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Background: Microarray analysis represents a powerful way to test scientific hypotheses on the functionality of cells. The measurements consider the whole genome, and the large number of generated data requires sophisticated analysis. To date, no gold-standard for the analysis of microarray images has been established. Due to the lack of a standard approach there is a strong need to identify new processing algorithms.
Methods: We propose a novel approach based on hyperbolic partial differential equations (PDEs) for unsupervised spot segmentation. Prior to segmentation, morphological operations were applied for the identification of co-localized groups of spots. A grid alignment was performed to determine the borderlines between rows and columns of spots. PDEs were applied to detect the inflection points within each column and row; vertical and horizontal luminance profiles were evolved respectively. The inflection points of the profiles determined borderlines that confined a spot within adapted rectangular areas. A subsequent k-means clustering determined the pixels of each individual spot and its local background.
Results: We evaluated the approach for a data set of microarray images taken from the Stanford Microarray Database (SMD). The data set is based on two studies on global gene expression profiles of Arabidopsis Thaliana. We computed values for spot intensity, regression ratio, and coefficient of determination. For spots with irregular contours and inner holes, we found intensity values that were significantly different from those determined by the GenePix Pro microarray analysis software. We determined the set of differentially expressed genes from our intensities and identified more activated genes than were predicted by the GenePix software.
Conclusions: Our method represents a worthwhile alternative and complement to standard approaches used in industry and academy. We highlight the importance of our spot segmentation approach, which identified supplementary important genes, to better explains the molecular mechanisms that are activated in a defense responses to virus and pathogen infection.
Background: High-dimensional biomedical data are frequently clustered to identify subgroup structures pointing at distinct disease subtypes. It is crucial that the used cluster algorithm works correctly. However, by imposing a predefined shape on the clusters, classical algorithms occasionally suggest a cluster structure in homogenously distributed data or assign data points to incorrect clusters. We analyzed whether this can be avoided by using emergent self-organizing feature maps (ESOM).
Methods: Data sets with different degrees of complexity were submitted to ESOM analysis with large numbers of neurons, using an interactive R-based bioinformatics tool. On top of the trained ESOM the distance structure in the high dimensional feature space was visualized in the form of a so-called U-matrix. Clustering results were compared with those provided by classical common cluster algorithms including single linkage, Ward and k-means.
Results: Ward clustering imposed cluster structures on cluster-less "golf ball", "cuboid" and "S-shaped" data sets that contained no structure at all (random data). Ward clustering also imposed structures on permuted real world data sets. By contrast, the ESOM/U-matrix approach correctly found that these data contain no cluster structure. However, ESOM/U-matrix was correct in identifying clusters in biomedical data truly containing subgroups. It was always correct in cluster structure identification in further canonical artificial data. Using intentionally simple data sets, it is shown that popular clustering algorithms typically used for biomedical data sets may fail to cluster data correctly, suggesting that they are also likely to perform erroneously on high dimensional biomedical data.
Conclusions: The present analyses emphasized that generally established classical hierarchical clustering algorithms carry a considerable tendency to produce erroneous results. By contrast, unsupervised machine-learned analysis of cluster structures, applied using the ESOM/U-matrix method, is a viable, unbiased method to identify true clusters in the high-dimensional space of complex data.
Graphical abstract: 3-D representation of high dimensional data following ESOM projection and visualization of group (cluster) structures using the U-matrix, which employs a geographical map analogy of valleys where members of the same cluster are located, separated by mountain ranges marking cluster borders.
Mit der Smart Learning Infrastruktur wurde ein neuartiges didaktisches Konzept für Kurse in der Weiterbildung entwickelt. Diese Infrastruktur ist vielfältig anwendbar. Erste Analysen von Kursen zeigen, dass TeilnehmerInnen, die alle Übungen korrekt abgearbeitet haben, eine bessere Note erreichen als die Durchschnittsnote. Dieser Beitrag beschreibt ein Konzept für ein Gamification-Modul, welches mit spielerischen Elementen möglichst frühzeitig dazu animiert, alle Übungen eines Kurses korrekt und mit Verstand abzuarbeiten.
Industry classification groups firms into finer partitions to help investments and empirical analysis. To overcome the well-documented limitations of existing industry definitions, like their stale nature and coarse categories for firms with multiple operations, we employ a clustering approach on 69 firm characteristics and allocate companies to novel economic sectors maximizing the within-group explained variation. Such sectors are dynamic yet stable, and represent a superior investment set compared to standard classification schemes for portfolio optimization and for trading strategies based on within-industry mean-reversion, which give rise to a latent risk factor significantly priced in the cross-section. We provide a new metric to quantify feature importance for clustering methods, finding that size drives differences across classical industries while book-to-market and financial liquidity variables matter for clustering-based sectors.