Group Analysis of Self-organizing Maps based on Functional MRI using Restricted Frechet Means

Studies of functional MRI data are increasingly concerned with the estimation of differences in spatio-temporal networks across groups of subjects or experimental conditions. Unsupervised clustering and independent component analysis (ICA) have been used to identify such spatio-temporal networks. While these approaches have been useful for estimating these networks at the subject-level, comparisons over groups or experimental conditions require further methodological development. In this paper, we tackle this problem by showing how self-organizing maps (SOMs) can be compared within a Frechean inferential framework. Here, we summarize the mean SOM in each group as a Frechet mean with respect to a metric on the space of SOMs. We consider the use of different metrics, and introduce two extensions of the classical sum of minimum distance (SMD) between two SOMs, which take into account the spatio-temporal pattern of the fMRI data. The validity of these methods is illustrated on synthetic data. Through these simulations, we show that the three metrics of interest behave as expected, in the sense that the ones capturing temporal, spatial and spatio-temporal aspects of the SOMs are more likely to reach significance under simulated scenarios characterized by temporal, spatial and spatio-temporal differences, respectively. In addition, a re-analysis of a classical experiment on visually-triggered emotions demonstrates the usefulness of this methodology. In this study, the multivariate functional patterns typical of the subjects exposed to pleasant and unpleasant stimuli are found to be more similar than the ones of the subjects exposed to emotionally neutral stimuli. Taken together, these results indicate that our proposed methods can cast new light on existing data by adopting a global analytical perspective on functional MRI paradigms.Comment: 23 pages, 5 figures, 4 tables. Submitted to Neuroimag

Winner-Relaxing Self-Organizing Maps

A new family of self-organizing maps, the Winner-Relaxing Kohonen Algorithm, is introduced as a generalization of a variant given by Kohonen in 1991. The magnification behaviour is calculated analytically. For the original variant a magnification exponent of 4/7 is derived; the generalized version allows to steer the magnification in the wide range from exponent 1/2 to 1 in the one-dimensional case, thus provides optimal mapping in the sense of information theory. The Winner Relaxing Algorithm requires minimal extra computations per learning step and is conveniently easy to implement.Comment: 14 pages (6 figs included). To appear in Neural Computatio

SOTXTSTREAM: Density-based self-organizing clustering of text streams

A streaming data clustering algorithm is presented building upon the density-based selforganizing stream clustering algorithm SOSTREAM. Many density-based clustering algorithms are limited by their inability to identify clusters with heterogeneous density. SOSTREAM addresses this limitation through the use of local (nearest neighbor-based) density determinations. Additionally, many stream clustering algorithms use a two-phase clustering approach. In the first phase, a micro-clustering solution is maintained online, while in the second phase, the micro-clustering solution is clustered offline to produce a macro solution. By performing self-organization techniques on micro-clusters in the online phase, SOSTREAM is able to maintain a macro clustering solution in a single phase. Leveraging concepts from SOSTREAM, a new density-based self-organizing text stream clustering algorithm, SOTXTSTREAM, is presented that addresses several shortcomings of SOSTREAM. Gains in clustering performance of this new algorithm are demonstrated on several real-world text stream datasets

Self-organization and clustering algorithms

Kohonen's feature maps approach to clustering is often likened to the k or c-means clustering algorithms. Here, the author identifies some similarities and differences between the hard and fuzzy c-Means (HCM/FCM) or ISODATA algorithms and Kohonen's self-organizing approach. The author concludes that some differences are significant, but at the same time there may be some important unknown relationships between the two methodologies. Several avenues of research are proposed

Multiorder neurons for evolutionary higher-order clustering and growth

This letter proposes to use multiorder neurons for clustering irregularly shaped data arrangements. Multiorder neurons are an evolutionary extension of the use of higher-order neurons in clustering. Higher-order neurons parametrically model complex neuron shapes by replacing the classic synaptic weight by higher-order tensors. The multiorder neuron goes one step further and eliminates two problems associated with higher-order neurons. First, it uses evolutionary algorithms to select the best neuron order for a given problem. Second, it obtains more information about the underlying data distribution by identifying the correct order for a given cluster of patterns. Empirically we observed that when the correlation of clusters found with ground truth information is used in measuring clustering accuracy, the proposed evolutionary multiorder neurons method can be shown to outperform other related clustering methods. The simulation results from the Iris, Wine, and Glass data sets show significant improvement when compared to the results obtained using self-organizing maps and higher-order neurons. The letter also proposes an intuitive model by which multiorder neurons can be grown, thereby determining the number of clusters in data

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