Principal Component Analysis
Mathematics, rightly viewed, possesses not only truth, but supreme beauty (Bertrand Russell, Philosophical Essays No. 4, 1910).
One of the aims in multivariate data analysis is to summarise the data in fewer than the original number of dimensions without losing essential information. More than a century ago, Pearson (1901) considered this problem, and Hotelling (1933) proposed a solution to it: instead of treating each variable separately, he considered combinations of the variables. Clearly, the average of all variables is such a combination, but many others exist. Two fundamental questions arise:
1.How should one choose these combinations?
2.How many such combinations should one choose?