Geometric data analysis comprises
geometric
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ca ...
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
Pattern recognition is the automated recognition of patterns and regularities in data. It has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer graphics ...
, 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 Eucl ...
,
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 Algebraic statistics is the use of algebra to advance statistics. Algebra has been useful for experimental design, parameter estimation, and hypothesis testing.
Traditionally, algebraic statistics has been associated with the design of experiments ...
for algebraic-geometry in statistics
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Combinatorial data analysis
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Computational anatomy for the study of shapes and forms at the morphome scale
*
Structured data analysis (statistics)
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