We discuss recent work based on multiscale geometric analysis for the study of large data sets that lie in high-dimensional spaces but have low-dimensional structure. We present three applications: the first one to the estimation of intrinsic dimension of sampled manifolds, the second one to the construction of multiscale dictionaries, called geometric wavelets, for the analysis of point clouds...

In this paper, a new wavelet-packet multiscale image segmentation method is presented first. By combining this new method with a multiscale region-based segmentation method, we develop a new generic systematic scheme to segment targets in images based on multiscale analysis in both grayscale and space. Based on the new scheme, a system framework is constructed to intelligently segment targets a...

Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting underlying structures. One of the equivalent definitions of PCA is that it seeks the subspaces that maximize the sum of squared pairwise distances between d...

Within the conceptual framework of Complex Systems, we discuss the importance and challenges in extracting and linking multiscale objects from high-resolution remote sensing imagery to improve the monitoring, modeling and management of complex landscapes. In particular, we emphasize that remote sensing data are a particular case of the modifiable areal unit problem (MAUP) and describe how image...

Article history: Received 29 July 2015 Received in revised form 5 February 2016 Accepted 8 February 2016 Available online 29 March 2016

This paper introduces a multiscale analysis based on optimal piecewise linear approximations of time series. An optimality criterion is formulated and on its base a computationally effective algorithm is constructed for decomposition of a time series into a hierarchy of trends (local linear approximations) at different scales. The top of the hierarchy is the global linear approximation over the...

This paper introduces a new multiscale framework for estimating the tail probability of a queue fed by an arbitrary traffic process. Using traffic statistics at a small number of time scales, our analysis extends the theoretical concept of the critical time scale and provides practical approximations for the tail queue probability. These approximations are non-asymptotic; that is they apply to ...