Download LYNGBY Matlab toolbox for functional neuroimaging analysis

Section 4.6
52
K-means Clustering
Data vectors are assigned
closest cluster center
Figure 4.2: In a high dimensional space the data vectors are clustered to the nearest cluster
center.
(i+1)
3. Set new cluster centers Ck
to the center of gravity of each cluster:
(i+1)
Ck
= E{xj }x
(i)
j ∈Ck
(4.19)
This formula can also be modified to use the median and/or to include an inertia term.
4. Goto step 2 until convergence.
4.6.1
Our implementation
Instead of using the time series directly as the input to the K-means algorithm, we have made it
possible to use the cross-correlation of the fMRI time series and the paradigm. This has a major
impact of the results of K-means algorithm, which will make it far easier to find the activated
voxels (Toft et al., 1997).
When clustering on the cross-correlation function or the raw time series, the final clusters
centers will be affected by the amplitude level and a possible lag. For instance, if two spatially
separated regions have similar response strength but different delays, then they will be clustered
into two different clusters according to their delay values.
The toolbox enables clustering using K-means or K-median (K-mediod). The range of the
variables can be “standardized” (normalized) to unit variance or standardized according to the
min-max-range. The cluster centers can be initialized randomly (In (Toft et al., 1997) it has
been found that this strategy works rather well for the cross-correlation clustering) or according
to the correlation with the paradigm function. The variable to cluster on can be set to the raw
time series or the cross-correlation function.
It is implemented in the lyngby km main matlab function.
4.6.2
References
The K-means clustering algorithm was first described in (MacQueen, 1967). Other “non-neuroimaging” descriptions of this algorithm are available in (Ripley, 1996, section 9.3), (Sonka et al.,
1993, section 7.2.4) or (Hartigan and Wong, 1979). Our approach in connection with functional
neuroimaging is published in (Goutte et al., 1999) and described shortly in (Goutte et al., 1998;
c
°Lars
Kai Hansen et al 1997