Evaluating a Self-Organizing Map for Clustering and Visualizing Optimum Currency Area Criteria

Optimum currency area (OCA) theory attempts to define the geographical region in which it would maximize economic efficiency to have a single currency. In this paper, the focus is on prospective and current members of the Economic and Monetary Union. For this task, a self-organizing neural network, the Self-organizing map (SOM), is combined with hierarchical clustering for a two-level approach to clustering and visualizing OCA criteria. The output of the SOM is a topologically preserved two-dimensional grid. The final models are evaluated based on both clustering tendencies and accuracy measures. Thereafter, the two-dimensional grid of the chosen model is used for visual assessment of the OCA criteria, while its clustering results are projected onto a geographic map.Self-organizing maps, Optimum Currency Area, projection, clustering, geospatial visualization

Level set segmentation using non-negative matrix factorization with application to brain MRI

We address the problem of image segmentation using a new deformable model based on the level set method (LSM) and non-negative matrix factorization (NMF). We describe the use of NMF to reduce the dimension of large images from thousands of pixels to a handful of metapixels or regions. In addition, the exact number of regions is discovered using the nuclear norm of the NMF factors. The proposed NMF-LSM characterizes the histogram of the image, calculated over the image blocks, as nonnegative combinations of basic histograms computed using NMF (V ~ W H). The matrix W represents the histograms of the image regions, whereas the matrix H provides the spatial clustering of the regions. NMF-LSM takes into account the bias field present particularly in medical images. We define two local clustering criteria in terms of the NMF factors. The first criterion defines a local intensity clustering property based on the matrix W by computing the average intensity and standard deviation of every region. The second criterion defines a local spatial clustering using the matrix H. The local clustering is then summed over all regions to give a global criterion of image segmentation. In LSM, these criteria define an energy minimized w.r.t. LSFs and the bias field to achieve the segmentation. The proposed method is validated on synthetic binary and gray-scale images, and then applied to real brain MRI images. NMF-LSM provides a general approach for robust region discovery and segmentation in heterogeneous images

A Statistical Toolbox For Mining And Modeling Spatial Data

Most data mining projects in spatial economics start with an evaluation of a set of attribute variables on a sample of spatial entities, looking for the existence and strength of spatial autocorrelation, based on the Moran’s and the Geary’s coefficients, the adequacy of which is rarely challenged, despite the fact that when reporting on their properties, many users seem likely to make mistakes and to foster confusion. My paper begins by a critical appraisal of the classical definition and rational of these indices. I argue that while intuitively founded, they are plagued by an inconsistency in their conception. Then, I propose a principled small change leading to corrected spatial autocorrelation coefficients, which strongly simplifies their relationship, and opens the way to an augmented toolbox of statistical methods of dimension reduction and data visualization, also useful for modeling purposes. A second section presents a formal framework, adapted from recent work in statistical learning, which gives theoretical support to our definition of corrected spatial autocorrelation coefficients. More specifically, the multivariate data mining methods presented here, are easily implementable on the existing (free) software, yield methods useful to exploit the proposed corrections in spatial data analysis practice, and, from a mathematical point of view, whose asymptotic behavior, already studied in a series of papers by Belkin & Niyogi, suggests that they own qualities of robustness and a limited sensitivity to the Modifiable Areal Unit Problem (MAUP), valuable in exploratory spatial data analysis

The specificity and robustness of long-distance connections in weighted, interareal connectomes

Brain areas' functional repertoires are shaped by their incoming and outgoing structural connections. In empirically measured networks, most connections are short, reflecting spatial and energetic constraints. Nonetheless, a small number of connections span long distances, consistent with the notion that the functionality of these connections must outweigh their cost. While the precise function of these long-distance connections is not known, the leading hypothesis is that they act to reduce the topological distance between brain areas and facilitate efficient interareal communication. However, this hypothesis implies a non-specificity of long-distance connections that we contend is unlikely. Instead, we propose that long-distance connections serve to diversify brain areas' inputs and outputs, thereby promoting complex dynamics. Through analysis of five interareal network datasets, we show that long-distance connections play only minor roles in reducing average interareal topological distance. In contrast, areas' long-distance and short-range neighbors exhibit marked differences in their connectivity profiles, suggesting that long-distance connections enhance dissimilarity between regional inputs and outputs. Next, we show that -- in isolation -- areas' long-distance connectivity profiles exhibit non-random levels of similarity, suggesting that the communication pathways formed by long connections exhibit redundancies that may serve to promote robustness. Finally, we use a linearization of Wilson-Cowan dynamics to simulate the covariance structure of neural activity and show that in the absence of long-distance connections, a common measure of functional diversity decreases. Collectively, our findings suggest that long-distance connections are necessary for supporting diverse and complex brain dynamics.Comment: 18 pages, 8 figure