A novel classifier, named Nearest Linear Manifold uses a small number of prototypes to represent a class and extend their resentational capacity by using the linear manifold of the prototypes to provide more sufficient feature information for classification.

Manifold clustering, which regards clusters as groups of points around compact manifolds, has been realized as a promising generalization of traditional clustering. A number of linear or nonlinear manifold clustering approaches have been developed recently. Although they have attained better performances than traditional clustering methods in many scenarios, most of these approaches suffer from...

The need to reduce the dimensionality of a dataset whilst retaining inherent manifold structure is key in many pattern recognition, machine learning and computer vision tasks. This process is often referred to as manifold learning since the structure is preserved during dimensionality reduction by learning the intrinsic low-dimensional manifold that the data lies on. Since the inception of mani...

In [1] we have constructed a fake smooth structure on a contractible 4-manifold W relative to boundary. This is a smooth manifold V with d V = d W such that the identity map d V —• d W extends to a homeomorphism but not to a difFeomorphism V -+ W. This is a relative result in the sense that V itself is diffeomorphic to W, even though no such diffeomorphism can extend the identity map on the bou...

Inputs coming from high-dimensional spaces are common in many real-world problems such as a robot control with visual inputs. Yet learning in such cases is in general difficult, a fact often referred to as the “curse of dimensionality”. In particular, in regression or classification, in order to achieve a certain accuracy algorithms are known to require exponentially many samples in the dimensi...

A variety of inferential tasks require drawing samples from a probability distribution on a manifold. This occurs in sampling from the posterior distribution on constrained parameter spaces (eg covariance matrices), in testing goodness of fit for exponential families conditional on sufficient statistics (eg the sum and product of the observations in a Gamma family), and in generating data to te...

We present a novel method, Manifold Sensing, for the adaptive sampling of the visual world based on manifolds of increasing but low dimensionality that have been learned with representative data. Because the data set is adapted during sampling, every new measurement (sample) depends on the previously acquired measurements. This leads to an efficient sampling strategy that requires a low total n...

In his 1974 thesis, Martin Scharlemann constructed a fake homotopy equivalence from a closed smooth manifold f : Q → S3 × S1#S2 × S2, and asked the question whether or not the manifold Q itself is diffeomorphic to S3 × S1#S2 × S2. Here we answer this question affirmatively. In [Sc] Scharlemann showed that if Σ3 is the Poincaré homology 3-sphere, by surgering the 4-manifold Σ× S, along a loop in...

This paper proposes a straightforward method of parameterizing manifold triangulations where the parameter domain is a coarser triangulation of the same topology. The method partitions the given triangulation into triangular patches bounded by geodesic curves and parameterizes each patch individually. We apply the global parameterization to remeshing and wavelet decomposition.

We describe the Information Manifold (IM), a system for browsing and querying of multiple networked information sources. As a first contribution, the system demonstrates the viability of knowledge representation technology for retrieval and organization of information from disparate (structured and unstructured) information sources. Such an organization allows the user to pose high-level querie...