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Geometric Data Analysis
Geometric data analysis comprises geometric aspects of image analysis, pattern analysis, and shape analysis, and the approach of multivariate statistics, which treat arbitrary data sets as ''clouds of points'' in a space that is ''n''-dimensional. This includes topological data analysis, cluster analysis, inductive data analysis, correspondence analysis, multiple correspondence analysis, principal components analysis and iconography of correlations. See also * Algebraic statistics for algebraic-geometry in statistics *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 se ... * Computational anatomy for the study of shapes and forms at the morphome scale * Structured data analysis (statistics) References * * * Approximation of Geodesic Distances for Geom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Iconography Of Correlations
In exploratory data analysis, the iconography of correlations, or ''representation of correlations'', is a data visualization technique which replaces a numeric correlation matrix by its graphical projection onto a diagram, on which the “remarkable” correlations are plotted as solid lines (positive correlations) or dotted lines (negative correlations); either shorter lengths, or thicker lines, or both, represent greater correlation projection components. History This idea is used in Gaussian graphic models for genome mapping, particularly. But the iconography of correlations is more general, since it does not assume that the data is Gaussian; it only relies on representing the correlation coefficients geometrically. The ''iconography of correlations'' first dates to 1975, applied to marine geochemistry in a 1981 thesis, and later in a 1982 data analysis article. Afterward, the method was applied widely in the aerospace industry but for about fifteen years manufacturers kept ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Multivariate Statistics
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., '' multivariate random variables''. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical application of multivariate statistics to a particular problem may involve several types of univariate and multivariate analyses in order to understand the relationships between variables and their relevance to the problem being studied. In addition, multivariate statistics is concerned with multivariate probability distributions, in terms of both :*how these can be used to represent the distributions of observed data; :*how they can be used as part of statistical inference, particularly where several different quantities are of interest to the same analysis. Certain types of problems involving multivariate da ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Fields Of Geometry
Fields may refer to: Music *Fields (band), an indie rock band formed in 2006 *Fields (progressive rock band), a progressive rock band formed in 1971 * ''Fields'' (album), an LP by Swedish-based indie rock band Junip (2010) * "Fields", a song by Sponge from '' Rotting Piñata'' (1994) Businesses * Field's, a shopping centre in Denmark * Fields (department store), a chain of discount department stores in Alberta and British Columbia, Canada Places in the United States * Fields, Louisiana, an unincorporated community * Fields, Oregon, an unincorporated community * Fields (Frisco, Texas), an announced planned community * Fields Landing, California, a CDP Other uses * Fields (surname), a list of people with that name * Fields Avenue (other), various roads * Fields Institute, a research centre in mathematical sciences at the University of Toronto * Fields Medal, for outstanding achievement in mathematics * Caulfield Grammarians Football Club, also known as The Fields * FIE ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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. This structure can then be used for making comparisons, predictions, manipulations etc. Types of structured data analysis * Algebraic data analysis *Bayesian analysis *Cluster analysis *Combinatorial data analysis * Formal concept analysis * Functional data analysis *Geometric data analysis Geometric data analysis comprises geometric aspects of image analysis, pattern analysis, and shape analysis, and the approach of multivariate statistics, which treat arbitrary data sets as ''clouds of points'' in a space that is ''n''-dimension ... * Regression analysis * Shape analysis * Topological data analysis * Tree structured data analysis References Further reading * * * Leland Wilkinson ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 methods for modelling and simulation of biological structures. The field is broadly defined and includes foundations in anatomy, applied mathematics and pure mathematics, machine learning, computational mechanics, computational science, biological imaging, neuroscience, physics, probability, and statistics; it also has strong connections with fluid mechanics and geometric mechanics. Additionally, it complements newer, interdisciplinary fields like bioinformatics and neuroinformatics in the sense that its interpretation uses metadata derived from the original sensor imaging modalities (of which magnetic resonance imaging is one example). It focuses on the anatomical structures being imaged, rather than the medical imaging devices. It is similar i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 search for a suitable combinatorial construct that does fit the data. See also *Cluster analysis Cluster analysis or clustering is the data analyzing technique in which task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more Similarity measure, similar (in some specific sense defined by the ... * Geometric data analysis * Structured data analysis (statistics) * Seriation (statistics) References Combinatorics Data analysis Combinatorial optimization {{combin-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 and multivariate analysis (especially time series). In recent years, the term "algebraic statistics" has been sometimes restricted, sometimes being used to label the use of algebraic geometry and commutative algebra in statistics. The tradition of algebraic statistics In the past, statisticians have used algebra to advance research in statistics. Some algebraic statistics led to the development of new topics in algebra and combinatorics, such as association schemes. Design of experiments For example, Ronald A. Fisher, Henry B. Mann, and Rosemary A. Bailey applied Abelian groups to the design of experiments. Experimental designs were also studied with affine geometry over finite fields and then with the introduction of association sche ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Principal Components Analysis
Principal component analysis (PCA) is a Linear map, linear dimensionality reduction technique with applications in exploratory data analysis, visualization and Data Preprocessing, data preprocessing. The data is linear map, linearly transformed onto a new coordinate system such that the directions (principal components) capturing the largest variation in the data can be easily identified. The principal components of a collection of points in a real coordinate space are a sequence of p unit vectors, where the i-th vector is the direction of a line that best fits the data while being orthogonal to the first i-1 vectors. Here, a best-fitting line is defined as one that minimizes the average squared perpendicular distance, perpendicular Distance from a point to a line, distance from the points to the line. These directions (i.e., principal components) constitute an orthonormal basis in which different individual dimensions of the data are Linear correlation, linearly uncorrelated. Ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 barcode, bar coded tags or as sophisticated as facial recognition system, identifying a person from their face. Computers are indispensable for the analysis of large amounts of data, for tasks that require complex computation, or for the extraction of quantitative information. On the other hand, the human visual cortex is an excellent image analysis apparatus, especially for extracting higher-level information, and for many applications — including medicine, security, and remote sensing — human analysts still cannot be replaced by computers. For this reason, many important image analysis tools such as edge detection, edge detectors and Artificial neural network, neural networks are inspired by human visual perception models. Digital Digital Image Analy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 Euclidean space. The procedure thus appears to be the counterpart of principal component analysis for categorical data. MCA can be viewed as an extension of simple correspondence analysis (CA) in that it is applicable to a large set of categorical variables. As an extension of correspondence analysis MCA is performed by applying the CA algorithm to either an indicator matrix (also called ''complete disjunctive table'' – CDT) or a ''Burt table'' formed from these variables. An indicator matrix is an individuals × variables matrix, where the rows represent individuals and the columns are dummy variables representing categories of the variables. Analyzing the indicator matrix allows the direct representation of individuals as points in ge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Correspondence Analysis
Correspondence analysis (CA) is a multivariate statistical technique proposed by Herman Otto Hartley (Hirschfeld) and later developed by Jean-Paul Benzécri. It is conceptually similar to principal component analysis, but applies to categorical rather than continuous data. In a similar manner to principal component analysis, it provides a means of displaying or summarising a set of data in two-dimensional graphical form. Its aim is to display in a biplot any structure hidden in the multivariate setting of the data table. As such it is a technique from the field of multivariate ordination. Since the variant of CA described here can be applied either with a focus on the rows or on the columns it should in fact be called simple (symmetric) correspondence analysis. It is traditionally applied to the contingency table of a pair of nominal variables where each cell contains either a count or a zero value. If more than two categorical variables are to be summarized, a variant called ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
