We present a fast alternative for the Isomap algorithm. A set of quantizers is fit to the data and a neighborhood structure based on the competitive Hebbian rule is imposed on it. This structure is used to obtain low-dimensional description of the data by means of computing geodesic distances and multi dimensional scaling. The quantization allows for faster processing of the data. The speed-up ...

The computation of compact and meaningful representations of high dimensional sensor data has recently been addressed through the development of Nonlinear Dimensional Reduction (NLDR) algorithms. The numerical implementation of spectral NLDR techniques typically leads to a symmetric eigenvalue problem that is solved by traditional batch eigensolution algorithms. The application of such algorith...

Since the introduction of LLE (Roweis and Saul, 2000) and Isomap (Tenenbaum et al., 2000), a large number of non-linear dimensionality reduction techniques (manifold learners) have been proposed. Many of these non-linear techniques can be viewed as instantiations of Kernel PCA; they employ a cleverly designed kernel matrix that preserves local data structure in the “feature space” (Bengio et al...

From climatology to biofluidics, the characterization of complex flows relies on computationally expensive kinematic and kinetic measurements. In addition, such big data are difficult to handle in real time, thereby hampering advancements in the area of flow control and distributed sensing. Here, we propose a novel framework for unsupervised characterization of flow patterns through nonlinear m...

Regularization of covariance matrices in high dimensions is usually either based on a known ordering of variables or ignores the ordering entirely. This paper proposes a method for discovering meaningful orderings of variables based on their correlations using the Isomap, a non-linear dimension reduction technique designed for manifold embeddings. These orderings are then used to construct a sp...

Locally Linear Embedding (LLE) [2] and Isomap [1] techniques can be used to process and analyze high-dimensional data domains, such as semantics, images, and colour. These techniques allow creation of low-dimensional embeddings of the original data that are much easier to visualize and work with then the initial, high-dimensional data. In particular, the dimensionality of such embeddings is sim...

0 Introduction In [1] Tenenbaum, de Silva and Langford consider the problem of non-linear dimensionality reduction: discovering intrinsically low-dimensional structures embedded in high-dimensional data sets. They describe an algorithm, called Isomap, and demonstrate its successful application to several real and synthetic data sets. In this paper, we discuss some of the theoretical claims for ...