Changes

The typical objectives of multivariate data analysis can be divided broadly into three categories.

The typical objectives of multivariate data analysis can be divided broadly into three categories.

;1. Data description or exploratory data analysis (EDA)

#'''Data description or exploratory data analysis (EDA)'''--The basic tools of this objective include univariate statistics, such as the mean, variance, and quantiles applied to each variable separately, and the covariance or correlation matrix between any two of the P quantities. Some of the P quantities can be transformed (for example, by taking the logarithm) prior to establishing the correlation matrix. Because the matrix is symmetrical, there are P(P - 1)/2 potentially different correlation values.

:The basic tools of this objective include univariate statistics, such as the mean, variance, and quantiles applied to each variable separately, and the covariance or correlation matrix between any two of the P quantities. Some of the P quantities can be transformed (for example, by taking the logarithm) prior to establishing the correlation matrix. Because the matrix is symmetrical, there are P(P - 1)/2 potentially different correlation values.

#'''Data grouping (discrimination and clustering)'''--Discrimination or classification aim at optimally assigning multivariate data vectors (arrays) into a set of previously defined classes or groups.<ref name=Everitt_1974>Everitt, B., 1974, Cluster analysis: London, Heinemann Educational Books Ltd., 122 p.</ref> Clustering, however, aims at defining classes of multivariate similarity and regrouping the initial sample values into these classes. Discrimination is a supervised act of pattern recognition, whereas clustering is an unsupervised act of pattern cognition.<ref name=Miller_etal_1962>Miller, R. L., and J. S. Kahn, 1962, Statistical analysis in the geological sciences: New York, John Wiley, 481 p.</ref> Principal component analysis (PCA) allows analysis of the covariance (correlation) matrix with a minimum of statistical assumptions. PCA aims at reducing the dimensionality P of the multivariate data set available by defining a limited number (fewer than P) of linear combinations of these quantities, with each combination reflecting some of the data structures (relationships) implicit in the original covariance matrix.

 

#'''Regression'''--Regression is the generic term for relating two sets of variables. The first set, usually denoted by y, constitutes the dependent variables(s). It is related linearly to the second set, denoted x, called the independent variable(s). (For details of multiple and multivariate regression analysis, see [[Correlation and Regression Analysis]].)

;2. Data grouping (discrimination and clustering)

:Discrimination or classification aim at optimally assigning multivariate data vectors (arrays) into a set of previously defined classes or groups (Everitt, 1974)<ref name=Everitt_1974>Everitt, B., 1974, Cluster analysis: London, Heinemann Educational Books Ltd., 122 p.</ref>. Clustering, however, aims at defining classes of multivariate similarity and regrouping the initial sample values into these classes. Discrimination is a supervised act of pattern recognition, whereas clustering is an unsupervised act of pattern cognition (Miller and Kahn, 1962)<ref name=Miller_etal_1962>Miller, R. L., and J. S. Kahn, 1962, Statistical analysis in the geological sciences: New York, John Wiley, 481 p.</ref>.

 

:Principal component analysis (PCA) allows analysis of the covariance (correlation) matrix with a minimum of statistical assumptions. PCA aims at reducing the dimensionality P of the multivariate data set available by defining a limited number (fewer than P) of linear combinations of these quantities, with each combination reflecting some of the data structures (relationships) implicit in the original covariance matrix.

 

;3. Regression

:Regression is the generic term for relating two sets of variables. The first set, usually denoted by y, constitutes the dependent variables(s). It is related linearly to the second set, denoted x, called the independent variable(s). (For details of multiple and multivariate regression analysis, see the chapter on "Correlation and Regression Analysis" in Part 6.)

==A note about outliers==

==A note about outliers==

==A note about data representativeness==

==A note about data representativeness==

As mentioned in the chapter on [[Statistics overview]] (in Part 6), the available sample data are an incomplete image of the underlying population. Statistical features and relationships seen in the data may not be representative of the characteristics of the underlying population if there are biases in the data. Sources of biases are multiple, from the most obvious measurement biases to imposed spatial clustering. Spatial clustering results from preferential location of data (drilling patterns and core plugs), a prevalent problem in exploration and development. Such preferential selection of data points can severely bias one's image of the reservoir, usually in a nonconservative way. Remedies include defining representative subsets of the data, weighting the data, and careful interpretation of the data analysis results.

As mentioned in the article on [[Statistics overview]], the available sample data are an incomplete image of the underlying population. Statistical features and relationships seen in the data may not be representative of the characteristics of the underlying population if there are biases in the data. Sources of biases are multiple, from the most obvious measurement biases to imposed spatial clustering. Spatial clustering results from preferential location of data (drilling patterns and core plugs), a prevalent problem in exploration and development. Such preferential selection of data points can severely bias one's image of the reservoir, usually in a nonconservative way. Remedies include defining representative subsets of the data, weighting the data, and careful interpretation of the data analysis results.

==Principal component analysis==

==Principal component analysis==