A comparison between neural and fuzzy cluster analysis techniques for functional MRI

Abstract

Exploratory data-driven methods such as unsupervised clustering and independent component analysis (ICA) are considered to be hypothesis-generating procedures, and are complementary to the hypothesis-led statistical inferential methods in functional magnetic resonance imaging (fMRI). In this paper, we present a comparison between neural and fuzzy clustering techniques in a systematic fMRI study. For the fMRI data, a comparative quantitative evaluation based on ROC analysis between the Gath–Geva algorithm, the fuzzy n-means algorithm, Kohonen's self-organizing map, fuzzy n-means algorithm with unsupervised initialization, minimal free energy vector quantizer and the “neural-gas” network was performed. The most important findings in this paper are: (1) SOM is outperformed by all other neural and fuzzy techniques regardless of the chosen number of codebook vectors in terms of detecting small activation areas, (2) the variations among the other techniques are minimal, and (3) a small number of codebook vectors is in general required to obtain consistent task-related activation maps, as determined by the performance evaluation based on cluster validity indices.

Introduction

Functional magnetic resonance imaging represents a powerful research tool due to its noninva-siveness and high spatial-temporal resolution property for recording activity in the working brain and drawing inferences about brain functioning [1]. However, an activated signal variation appears very low on a clinical scanner [2] and is subject to physiological and scanner noise. This motivates the application of analysis methods to determine the response waveforms and associated activated regions. The current fMRI literature reports a wide range of experimental protocols, involving both hypothesis- and data-driven analysis techniques [3]. Several sources [4], [5] demonstrated the applicability of data-driven approaches as an alternative technique for the analysis of temporally varying signals collected during fMRI experiments. These techniques do not require prior knowledge about activation patterns and demonstrate additional advantages to the traditional methods of data analysis. The most known traditional method of fMRI data is based on fitting a general linear model (GLM). Its functional form depends heavily on the a priori experimental procedure, in most cases convolved with a hemodynamic response function, testing the accuracy of this model on a voxel by voxel basis [3]. On the other hand, data-driven techniques extract the key patterns in time and the corresponding spatial profiles, and thus provides a quick overview of the data collected during an experiment. Since they do not use a priori information regarding the signal variation, they might detect unexpected temporal signals. Therefore, analysis methods that do not rely on any assumed model of functional response are considered more powerful and relevant.

We distinguish two groups of model-free methods: transformation- and clustering-based. The first method, principal component analysis (PCA) [6], [7] or independent component analysis (ICA) [5], [8], [9], [10], transforms original data into high-dimensional vector space to separate functional response and various noise sources from each other. The second method, fuzzy clustering analysis [11], [12], [13], [14] self-organizing map [14], [15], [16], or general clustering techniques [17], [18], attempts to classify time signals of the brain into several patterns according to temporal similarity among these signals.

In this paper, we perform a detailed comparative study among neural and fuzzy clustering techniques when applied to fMRI data analysis. Thus, our study will focus on fuzzy and neural clustering methods such as the Gath–Geva algorithm, the traditional Kohonen's self-organizing map (SOM), the fuzzy n-means algorithms, the “neural-gas” network, the fuzzy n-means algorithm with unsupervised initialization, and the minimal free energy vector quantization (VQ) [14]. In a systematic manner, we will compare and evaluate the results obtained based on each technique and present the benefits associated with each paradigm.

Two main categories of clustering algorithms will be employed in this paper: the adaptive and nonadaptive fuzzy techniques and the topology and neighborhood preserving mapping as neural clustering techniques.

Our work extends previous applications of fuzzy logic concepts to fMRI data analysis. In both [13], [19], only fuzzy n-means applied to fMRI data analysis is considered. Other work [12], [14], [16] concentrates only on applying non-fuzzy clustering algorithms to fMRI but there is – to the best of our knowledge – no unifying framework for analyzing the application of several fuzzy and neural algorithms including previous ones to fMRI exploratory data analysis.

The following sections are dedicated to presenting the neural and fuzzy clustering algorithms and evaluate the discriminatory power of these exploratory data analysis methods.

Let n denote the number of subsequent scans in a fMRI study, and let M be the number of pixels in each scan. The dynamics of each pixel μ ∈ {1, …, M}, i.e. the sequence of signal values {x^μ(1), …, x^μ(n)} can be interpreted as a vector x^μ(i) ∈ Rⁿ in the n-dimensional feature space of possible signal time-series at each pixel (pixel time course, PTC).

Cluster analysis groups image pixels together based on the similarity of their intensity profile in time. In the clustering process, a time course with n points is represented by one point in an n-dimensional Euclidean space which is subsequently partitioned into clusters based on the proximity of the input data.

Here, we employ several vector quantization (VQ) approaches as a method for unsupervised image time-series analysis. VQ clustering identifies several groups of pixels with similar PTC, while these groups or clusters are represented by prototypical time-series called codebook vectors (CV) located at the center of the corresponding clusters. The CVs represent prototypical PTCs sharing similar temporal characteristics. Thus, each PTC can be assigned in the crisp clustering scheme to a specific CV according to a minimal distance criterion, while in the fuzzy scheme according to a membership to several CVs. Accordingly, the outcomes of VQ approaches for fMRI data analysis can be plotted as “crisp” or “fuzzy” cluster assignment maps.

In the following we will give a review on neural and fuzzy clustering algorithms to be applied to fMRI exploratory data analysis.