Abstract: A Kohonen self-organizing map (SOM) is a type of unsupervised artificial neural network that results in a self-organized projection of high-dimensional data onto a low-dimensional feature map, wherein vector similarity is implicitly translated into topological closeness, enabling clusters to be identified. In recently published work , 209 microbial variables from 22 monitoring wells around the leaking Schuyler Falls Landfill in Clinton, NY  were analyzed using a multi-stage non-parametric process to explore how microbial communities may act as indicators for the gradient of contamination in groundwater. The final stage of their analysis used a weighted SOM to identify microbial signatures in this high dimensionality data set that correspond to clean, fringe, and contaminated soils. Resulting clusters were visualized with the standard unified distance matrix (U-matrix). However, while the results of this analysis were very promising, visualized boundaries between clusters in the SOM were indistinct and required manual and somewhat arbitrary identification. In this contribution, we introduce (i) a new cluster reinforcement (CR) phase to be run subsequent to traditional SOM training for automatic sharpening of cluster boundaries, and (ii) a new boundary matrix (B-matrix) approach for visualization of the resulting cluster boundaries. The CR-phase differs from standard SOM training in several ways, most notably by using a feature-based neighborhood function rather than a topologically-based neighborhood function. In contrast to the U-matrix, the B-matrix can be directly superimposed on heat maps of the individual features (as output by the SOM) using grid lines whose thickness corresponds to inter-cluster distances. By thresholding the displayed lines, one obtains hierarchical control of the visual level of cluster resolution. We first illustrate the advantages of these methods on a small synthetic test case, and then apply them to the Schuyler Falls landfill data to demonstrate how the proposed methods facilitate automatic identification and visualization of clusters in real-world, high-dimensional biogeochemical data with complex relationships. The proposed methods are quite general and are applicable to a wide range of geophysical problems.
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Bongard's work focuses on understanding the general nature of cognition, regardless of whether it is found in humans, animals or robots. This unique approach focuses on the role that morphology and evolution plays in cognition. Addressing these questions has taken him into the fields of biology, psychology, engineering and computer science.
Danforth is an applied mathematician interested in modeling a variety of physical, biological, and social phenomenon. He has applied principles of chaos theory to improve weather forecasts as a member of the Mathematics and Climate Research Network, and developed a real-time remote sensor of global happiness using messages from Twitter: the Hedonometer. Danforth co-runs the Computational Story Lab with Peter Dodds, and helps run UVM's reading group on complexity.
Laurent studies the interaction of structure and dynamics. His research involves network theory, statistical physics and nonlinear dynamics along with their applications in epidemiology, ecology, biology, and sociology. Recent projects include comparing complex networks of different nature, the coevolution of human behavior and infectious diseases, understanding the role of forest shape in determining stability of tropical forests, as well as the impact of echo chambers in political discussions.
Hines' work broadly focuses on finding ways to make electric energy more reliable, more affordable, with less environmental impact. Particular topics of interest include understanding the mechanisms by which small problems in the power grid become large blackouts, identifying and mitigating the stresses caused by large amounts of electric vehicle charging, and quantifying the impact of high penetrations of wind/solar on electricity systems.
Bagrow's interests include: Complex Networks (community detection, social modeling and human dynamics, statistical phenomena, graph similarity and isomorphism), Statistical Physics (non-equilibrium methods, phase transitions, percolation, interacting particle systems, spin glasses), and Optimization(glassy techniques such as simulated/quantum annealing, (non-gradient) minimization of noisy objective functions).