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Data and Dimension Reduction

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Mapping Financial Stability

Part of the book series: Computational Risk Management ((Comp. Risk Mgmt))

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Abstract

Data and dimension reduction techniques hold promise for representing data in easily understandable formats, as has been shown by their wide scope of applications. Data reductions provide summarizations of data by compressing information into fewer partitions, whereas dimension reductions provide low-dimensional overviews of similarity relations in data. Thus, these techniques provide means for exploratory data analysis (EDA). From a broader perspective, EDA is only one approach out of many in data mining, and knowledge discovery includes data mining as only one of its steps. To provide a holistic view in a top-down manner, we start by the broader concepts, and end with discussions of data and dimension reductions and their combination. As the aim of Chap. 5 is to provide a comparison of early dimension reduction methods, the focus of this chapter is also on more detailed presentations of so-called first-generation methods, including Multidimensional Scaling (MDS), Sammon’s mapping and the Self-Organizing Map (SOM).

The eye, which is called the window of the soul, is the principal means by which the central sense can most completely and abundantly appreciate the infinite works of nature

– Leonardo da Vinci

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Notes

  1. 1.

    There are several software implementations of the SOM. The seminal packages—SOM_PAK, SOM Toolbox for Matlab, Nenet, etc—are not regularly updated or adapted to their environment. Out of the newer implementations, Viscovery SOMine provides the needed means for interactive exploratory analysis. The most recent addition to the list of implementations is the interactive, web-based implementation provided by infolytika (http://risklab.fi/demo/macropru/). For a description, see Sarlin (2014a). For a practical discussion of SOM software and an early version of the implementation in Viscovery SOMine, see Deboeck (1998b, a). See also Moehrmann et al. (2011), for a comparison of SOM implementations. The first analyses of this book were performed in the Viscovery SOMine 5.1 package due to its easily interpretable visual representation and interaction features, not the least when introducing it to practitioners in general and policymakers in particular. Recently, the packages available in the statistical computing environment R have significantly improved, in particular regarding the visualization of SOM outputs. Thus, the final parts of the research in this book, including the figures, have been produced in R. Moreover, the above mentioned interface by infolytika provides an interactive implementation of the R-based models.

  2. 2.

    In the literature, learning of the SOM has been defined through the entire spectrum of supervision. For instance, van Heerden and Engelbrecht (2008) define semi-supervised SOMs as similar to the supervised ones, except for them not being included in the matching phase (Eq. 4.9), whereas the semi-supervised version herein is their supervised SOM. However, as the SOM is never fully supervised, we stick to the definition of an unsupervised and a semi-supervised version.

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Authors and Affiliations

  1. Centre of Excellence SAFE, Goethe University Frankfurt, Grüneburgplatz 1, 60323, Frankfurt am Main, Germany

    Peter Sarlin

  2. RiskLab Finland, IAMSR Åbo Akademi University, Turku, Finland

    Peter Sarlin

  3. Arcada University of Applied Sciences, Helsinki, Finland

    Peter Sarlin

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Sarlin, P. (2014). Data and Dimension Reduction. In: Mapping Financial Stability. Computational Risk Management. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54956-4_4

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