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Finding subgroups in biomedical data is a key task in biomedical research and precision medicine. Already one-dimensional data, such as many different readouts from cell experiments, preclinical or human laboratory experiments or clinical signs, often reveal a more complex distribution than a single mode. Gaussian mixtures play an important role in the multimodal distribution of one-dimensional data. However, although fitting of Gaussian mixture models (GMM) is often aimed at obtaining the separate modes composing the mixture, current technical implementations, often using the Expectation Maximization (EM) algorithm, are not optimized for this task. This occasionally results in poorly separated modes that are unsuitable for determining a distinguishable group structure in the data. Here, we introduce “Distribution Optimization” an evolutionary algorithm to GMM fitting that uses an adjustable error function that is based on chi-square statistics and the probability density. The algorithm can be directly targeted at the separation of the modes of the mixture by employing additional criterion for the degree by which single modes overlap. The obtained GMM fits were comparable with those obtained with classical EM based fits, except for data sets where the EM algorithm produced unsatisfactory results with overlapping Gaussian modes. There, the proposed algorithm successfully separated the modes, providing a basis for meaningful group separation while fitting the data satisfactorily. Through its optimization toward mode separation, the evolutionary algorithm proofed particularly suitable basis for group separation in multimodally distributed data, outperforming alternative EM based methods.
Optimal distribution-preserving downsampling of large biomedical data sets (opdisDownsampling)
(2021)
Motivation: The size of today’s biomedical data sets pushes computer equipment to its limits, even for seemingly standard analysis tasks such as data projection or clustering. Reducing large biomedical data by downsampling is therefore a common early step in data processing, often performed as random uniform class-proportional downsampling. In this report, we hypothesized that this can be optimized to obtain samples that better reflect the entire data set than those obtained using the current standard method. Results: By repeating the random sampling and comparing the distribution of the drawn sample with the distribution of the original data, it was possible to establish a method for obtaining subsets of data that better reflect the entire data set than taking only the first randomly selected subsample, as is the current standard. Experiments on artificial and real biomedical data sets showed that the reconstruction of the remaining data from the original data set from the downsampled data improved significantly. This was observed with both principal component analysis and autoencoding neural networks. The fidelity was dependent on both the number of cases drawn from the original and the number of samples drawn. Conclusions: Optimal distribution-preserving class-proportional downsampling yields data subsets that reflect the structure of the entire data better than those obtained with the standard method. By using distributional similarity as the only selection criterion, the proposed method does not in any way affect the results of a later planned analysis.