Jacques van Helden Jacques.van.Heldenulb.ac.be

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Multivariate analysisSummary

• Statistics Applied to Bioinformatics

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Typical questions in multivariate analysis

• No criterion variable
• Can the objects be separated in distinct classes
  on the basis of the variables ? ? Cluster
  analysis
• Which variables, or combiations of variables
  (factors), are the most explanatory for the
  differences between objects ? ? Factor
  analysis
• Quantitative criterion variable
• Is the criterion variable correlated with the
  predictor variables ? ? Correlation analysis
• Can we predict the value of the criterion
  variable on the basis of the predictor variables
  ? ? Regression analysis
• Nominal criterion variable
• Can we predict the value of the criterion
  variable on the basis of the predictor variables
  ? ? Discriminant analysis

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Flowchart of the approaches in multivariate
analysis
Principal component analysis
Cluster analysis
Clusters
none
criterionvariable ?
multivariate table
Regression analysis
Predicted value
quantitative
Discriminant analysis
Predicted class
nominal
Multidimensionalscaling
distance matrix
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Adapted from Gilbert et al. (2000). Trends
Biotech. 18(Dec), 487-495.
Raw data
Visualization
Processing

• Matrix
• n rows
• p columns
• coloring

• Ordering (optional)
• row swapping
• column swapping

Matrix viewer

• Dendrogram
• rooted
• unrooted
• n leaves

Tree drawing
Clusters,Tree
Clustering

• Multivariate data matrix
• n objects
• p variables

Pairwise distance measurement

• Distance matrix
• n x n distances
• symmetrical

Coloring (optional)

• Euclidian space
• 1D to 3D
• n dots
• coloring
• dot volume
• interactive

• Multidimensional scaling
• PCoA
• spring embedding

Space explorer (VRML)

• Coordinates
• n elements
• d dimensions

Principal component analysis

• Normalization
• mean
• variance
• covariance

• Normalized table
• n elements
• p dimensions

Reduction to significant dimensions