Geometric data analysis comprises
geometric aspects of
image analysis
Image analysis or imagery analysis is the extraction of meaningful information from images; mainly from digital images by means of digital image processing techniques. Image analysis tasks can be as simple as reading bar coded tags or as sophi ...
,
pattern analysis, and
shape analysis, and the approach of
multivariate statistics
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable.
Multivariate statistics concerns understanding the different aims and background of each of the dif ...
, which treat arbitrary data sets as ''clouds of points'' in a space that is ''n''-dimensional. This includes
topological data analysis
In applied mathematics, topological based data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information from datasets that are high-dimensional, incomplete and noisy is generally challengin ...
,
cluster analysis
Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters). It is a main task of ...
, inductive data analysis,
correspondence analysis,
multiple correspondence analysis In statistics, multiple correspondence analysis (MCA) is a data analysis technique for nominal categorical data, used to detect and represent underlying structures in a data set. It does this by representing data as points in a low-dimensional Eucli ...
,
principal components analysis
Principal component analysis (PCA) is a popular technique for analyzing large datasets containing a high number of dimensions/features per observation, increasing the interpretability of data while preserving the maximum amount of information, and ...
and
See also
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Algebraic statistics for algebraic-geometry in statistics
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Combinatorial data analysis In statistics, combinatorial data analysis (CDA) is the study of data sets where the order in which objects are arranged is important. CDA can be used either to determine how well a given combinatorial construct reflects the observed data, or to sea ...
*
Computational anatomy
Computational anatomy is an interdisciplinary field of biology focused on quantitative investigation and modelling of anatomical shapes variability. It involves the development and application of mathematical, statistical and data-analytical metho ...
for the study of shapes and forms at the morphome scale
*
Structured data analysis (statistics)
Structured data analysis is the statistical data analysis of structured data. This can arise either in the form of an ''a priori'' structure such as multiple-choice questionnaires or in situations with the need to search for structure that fits t ...
References
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*
Approximation of Geodesic Distances for Geometric Data Analysis
Differential geometry and data analysis
Differential Geometry and Statistics M.K. Murray, J.W. Rice, Chapman and Hall/CRC,
Ridges in image and data analysis David Eberly, Springer, 1996, {{ISBN, 978-0-7923-4268-7
Fields of geometry
Multivariate statistics
Spatial analysis