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In this short letter we present the construction of a bi-stochastic kernel p for an arbitrary data set X that is derived from an asymmetric affinity function α. The affinity function α measures the similarity between points in X and some reference set Y. Unlike other methods that construct bi-stochastic kernels via some convergent iteration process or… (More)

Graph Laplacians and related nonlinear mappings into low dimensional spaces have been shown to be powerful tools for organizing high dimensional data. Here we consider a data set X in which the graph associated with it changes depending on some set of parameters. We analyze this type of data in terms of the diffusion distance and the corresponding diffusion… (More)

- J J Benedetto, W Czaja, M Ehler, C Flake, M Hirn
- 2010

State of the art dimension reduction and classification schemes in multi-and hyper-spectral imaging rely primarily on the information contained in the spectral component. To better capture the joint spatial and spectral data distribution we combine the Wavelet Packet Transform with the linear dimension reduction method of Principal Component Analysis. Each… (More)

We consider a collection of n points in R d measured at m times, which are encoded in an n × d × m data tensor. Our objective is to define a single embedding of the n points into Euclidean space which summarizes the geometry as described by the data tensor. In the case of a fixed data set, diffusion maps (and related graph Laplacian methods) define such an… (More)

We consider the following interpolation problem. Suppose one is given a finite set E ⊂ R d , a function f : E → R, and possibly the gradients of f at the points of E. We want to interpolate the given information with a function F ∈ C 1,1 (R d) with the minimum possible value of Lip(∇F). We present practical, efficient algorithms for constructing an F such… (More)

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