying
to imitate the linear observer theory, the problem of constructing a nonlinear observer can be …

Recently, manifold learning has been widely exploited in pattern recognition, data analysis,
and machine learning. This paper presents a novel framework, called Riemannian manifold …

… to estimate the manifold all that is needed are unlabeled data (the x s). Once the manifold is
… The (slightly reformulated) observation made by Cheeger was that if our manifold is nicely …

… a class of Laplacian-based manifold methods. These methods utilize … manifold. Theorem
3.1 contains the first result showing convergence of a random graph Laplacian to the manifold …

… This means that we are concerned with the action of the flow on tangent and normal
vectors of the invariant manifold. The crucial observation in the proof of each theorem is that …

… ’s premotor cortex an activation pattern resembling that occurring when the observer … as
the shared manifold of intersubjectivity. I posit that it is by means of this shared manifold that we …

… a reduced-order observer. Furthermore, the … observer is used for estimating the link
velocities and elastic force time derivatives. A controller design based on the integral manifold …

… [16], the observer design is reduced to finding certain mappings so that a chosen manifold,
… The order of the observer can be higher than the order of the state to be estimated, so the …