Abstract
Data can often be very effectively analyzed using visualization techniques. Standard visualization methods for object data are plots and scatter plots. To visualize high-dimensional data, projection methods are necessary. We present linear projection (principal component analysis, Karhunen-Loève transform, singular value decomposition, eigenvector projection, Hotelling transform, proper orthogonal decomposition, multidimensional scaling) and nonlinear projection methods (Sammon mapping, auto-encoder). Data distributions can be estimated and visualized using histogram techniques. Periodic data (such as time series) can be analyzed and visualized using spectral analysis (cosine and sine transforms, amplitude and phase spectra).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Y. Bengio. Learning deep architectures for AI. Foundations and Trends in Machine Learning, 2(1):1–127, 2009.
R. O. Duda and P. E. Hart. Pattern Classification and Scene Analysis. Wiley, New York, 1973.
D. Freedman and P. Diaconis. On the histogram as a density estimator: L2 theory. Probability Theory and Related Fields, 57(4):453–476, December 1981.
G. E. Hinton. Connectionist learning procedures. Artificial Intelligence, 40:185–234, 1989.
A. K. Jain. Fundamentals of Digital Image Processing. Prentice Hall, Englewood Cliffs, 1986.
D. Keim, G. Andrienko, J.-D. Fekete, C. Görg, J. Kohlhammer, and G. Melançon. Visual analytics: Definition, process, and challenges. In Information visualization, pages 154–175. Springer, 2008.
K. Pearson. On lines and planes of closest fit to systems of points in space. Philosophical Magazine, 2(6):559–572, 1901.
T. A. Runkler. Fuzzy histograms and fuzzy chi–squared tests for independence. In IEEE International Conference on Fuzzy Systems, volume 3, pages 1361–1366, Budapest, July 2004.
J. W. Sammon. A nonlinear mapping for data structure analysis. IEEE Transactions on Computers, C-18(5):401–409, 1969.
D. W. Scott. On optimal and data–based histograms. Biometrika, 66(3):605–610, 1979.
H. A. Sturges. The choice of a class interval. Journal of the American Statistical Association, pages 65–66, 1926.
W. S. Torgerson. Theory and Methods of Scaling. Wiley, New York, 1958.
J. W. Tukey. Exploratory Data Analysis. Addison Wesley, Reading, 1987.
G. Young and A. S. Householder. Discussion of a set of points in terms of their mutual distances. Psychometrika, 3:19–22, 1938.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Fachmedien Wiesbaden GmbH, part of Springer Nature
About this chapter
Cite this chapter
Runkler, T.A. (2020). Data Visualization. In: Data Analytics. Springer Vieweg, Wiesbaden. https://doi.org/10.1007/978-3-658-29779-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-658-29779-4_4
Published:
Publisher Name: Springer Vieweg, Wiesbaden
Print ISBN: 978-3-658-29778-7
Online ISBN: 978-3-658-29779-4
eBook Packages: Computer Science and Engineering (German Language)