In multivariate analysis

Multivariate analysis

Multivariate analysis is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical variable at a time...

, ordination is a method complementary to data clustering

Data clustering

Cluster analysis or clustering is the task of assigning a set of objects into groups so that the objects in the same cluster are more similar to each other than to those in other clusters....

, and used mainly in exploratory data analysis

Exploratory data analysis

In statistics, exploratory data analysis is an approach to analysing data sets to summarize their main characteristics in easy-to-understand form, often with visual graphs, without using a statistical model or having formulated a hypothesis...

 (rather than in hypothesis testing). Ordination orders

Partially ordered set

In mathematics, especially order theory, a partially ordered set formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary relation that indicates that, for certain pairs of elements in the...

 objects that are characterized by values on multiple variables (i.e., multivariate objects) so that similar objects are near each other and dissimilar objects are farther from each other. These 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

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...

 (PCA), non-metric multidimensional scaling

Multidimensional scaling

Multidimensional scaling is a set of related statistical techniques often used in information visualization for exploring similarities or dissimilarities in data. MDS is a special case of ordination. An MDS algorithm starts with a matrix of item–item similarities, then assigns a location to each...

 (NMDS), 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...

 (CA) and its derivatives (detrended CA (DCA)

Detrended Correspondence Analysis

Detrended correspondence analysis is a multivariate statistical technique widely used by ecologists to find the main factors or gradients in large, species-rich but usually sparse data matrices that typify ecological community data. For example, Hill and Gauch analyse the data of a vegetation...

, canonical CA (CCA)), Bray–Curtis ordination, and redundancy analysis (RDA), among others.

Applications

• Ordination can be used on the analysis of any set of multivariate objects. It is frequently used in several environmental or ecological sciences, particularly plant community ecology. It is also used in genetics
  Genetics
  Genetics , a discipline of biology, is the science of genes, heredity, and variation in living organisms....
  
   and systems biology
  Systems biology
  Systems biology is a term used to describe a number of trends in bioscience research, and a movement which draws on those trends. Proponents describe systems biology as a biology-based inter-disciplinary study field that focuses on complex interactions in biological systems, claiming that it uses...
  
   for microarray
  Microarray
  A microarray is a multiplex lab-on-a-chip. It is a 2D array on a solid substrate that assays large amounts of biological material using high-throughput screening methods.Types of microarrays include:...
  
   data analysis, and in psychometrics
  Psychometrics
  Psychometrics is the field of study concerned with the theory and technique of psychological measurement, which includes the measurement of knowledge, abilities, attitudes, personality traits, and educational measurement...
  
  .

See also

• 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...
  
  
• 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...
  
  
• 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...
  
  
• Detrended correspondence analysis
  Detrended Correspondence Analysis
  Detrended correspondence analysis is a multivariate statistical technique widely used by ecologists to find the main factors or gradients in large, species-rich but usually sparse data matrices that typify ecological community data. For example, Hill and Gauch analyse the data of a vegetation...
  
  
• Intrinsic dimension
  Intrinsic dimension
  In signal processing of multidimensional signals, for example in computer vision, the intrinsic dimension of the signal describes how many variables are needed to represent the signal. For a signal of N variables, its intrinsic dimension M satisfies 0 ≤ M ≤ N.Usually the intrinsic dimension...
  
  

External links

1. General
   • http://ordination.okstate.edu/ The Ordination Web Page - Ordination Methods for Ecologists
   • http://userwww.sfsu.edu/~efc/classes/biol710/ordination/ordination.htm
2. Specific Techniques
   • http://www.statsoft.com/textbook/stcoran.html
   • http://userwww.sfsu.edu/~efc/classes/biol710/ordination/CA.htm
   • http://www.statsoft.com/textbook/stmulsca.html
   • http://www2.chass.ncsu.edu/garson/pa765/correspondence.htm
   • http://www.statsoft.com/textbook/glosfra.html
3. Software
   • http://home.centurytel.net/~mjm/pcordwin.htm
   • http://www.microcomputerpower.com/catalog/canoco.html
   • http://www.brodgar.com
   • http://www.VisuMap.com
   • http://cc.oulu.fi/~jarioksa/softhelp/ceprog.html DECORANA
   • http://cc.oulu.fi/~jarioksa/softhelp/casvd.html Correspondence Analysis with SVD