Browsing by Subject "Multi-dimensional scaling"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Embedding graphs under centrality constraints(2013-05) Baingana, BrianVisual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of structural network properties. This thesis advocates two graph embedding approaches with centrality considerations to comply with node hierarchy. The embedding problem is formulated first as one of constrained multi-dimensional scaling (MDS), and it is solved via block coordinate descent iterations with successive approximations and guaranteed convergence to a Karush-Kuhn-Tucker (KKT) point. In addition, a regularization term enforcing graph smoothness is incorporated with the goal of reducing edge crossings. A second approach leverages the locally-linear embedding (LLE) algorithm which assumes that the graph encodes data sampled from a low-dimensional manifold. Closed-form solutions to the resulting centrality-constrained optimization problems are determined yielding meaningful embeddings. Experimental results demonstrate the efficacy of both approaches, especially for visualizing large networks on the order of thousands of nodes.Item Statistical Analysis of the Soil Chemical Survey Data(Minnesota Department of Transportation Research Services Section, 2010-06) Dhar, Sauptik; Cherkassky, VladimirThis report describes data-analytic modeling of the Minnesota soil chemical data produced by the 2001 metro soil survey and by the 2003 state-wide survey. The chemical composition of the soil is characterized by the concentration of many metal and non-metal constituents, resulting in high-dimensional data. This high dimensionality and possible unknown (nonlinear) correlations in the data make it difficult to analyze and interpret using standard statistical techniques. This project applies a machine learning technique, called Self Organizing Map (SOM), to present the high-dimensional soil data in a 2D format suitable for human understanding and interpretation. This SOM representation enables analysis of the soil chemical concentration trends within the metro area and in the state of Minnesota. These trends are important for various Minnesota regulatory agencies concerned with the concentration of polluting chemical elements due to both (a) human activities, i.e., different industrial land usage, and (b) natural geological factors, such as the geomorphic codes and provenance of glacial sediments.