Geometric data analysis
Encyclopedia
Geometric data analysis can refer to geometric
aspects of image analysis
, pattern analysis and shape analysis
or the approach of multivariate statistics
that treats arbitrary data sets as clouds of points in n-dimensional space. This includes topological data analysis
, cluster analysis, inductive data analysis, correspondence analysis
, multiple correspondence analysis
and principal components analysis
.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
aspects of image analysis
Image analysis
Image analysis is the extraction of meaningful information from images; mainly from digital images by means of digital image processing techniques...
, pattern analysis and shape analysis
Shape analysis
This article describes shape analysis to analyze and process geometric shapes.The shape analysis described here is related to the statistical analysis of geometric shapes, to shape matching and shape recognition...
or the approach of multivariate statistics
Multivariate statistics
Multivariate statistics is a form of statistics encompassing the simultaneous observation and analysis of more than one statistical variable. The application of multivariate statistics is multivariate analysis...
that treats arbitrary data sets as clouds of points in n-dimensional space. This includes topological data analysis
Topological data analysis
Topological data analysis is a new area of study aimed at having applications in areas such as data mining and computer vision.The main problems are:# how one infers high-dimensional structure from low-dimensional representations; and...
, cluster analysis, inductive data analysis, correspondence analysis
Correspondence analysis
Correspondence analysis is a multivariate statistical technique proposed by Hirschfeld and later developed by Jean-Paul Benzécri. It is conceptually similar to principal component analysis, but applies to categorical rather than continuous data...
, multiple correspondence analysis
Multiple correspondence analysis
In statistics, multiple correspondence analysis 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 Euclidean space. The procedure thus appears to be the...
and principal components analysis
Principal components analysis
Principal component analysis is a mathematical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of uncorrelated variables called principal components. The number of principal components is less than or equal to...
.
See also
- Combinatorial data analysisCombinatorial data analysisCombinatorial data analysis is the study of data sets where the arrangement of objects is important. CDA can be used either to determine how well a given combinatorial construct reflects the observed data, or to search for a suitable combinatorial construct that does fit the data.-See...
- Structured data analysis (statistics)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 the given data, either exactly or approximately...
- Algebraic statisticsAlgebraic statisticsAlgebraic statistics is the use of algebra to advance statistics. Algebra has been useful for experimental design, parameter estimation, and hypothesis testing....
for algebraic-geometry in statistics
Differential geometry and data analysis
- Differential Geometry and Statistics, M.K. Murray, J.W. Rice, Chapman and Hall/CRC, ISBN 978-0412398605
- Ridges in image and data analysis, David Eberly, Springer, 1996, ISBN 9780792342687