… 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…

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

… 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 …

… 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 …

… The basic idea of SMC is to drive the state trajectory of the system onto some specified smooth
manifold (sliding surface) passing through the zero state in the state space, and maintains …

… 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 …