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We propose a noise reduction method for magnetocardiograms(MCGs) based on independent componentanalysis (ICA). ICA is useful to separate the noise andsignal components, but ICA-based automatic noise reductionfaces two main difficulties: the dimensional contractionprocess applied after the principal component analysis(PCA) used for preprocessing, and the component selectionapplied after ICA. The results of noise reduction varyamong people, because these two processes typicallydepend on personal qualitative evaluations of the obtainedcomponents. Therefore, automatic quantitative ICA-basednoise reduction is highly desirable. We will focus on thefirst difficulty, by improving the index used in the dimensionalcontraction process. The index used for componentordering after PCA affects the accuracy of separationobtained with ICA. The contribution ratio is often used asan index. However, its efficacy is highly dependent on thesignal-to-noise ratio (SNR) it unsuitable for automation. We propose a kurtosis-based index, whose efficacy doesnot depend on SNR. We compare the two decision indexesthrough simulation. First, we evaluate their preservationrate of the MCG information after dimensional contraction. In addition, we evaluate their effect on the accuracy of theICA-based noise reduction method. The obtained resultsshow that the kurtosis-based index does preserve the MCGsignal information through dimensional contraction, andhas a more consistent behavior when the number ofcomponents increases. The proposed index performs betterthan the traditional index, especially in low SNRs. As such,it paves the way for the desired noise reduction processautomation.