Self-organizing maps and entropy applied to data analysis of functional magnetic resonance images

Abstract

Kohonen self-organizing maps (SOM) and Shannon entropy were applied together for the analysis of data from functional magnetic resonance imaging (fMRI). To increase the efficiency of SOM in the search for patterns of activation in fMRI data, first, we applied the Shannon entropy in order to eliminate signals possibly related to noise sources. The procedure with these techniques was applied to simulated data and on real hearing experiment, the results showed that the application of entropy and SOM is a good tool to the identification of areas of activity.

Understanding Internal Cluster Variability Through Subcluster Metric Analysis in a Geophysical Context

“…Therefore, we introduce the subsom entropy which quantifies how even the occurrence rates are across different subclusters. Entropy is often used as a statistical measure of randomness in a system which consists of several microstates (Shannon, 2001) and has also been used for many different purposes in several studies in the atmospheric sciences (Bannon, 2015; Krützmann et al., 2008; McDonald & Cairns, 2020) and in past clustering‐based studies (Campelo et al., 2014; De Mántaras, 1991; Halkidi et al., 2002b). By understanding that the occurrence rate of subclusters are equivalent to the probability of the occurrence of a given microstate, entropy can be used as a measure of the evenness of the distribution of subcluster occurrence rates.…”

“…For this research, we choose to focus on clusters that were generated using the self‐organizing map (SOM) unsupervised learning algorithm. This algorithm has been used in a wide range of applications (Allinson & Ellis, 1992; Auger et al., 1992; Campelo et al., 2014), but is most commonly used as a clustering algorithm (Kohonen, 2013). Details about the design and operation of the SOM are given in Kohonen (1998) and Kohonen (2013).…”

Application of the Kalman Filter in Functional Magnetic Resonance Image Data

“…Each window is formed by a period of activation alternated with a period of rest. Figure 3 (Kohonen, 2001) using an implementation available in the literature (Fischer and Henning, 1999;Ngan et al, 2002;Peltier et al, 2003;Campelo et al, 2014).…”

“…Several methods for grouping of neurons in the SOM have been proposed, in this paper will apply the hierarchical clustering (HC), for more details see (Liao et al, 2008, Campelo et al, 2014.…”

“…It is made an adaptation in this method for filtering periodic signals so as to preserve morphology and amplitude of the original signal. To make the analysis of the data after the application of the Kalman-Bucy filter, it is used the Kohonen's self-organized map (SOM) (Campelo et al, 2014;Haykin, 2001;Liao et al, 2008). The data will be also analyzed by the SOM without the application of the Kalman-Bucy filter for purpose of comparison and efficiency analysis of the procedure adopted here.…”