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We live in a time when information is cheaply available and saved as data nearly everywhere. The amount of generated data is growing exponentially. By the end of the year 2016 alone, 9000 exabytes of data will have been generated, equal to 9 trillion gigabytes or the capacity of 360 billion Blu-ray Discs [Schiele, 2016].

The first section of this chapter familiarizes the reader with the definitions of the basic notation and terminology used in this thesis. Concepts of graph theory are introduced in the next section. They give rise to a new concept of neighborhoods, which is utilized in several chapters.

Many data mining methods rely on some concept of the similarity between pieces of information encoded in the data of interest. Various names have been applied to these clustering methods, depending largely on the field of application in data science. For example, in biology the term “numerical taxonomy” is used [Thorel et al., 1990], in psychology the term Q analysis is sometimes employed, market researchers often talk about “segmentation” [Arimond/Elfessi, 2001] and in the artificial intelligence literature, unsupervised pattern recognition is the favored label [Everitt et al., 2001, p. 4].

Dimensionality reduction techniques reduce the dimensions of the input space to facilitate the exploration of structures in high-dimensional data. Two general dimensionality reduction approaches exist: manifold learning and projection. Manifold-learning methods attempt to find a sub-space in which the high-dimensional distances can be preserved.

Projection methods are a common approach to dimensionality reduction with the aim of transforming high-dimensional data into a low-dimensional space. For data visualization purposes, projections into two dimensions are considered here. However, when the output space is limited to two dimensions, the low-dimensional similarities cannot completely represent the high-dimensional distances, which can result in a misleading interpretation of the underlying structures.

Dimensionality reduction techniques reduce the dimensions of the input space to facilitate the exploration of structures in high-dimensional data. Two general dimensionality reduction approaches exist: manifold learning and projection. Manifold learning methods attempt to find sub-spaces in which the high-dimensional distances are preserved.

Many technological advances have been achieved with the help of bionics, which is defined as the application of biological methods and systems found in nature. A related, rarely discussed subfield of information technology is called databionics. refers to the attempt to adopt information processing techniques from nature.

This chapter introduces a new concept for the use of swarm intelligence. It makes use of insights from the previous chapter and proposes a projection method based on a swarm of intelligent agents called DataBots [Ultsch, 2000c]. This new swarm is called a polar swarm (Pswarm) because its agents move in polar coordinates based on symmetry considerations (see [Feynman et al., 2007, pp. 147-153, 745]).

This chapter describes all the data sets used in the results chapter and the parameter settings for the various methods. In the final section, brief overviews of the Gene Ontology (GO) database and overrepresentation analysis (ORA) are provided. For general distribution analyses, the CRAN R package AdaptGauss [Thrun/Ultsch, 2015; Ultsch et al., 2015] was used.

This chapter has three sections. In the first section, the results of the Databionic swarm (DBS) clustering framework are compared with the given prior classifications for data sets from the Fundamental Clustering Problems Suite (FCPS) [Ultsch, 2005a]. The results for nine data sets analyzed using common clustering algorithms are compared in the first subsection.