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Recent advances in analysis of fMRI have established the existence of functional sub-networks in the human brain that are active during the performance of visual, motor, language, and other tasks. We describe two computational methods of delineating functional sub-networks that are active when an individual performs an approach-avoidance paradigm. The paradigm consisted of presentation of images of pleasant and unpleasant faces that were shown to nine volunteers for 10 seconds after a preceding rest period of 50 seconds during which a green computer screen was displayed. The subjects were instructed to squeeze a ball with their right hand if they judged the face to be unpleasant, in which case the unpleasant face would disappear. An fMRI BOLD activation was created and used as input for two different kinds of clustering method: The MCODE algorithm based on graph-theoretical analysis and a Conscious Self-Organizing Map (CSOM). Clustering obtained with both methods was based on the temporal variations of the fMRI BOLD signal activity. Both methods identified distinct regions in the brain which were separated by long-range connections. The MCODE algorithm was supplied with time-courses for activated voxels when performing the paradigm, while the CSOM clustering used all voxels in the brain. Both yielded similar clusters for activated voxels. The combination of MCODE and CSOM presents a new approach in identifying functional subunits in the human brain and warrants further investigation into the subject.

The self-organizing map (SOM) is a powerful method for visualization, cluster extraction, and data mining. It has been used successfully for data of high dimensionality and complexity where traditional methods may often be insufficient. In order to analyze data structure and capture cluster boundaries from the SOM, one common approach is to represent the SOM's knowledge by visualization methods. Different aspects of the information learned by the SOM are presented by existing methods, but data topology, which is present in the SOM's knowledge, is greatly underutilized. We show in this paper that data topology can be integrated into the visualization of the SOM and thereby provide a more elaborate view of the cluster structure than existing schemes. We achieve this by introducing a weighted Delaunay triangulation (a connectivity matrix) and draping it over the SOM. This new visualization, CONNvis, also shows both forward and backward topology violations along with the severity of forward ones, which indicate the quality of the SOM learning and the data complexity. CONNvis greatly assists in detailed identification of cluster boundaries. We demonstrate the capabilities on synthetic data sets and on a real 8-D remote sensing spectral image.

In this paper, we examine the scope of validity of the explicit self-organizing map (SOM) magnification control scheme of Bauer et al. (1996) on data for which the theory does not guarantee success, namely data that are n-dimensional, n > or =2, and whose components in the different dimensions are not statistically independent. The Bauer et al. algorithm is very attractive for the possibility of faithful representation of the probability density function (pdf) of a data manifold, or for discovery of rare events, among other properties. Since theoretically unsupported data of higher dimensionality and higher complexity would benefit most from the power of explicit magnification control, we conduct systematic simulations on "forbidden" data. For the unsupported n=2 cases that we investigate, the simulations show that even though the magnification exponent alpha achieved achieved by magnification control is not the same as the desired alpha desired, alpha achieved systematically follows alpha desired with a slowly increasing positive offset. We show that for simple synthetic higher dimensional data information, theoretically optimum pdf matching (alpha achieved = 1) can be achieved, and that negative magnification has the desired effect of improving the detectability of rare classes. In addition, we further study theoretically unsupported cases with real data.

We study the application of self-organizing maps (SOMs) for the analyses of remote sensing spectral images. Advanced airborne and satellite-based imaging spectrometers produce very high-dimensional spectral signatures that provide key information to many scientific investigations about the surface and atmosphere of Earth and other planets. These new, sophisticated data demand new and advanced approaches to cluster detection, visualization, and supervised classification. In this article we concentrate on the issue of faithful topological mapping in order to avoid false interpretations of cluster maps created by an SOM. We describe several new extensions of the standard SOM, developed in the past few years: the growing SOM, magnification control, and generalized relevance learning vector quantization, and demonstrate their effect on both low-dimensional traditional multi-spectral imagery and approximately 200-dimensional hyperspectral imagery.