Distribution Optimization: An evolutionary algorithm to separate Gaussian mixtures.

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.

Machine-learning based lipid mediator serum concentration patterns allow identification of multiple sclerosis patients with high accuracy.

Based on increasing evidence suggesting that MS pathology involves alterations in bioactive lipid metabolism, the present analysis was aimed at generating a complex serum lipid-biomarker. Using unsupervised machine-learning, implemented as emergent self-organizing maps of neuronal networks, swarm intelligence and Minimum Curvilinear Embedding, a cluster structure was found in the input data space comprising serum concentrations of d = 43 different lipid-markers of various classes. The structure coincided largely with the clinical diagnosis, indicating that the data provide a basis for the creation of a biomarker (classifier). This was subsequently assessed using supervised machine-learning, implemented as random forests and computed ABC analysis-based feature selection. Bayesian statistics-based biomarker creation was used to map the diagnostic classes of either MS patients (n = 102) or healthy subjects (n = 301). Eight lipid-markers passed the feature selection and comprised GluCerC16, LPA20:4, HETE15S, LacCerC24:1, C16Sphinganine, biopterin and the endocannabinoids PEA and OEA. A complex classifier or biomarker was developed that predicted MS at a sensitivity, specificity and accuracy of approximately 95% in training and test data sets, respectively. The present successful application of serum lipid marker concentrations to MS data is encouraging for further efforts to establish an MS biomarker based on serum lipidomics.

Quantitative sensory testing response patterns to capsaicin- and ultraviolet-B-induced local skin hypersensitization in healthy subjects: a machine-learned analysis.

The comprehensive assessment of pain-related human phenotypes requires combinations of nociceptive measures that produce complex high-dimensional data, posing challenges to bioinformatic analysis. In this study, we assessed established experimental models of heat hyperalgesia of the skin, consisting of local ultraviolet-B (UV-B) irradiation or capsaicin application, in 82 healthy subjects using a variety of noxious stimuli. We extended the original heat stimulation by applying cold and mechanical stimuli and assessing the hypersensitization effects with a clinically established quantitative sensory testing (QST) battery (German Research Network on Neuropathic Pain). This study provided a 246 × 10-sized data matrix (82 subjects assessed at baseline, following UV-B application, and following capsaicin application) with respect to 10 QST parameters, which we analyzed using machine-learning techniques. We observed statistically significant effects of the hypersensitization treatments in 9 different QST parameters. Supervised machine-learned analysis implemented as random forests followed by ABC analysis pointed to heat pain thresholds as the most relevantly affected QST parameter. However, decision tree analysis indicated that UV-B additionally modulated sensitivity to cold. Unsupervised machine-learning techniques, implemented as emergent self-organizing maps, hinted at subgroups responding to topical application of capsaicin. The distinction among subgroups was based on sensitivity to pressure pain, which could be attributed to sex differences, with women being more sensitive than men. Thus, while UV-B and capsaicin share a major component of heat pain sensitization, they differ in their effects on QST parameter patterns in healthy subjects, suggesting a lack of redundancy between these models.

Machine-Learned Data Structures of Lipid Marker Serum Concentrations in Multiple Sclerosis Patients Differ from Those in Healthy Subjects.

Lipid metabolism has been suggested to be a major pathophysiological mechanism of multiple sclerosis (MS). With the increasing knowledge about lipid signaling, acquired data become increasingly complex making bioinformatics necessary in lipid research. We used unsupervised machine-learning to analyze lipid marker serum concentrations, pursuing the hypothesis that for the most relevant markers the emerging data structures will coincide with the diagnosis of MS. Machine learning was implemented as emergent self-organizing feature maps (ESOM) combined with the U*-matrix visualization technique. The data space consisted of serum concentrations of three main classes of lipid markers comprising eicosanoids (d = 11 markers), ceramides (d = 10), and lyosophosphatidic acids (d = 6). They were analyzed in cohorts of MS patients (n = 102) and healthy subjects (n = 301). Clear data structures in the high-dimensional data space were observed in eicosanoid and ceramides serum concentrations whereas no clear structure could be found in lysophosphatidic acid concentrations. With ceramide concentrations, the structures that had emerged from unsupervised machine-learning almost completely overlapped with the known grouping of MS patients versus healthy subjects. This was only partly provided by eicosanoid serum concentrations. Thus, unsupervised machine-learning identified distinct data structures of bioactive lipid serum concentrations. These structures could be superimposed with the known grouping of MS patients versus healthy subjects, which was almost completely possible with ceramides. Therefore, based on the present analysis, ceramides are first-line candidates for further exploration as drug-gable targets or biomarkers in MS.