Transcription of Multivariate Data Analysis
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Multivariate Data Analysis
Multivariate Data AnalysisSusan Holmes susan/Bio-X and StatisticsIMA Workshop, October, do not really understand something unless you canexplain it to your grandmother-- Albert EinsteinI am your grandmother ..you do not really understand something unless you canexplain it to your grandmother-- Albert EinsteinI am your grandmother ..What are Multivariate data ?Simplest format: matrices:If we have measured 10,000 genes on hundreds of patientsand all the genes are independent, we can't do better thananalyze each gene's behavior by using histograms or boxplots, looking at the means, medians, variances and other `onedimensional statistics'. However if some of the genes areacting together, either that they are positively correlated orthat they inhibit each other, we will miss a lot of importantinformation by slicing the data up into those column vectorsand studying them separately. Thus important connectionsbetween genes are only available to us if we consider thedata as a whole.
1. Inertia: Trace(VQ) = Trace(WD) (inertia in the sense of Huyghens inertia formula for instance). Huygens,C. (1657), ∑n i=1 pid 2(x i;a) Inertia with regards to a pointaof a cloud ofpi-weighted points. PCAwithQ= Ip,D= 1 nIn,and the variables are centered,the inertia is the sum of the variances of all the variables.
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