Multivariate Dataset

A Multivariate Dataset is a labeled dataset with more than one dataset dependent variable.

• Context:
  • It can range from being an IID Multivariate Dataset to being a Sequential Multivariate Dataset.
  • It can be an input to a Multivariate Data Analysis Task.
• Example(s):
  • Bivariate Data.
  • …
• Counter-Example(s):
  • a Univariate Dataset.
  • a Mixed Multi-Predictor Dataset.
• See: Random Variable Vector, Multivariate, Multivariate Analysis, Probability Distribution, Multiple Regression.

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References

2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/multivariate_statistics Retrieved:2014-11-23.
  • Multivariate statistics is a form of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. The application of multivariate statistics is multivariate analysis.

    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 implementation 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 actual 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 problem involving multivariate data, for example simple linear regression and multiple regression, are NOT usually considered as special cases of multivariate statistics because the analysis is dealt with by considering the (univariate) conditional distribution of a single outcome variable given the other variables.

2009

• (Hair et al., 2009) ⇒ Joseph F. Hair, William C. Black, Rolph E. Anderson, and Barry J. Babin. (2009). “Multivariate Data Analysis, 7th edition.” Prentice Hall. ISBN:0138132631

2000

• (Hyvärinen & Oja, 2000) ⇒ Aapo Hyvärinen, and Erkki Oja. (2000). “Independent Component Analysis: Algorithms and Applications.” In: Neural Networks, 13(4-5). doi:10.1016/S0893-6080(00)00026-5.
  • A fundamental problem in neural network research, as well as in many other disciplines, is finding a suitable representation of multivariate data, i.e. random vectors.

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