Biological studies across all omics fields generate vast amounts of data. To understand these complex data, biologically motivated data mining techniques are indispensable. Evaluation of the high-throughput measurements usually relies on the identification of underlying signals as well as shared or outstanding characteristics. Therein, methods have been developed to recover source signals of present datasets, reveal objects which are more similar to each other than to other objects as well as to detect observations which are in contrast to the background dataset. Biological problems got individually addressed by using solutions from computer science according to their needs. The study of protein-protein interactions (interactome) focuses on the identification of clusters, the sub-graphs of graphs: A parameter-free graph clustering algorithm was developed, which was based on the concept of graph compression, in order to find sets of highly interlinked proteins sharing similar characteristics. The study of lipids (lipidome) calls for co-regulation analyses: To reveal those lipids similarly responding to biological factors, partial correlations were generated with differential Gaussian Graphical Models while accounting for solely disease-specific correlations. The study on single cell level (cytomics) aims to understand cellular systems often with the help of microscopy techniques: A novel noise robust source separation technique allowed to reliably extract independent components from microscopy images describing protein behaviors. The study of peptides (peptidomics) often requires the detection outstanding observations: By assessing regularities in the data set, an outlier detection algorithm was implemented based on compression efficacy of independent components of the dataset. All developed algorithms had to fulfill most diverse constraints in each omics field, but were met with methods derived from standard correlation and dependency analyses.