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Multiple Factor Analysis
Multiple factor analysis (MFA) is a Factorial experiment, factorial method devoted to the study of tables in which a group of individuals is described by a set of variables (quantitative and / or qualitative) structured in groups. It is a Multivariate statistics, multivariate method from the field of Ordination (statistics), ordination used to simplify Dimensionality reduction, multidimensional data structures. MFA treats all involved tables in the same way (symmetrical analysis). It may be seen as an extension of: * Principal component analysis (PCA) when variables are quantitative, * Multiple correspondence analysis (MCA) when variables are qualitative, * Factor analysis of mixed data (FAMD) when the active variables belong to the two types. Introductory example Why introduce several active groups of variables in the same factorial analysis? '' data'' Consider the case of quantitative variables, that is to say, within the framework of the PCA. An example of data from ecologic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorial Experiment
In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors. A full factorial design may also be called a fully crossed design. Such an experiment allows the investigator to study the effect of each factor on the response variable, as well as the effects of interactions between factors on the response variable. For the vast majority of factorial experiments, each factor has only two levels. For example, with two factors each taking two levels, a factorial experiment would have four treatment combinations in total, and is usually called a ''2×2 factorial design''. In such a design, the interaction between the variables is often the most important. This applies even to scenarios where a main effect and an interaction is present. If the number of combinations in a full factorial design i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 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 data, for example simple linear regression an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordination (statistics)
Ordination or gradient analysis, in multivariate analysis, is a method complementary to data clustering, and used mainly in exploratory data analysis (rather than in hypothesis testing). Ordination orders objects that are characterized by values on multiple variables (multivariate objects) so that similar objects are near each other and dissimilar objects are farther from each other. Such relationships between the objects, on each of several axes (one for each variable), are then characterized numerically and/or graphically. Many ordination techniques exist, including principal components analysis (PCA), non-metric multidimensional scaling (NMDS), correspondence analysis (CA) and its derivatives ( detrended CA (DCA), canonical CA (CCA)), Bray–Curtis ordination, and redundancy analysis (RDA), among others. Contemporary developments for ordination focus on machine learning techniques or using statistical models instead. Applications Ordination can be used on the analysis of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensionality Reduction
Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension. Working in high-dimensional spaces can be undesirable for many reasons; raw data are often sparse as a consequence of the curse of dimensionality, and analyzing the data is usually computationally intractable (hard to control or deal with). Dimensionality reduction is common in fields that deal with large numbers of observations and/or large numbers of variables, such as signal processing, speech recognition, neuroinformatics, and bioinformatics. Methods are commonly divided into linear and nonlinear approaches. Approaches can also be divided into feature selection and feature extraction. Dimensionality reduction can be used for noise reduction, data visualization, cluster analysis, or as an intermediat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principal Component 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 enabling the visualization of multidimensional data. Formally, PCA is a statistical technique for reducing the dimensionality of a dataset. This is accomplished by linearly transforming the data into a new coordinate system where (most of) the variation in the data can be described with fewer dimensions than the initial data. Many studies use the first two principal components in order to plot the data in two dimensions and to visually identify clusters of closely related data points. Principal component analysis has applications in many fields such as population genetics, microbiome studies, and atmospheric science. The principal components of a collection of points in a real coordinate space are a sequence of p unit vectors, where th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Factor Analysis Of Mixed Data
In statistics, factor analysis of mixed data or factorial analysis of mixed data (FAMD, in the French original: ''AFDM'' or ''Analyse Factorielle de Données Mixtes''), is the factorial method devoted to data tables in which a group of individuals is described both by quantitative and qualitative variables. It belongs to the exploratory methods developed by the French school called ''Analyse des données'' (data analysis) founded by Jean-Paul Benzécri. The term ''mixed'' refers to the use of both quantitative and qualitative variables. Roughly, we can say that FAMD works as a principal components analysis (PCA) for quantitative variables and as a multiple correspondence analysis (MCA) for qualitative variables. Scope When data include both types of variables but the active variables being homogeneous, PCA or MCA can be used. Indeed, it is easy to include supplementary quantitative variables in MCA by the correlation coefficients between the variables and factors on individuals ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pedology
Pedology (from Greek: πέδον, ''pedon'', "soil"; and λόγος, ''logos'', "study") is a discipline within soil science which focuses on understanding and characterizing soil formation, evolution, and the theoretical frameworks for modeling soil bodies, often in the context of the natural environment. Pedology is often seen as one of two main branches of soil inquiry, the other being edaphology which is traditionally more agronomically oriented and focuses on how soil properties influence plant communities (natural or cultivated). In studying the fundamental phenomenology of soils, e.g. soil formation (aka pedogenesis), pedologists pay particular attention to observing soil morphology and the geographic distributions of soils, and the placement of soil bodies into larger temporal and spatial contexts. In so doing, pedologists develop systems of soil classification, soil maps, and theories for characterizing temporal and spatial interrelations among soils . There are a few note ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AFM Fig1
AFM may refer to: Organizations * AFM Records, a German record label * Africa Fighting Malaria, a health campaign in Africa * Alex von Falkenhausen Motorenbau, a German racing car constructor * American Federation of Motorcyclists, a road racing club in the US * American Federation of Musicians, a labor union of musicians in North America * American Film Market, an annual event for the financing of film production and distribution * American Freedom Mortgage, Inc., a corporation based in Georgia, U.S. * Apostolic Faith Mission of South Africa, a Pentecostal Christian denomination in South Africa * Australia First Movement, an Australian fascist organisation during the second world war. * Autoriteit Financiële Markten, Netherlands financial markets regulator * Macau Football Association, the governing body of football in Macau * Armed Forces of Malta, the name given to the combined armed services of Malta Publications * '' Aquarium Fish Magazine'', a North American monthly m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AFM Fig2
AFM may refer to: Organizations * AFM Records, a German record label * Africa Fighting Malaria, a health campaign in Africa * Alex von Falkenhausen Motorenbau, a German racing car constructor * American Federation of Motorcyclists, a road racing club in the US * American Federation of Musicians, a labor union of musicians in North America * American Film Market, an annual event for the financing of film production and distribution * American Freedom Mortgage, Inc., a corporation based in Georgia, U.S. * Apostolic Faith Mission of South Africa, a Pentecostal Christian denomination in South Africa * Australia First Movement, an Australian fascist organisation during the second world war. * Autoriteit Financiële Markten, Netherlands financial markets regulator * Macau Football Association, the governing body of football in Macau * Armed Forces of Malta, the name given to the combined armed services of Malta Publications * '' Aquarium Fish Magazine'', a North American monthly m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Procrustes Analysis
In statistics, Procrustes analysis is a form of statistical shape analysis used to analyse the distribution of a set of shapes. The name ''Procrustes'' ( el, Προκρούστης) refers to a bandit from Greek mythology who made his victims fit his bed either by stretching their limbs or cutting them off. In mathematics: * an orthogonal Procrustes problem is a method which can be used to find out the optimal ''rotation and/or reflection'' (i.e., the optimal orthogonal linear transformation) for the Procrustes Superimposition (PS) of an object with respect to another. * a constrained orthogonal Procrustes problem, subject to det(''R'') = 1 (where ''R'' is a rotation matrix), is a method which can be used to determine the optimal ''rotation'' for the PS of an object with respect to another (reflection is not allowed). In some contexts, this method is called the Kabsch algorithm. When a shape is compared to another, or a set of shapes is compared to an arbitrarily selected refe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AFM Fig3
AFM may refer to: Organizations * AFM Records, a German record label * Africa Fighting Malaria, a health campaign in Africa * Alex von Falkenhausen Motorenbau, a German racing car constructor * American Federation of Motorcyclists, a road racing club in the US * American Federation of Musicians, a labor union of musicians in North America * American Film Market, an annual event for the financing of film production and distribution * American Freedom Mortgage, Inc., a corporation based in Georgia, U.S. * Apostolic Faith Mission of South Africa, a Pentecostal Christian denomination in South Africa * Australia First Movement, an Australian fascist organisation during the second world war. * Autoriteit Financiële Markten, Netherlands financial markets regulator * Macau Football Association, the governing body of football in Macau * Armed Forces of Malta, the name given to the combined armed services of Malta Publications * '' Aquarium Fish Magazine'', a North American monthly m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
