Isomap is one of widely-used low-dimensional embedding methods, where geodesic distances on a weighted graph are incorporated with the classical scaling (metric multidimensional scaling). In this paper we pay our attention to two critical issues that were not considered in Isomap, such as: (1) generalization property (projection property); (2) topological stability. Then we present a robust ker...

This report discusses dimensionality reduction techniques used to create a music map - a map where the distances between songs represent their similarity and that can be used to recommend songs. We evaluate two techniques: Isomap and L-Isomap.

Manifold learning techniques are used to preserve the original geometry of dataset after reduction by preserving the distance among data points. MDS (Multidimensional Scaling), ISOMAP (Isometric Feature Mapping), LLE (Locally Linear Embedding) are some of the geometrical structure preserving dimension reduction methods. In this paper, we have compared MDS and ISOMAP and considered similarity as...

The ISOMAP nonlinear dimensionality reduction method of Tenenbaum, de Silva and Langford, was originally implemented in MATLAB by the developers of the algorithm. One of the issues involved with ISOMAP is the need to determine the number of reduced dimensions that best represents the original data. For this purpose, Tenenbaum, de Silva and Langford provide a plot similar to the scree plot in pr...

We make use of the non-intrusive dimensionality reduction method Isomap in order to emulate nonlinear parametric flow problems that are governed by the Reynolds-averaged Navier-Stokes equations. Isomap is a manifold learning approach that provides a low-dimensional embedding space that is approximately isometric to the manifold that is assumed to be formed by the high-fidelity NavierStokes flow...

Most nonlinear dimensionality reduction approaches such as Isomap heavily depend on the neighborhood structure of manifold. They determine the neighborhood graph using Euclidean distance so that they often fail to nicely deal with sparsely sampled or noise contaminated data. This paper applies the graph algebra to optimize the neighborhood structure for Isomap. The improved Isomap outperforms t...

Isomap [4] is a manifold learning algorithm, which extends classical multidimensional scaling (MDS) by considering approximate geodesic distance instead of Euclidean distance. The approximate geodesic distance matrix can be interpreted as a kernel matrix, which implies that Isomap can be solved by a kernel eigenvalue problem. However, the geodesic distance kernel matrix is not guaranteed to be ...

in image understanding and image coding, it could be useful to ‘learn’ the structure of such image articulation manifolds and to recover the underlying parameters (location, scale, etc.) from unlabeled data. This could be important for recognizing articulated vehicles in target recognition, and for understanding articulated faces in facial recognition. The general problem of learning the shape ...

There has been a renewed interest in understanding thestructure of high dimensional data set based on manifoldlearning. Examples include ISOMAP [25], LLE [20]and Laplacian Eigenmap [2] algorithms. Most of thesealgorithms operate in a “batch” mode and cannot beapplied efficiently for a data stream. We propose anincremental version of ISOMAP. Our experiments notonly de...